Research ArticleParameter Estimation for the Field Strength of RadioEnvironment Maps

Zhisheng Gao Yaoshun Li and Chunzhi Xie

School of Computer and Software Engineering Xihua University Chengdu 610039 China

Correspondence should be addressed to Zhisheng Gao gzsds189cn

Received 21 July 2017 Revised 13 October 2017 Accepted 1 November 2017 Published 29 November 2017

Academic Editor Gianluigi Ferrari

Copyright copy 2017 Zhisheng Gao et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The parameters of a radio environment map play an important role in radio management and cognitive radio In this paper amethod for estimating the parameters of the radio environment map based on the sensing data of monitoring nodes is presentedAccording to the principles of radio transmission signal intensity losses a theoretical variogram model based on a propagationmodel is proposed and the improved theoretical variation function is more in line with the attenuation of radio signal propagationFurthermore a weight variogram fitting method is proposed based on the characteristics of field strength parameter estimationIn contrast to the traditional method this method is more closely related to the physical characteristics of the electromagneticenvironment parameters and the design of the variogram and fitting method is more in line with the spatial distribution ofelectromagnetic environment parameters Experiments on real and simulation data show that the proposedmethod performs betterthan the state-of-the-art method

1 Introduction

The radio environment map which was first proposed byZhao et al [1] is mainly used in cognitive radio [2 3] Aradio environment map is an integrated database that is usedto describe the electromagnetic environment Because of itswide range of applications for radio [4ndash8] it has been furtherextended The radio environment map is a comprehensivedatabase that contains many fields of information such asthe available spectrum profile geographical features rulesrelevant laws and regulations radio equipment situationand expert experience [9] The radio environment mapis fundamental to the construction of a communicationnetwork improving operation efficiency andmanaging radioresources Ojaniemi et al [10] believe that the core content ofthe radio environment map is the field strength estimationso accurately estimating the field strength of the radio signalin the geospatial space with a certain granularity is key Peskoet al [11] called this problem the construction of the radiofrequency layer In this paper we call it radio environmentmap parameter estimation This problem especially since2012 has been increasingly studied in depth [11ndash15]

Methods for estimating the parameters of the radioenvironment map can be divided into three categories [11]The first are based on direct spatial interpolation the secondare based on the propagation model and the third are thehybrid combinations of the first two methods Propagation-basedmethods require a large amount of information includ-ing the signal transmission source latitude and longitudecoordinates antenna height transmitting power and evengeographical information and climate information on thepropagation path which greatly limits the scope of appli-cation of this method At the same time because mostpropagation models are empirical models based on radiotransmission their universality is not strong Ojaniemi etal [10] showed that under certain conditions this methodhas lower prediction accuracy than spatial interpolationmethods

In recent years the focus of research on radio environ-ment map parameter estimation has transferred to spatialinterpolation-based methods especially methods based ongeostatistics In this kind of method the measured values ofground truth are obtained by radio monitoring sensors andthen the spatial environment parameters of the remaining

HindawiWireless Communications and Mobile ComputingVolume 2017 Article ID 2475439 13 pageshttpsdoiorg10115520172475439

2 Wireless Communications and Mobile Computing

locations are obtained using spatial interpolation estimationComparative studies of spatial interpolation methods weremade in [15ndash17] Comparative studies of the inverse distanceweighted (IDW) method Spline interpolation method andKriging interpolation method were presented in [15 16 18]and the IDW gradient plus inverse distance squared (GIDS)and Kriging methods were compared in [17] Predictionexperiments on indoor and outdoor electromagnetic envi-ronments showed that the IDWmethod ismore robust whilethe Kriging method is the most accurate method Reference[19] presented an approach that uses the spatial dependenceof ground truth data and constructs the signal intensity mapusing Kriging In [20] several spatial interpolation methodsbased on IDWwere analyzed and used to estimate the spatialdistribution of radio field strength Reference [21] proposeda geostatistical method for the radio environment map andthrough an actual case study demonstrated that the methodis superior to the method based on path loss model and datafitting At the same time this kind of method relies on thedata collected by the monitoring sensor so the distributionand quantity of the monitoring sensors affect the predicationaccuracy of the radio environment map parameters In[22] the relationship between the number of sensors andconstruction error of the radio environment map is analyzedin detail

Existing studies show that the Kriging method is the bestway to estimate the parameters of the radio environmentmap However the radio transmission process is affected byvarious factors such as the number of transmitting stationsgeographical environment and weather In practice thenumber ofmonitoring sensors is limited so the data samplingpoints are sparsely distributed which increases the difficultyof estimating the parameter space distribution At the sametime because the Kriging algorithm is based on a variogramits linear quadratic optimization is based on the assump-tion that the data set conforms to the normal distributionand meets the second-order stationary hypothesis or quasi-second-order stationary assumptionTherefore a nonnormaldistribution will affect the stability of the data and causethe variogram to produce a proportional effect That is itwill improve the sill and nugget values and increase theestimation error [23] To solve this problem we propose amethod to estimate the parameters of the radio environmentmap based on the radio propagation model and the Krigingmethod This method retains the advantages of both thepropagation model and the Kriging method and henceobtains better parameter space prediction precision than thesingle method The main contributions of this paper are asfollows (1) Using the radio propagation model to improvethe variogram of the Kriging algorithm a new theoreticalvariogram model for radio environment map parameterestimation is proposed (2) Based on the characteristics ofradio signal propagation and data acquisition a weightedoptimization of the variogram is proposed and particleswarm optimization (PSO) is applied to fit the modified var-iogram The modified Kriging algorithm can hence be betteradapted to the spatial distribution of the radio environmentparameters

The rest of the paper is organized as follows Section 2describes the related research on interpolation-based pre-diction of the radio environment Section 3 introduces theimproved Kriging method based on the electromagneticpropagation model and PSO-based weighting variogramfitting Section 4 presents the results of some comparativeexperiments on real and simulation data to examine theeffectiveness of the proposed method Finally Section 5concludes this work

2 Related Works

The IDW has been considered for radio environment mapparameter space estimation in many studies [14ndash18 20 2124] The estimated value of the forecast point parameter119874119890 can be calculated by the weighted sum of the actualobservation values of nearby observation pointsThismethodconsiders that the contributions of the observation pointscloser to the prediction point are greater otherwise thecontribution is smaller which can be expressed as follows

119874119890 = sum119899119894=1 (119889119894)minus119901 119874119889 (119894)sum119899119894=1 (119889119894)minus119901 (1)

where 119874119889(119894) is a sampled value of the actual parameter at the119894th observation point 119889119894 is the Euclidean distance betweenthe 119894th observation point and the predicted point and 119901 is astrength parameter that defines the decrease in weight as thedistance increases When 119901 equals one the method is calledIDW and when it equals two themethod is called the inversedistance squared weight

Spline interpolation is another widely used method forestimating the parameters of the radio environment map [1620 25] In these methods the Spline is generated using theactual measured values of all observation points to guaranteeglobal smoothness and then the parameter values of thepredicted points are calculated using polynomial fitting

TheKrigingmethod is amethodbased on the spatial anal-ysis of a variogram which is an unbiased optimal estimationof regionalized variables over a finite area and is consideredto be the best method for estimating the parameters of theradio environmentmap [11ndash13 13ndash21]The Krigingmethod isdivided into ordinary Kriging and universal Kriging depend-ing on the existence of space field drift Ordinary Krigingis more commonly used than universal Kriging [11] Thefollowing is a description of the ordinary Kriging method

For regionalized variable 119911(119909) the sample values fora series of observation points 1199091 1199092 119909119899 are 119911(1199091)119911(1199092) 119911(119909119899)Then the estimated value 119911(119909119905) of grid point119909119905 in a region can be estimated by a linear combination thatis

119911 (119909119905) = 119899sum119894=1

120582119894 sdot 119911 (119909119894) (2)

Wireless Communications and Mobile Computing 3

where 120582119894 is the 119894th weighting coefficient According to theprinciple of optimal unbiased estimation the value of 120582119894should satisfy the following conditions

119864 [119911 (119909119905) minus 1199111015840 (119909119905)] = 0119864 [119911 (119909119905) minus 1199111015840 (119909119905)]2 = min (3)

where 1199111015840(119909119905) is the real sample value Assuming that 119911(119909) sat-isfies the intrinsic hypothesis then according to the Lagrangetheorem the ordinary Kriging equations can be expressed asfollows

119899sum119895=1

120582119895120574 (119909119894 119909119895) + 120583 = 120574 (119909119894 119909119905) 119894 = 1 2 119899119899sum119894=1

120582119894 = 1(4)

where 120574(119909119894 119909119895) is the value of the variogram between sam-pling points 119909119894 and 119909119895 and 120583 is the Lagrange constantWeighting coefficient 120582119894 can be calculated by (4) When 120582119894 issubstituted into (2) the estimation value 119911(119909119905) of grid point119909119905 can be obtained

The process of solving 119911(119909119905) shows that the key of Kriginginterpolation is how to obtain the best estimate of variogram120574(ℎ)3 Proposed Method

31 Improved Variogram for Parameter Estimation of RadioEnvironment Map In geostatistics a variogram is a toolused to study the autocorrelation structure of regionalizedvariables The value of a variogram function is only relatedto the distance between two regionalized variables Largervalues of the variogram indicate smaller autocorrelationThevariogram function is defined as follows [10]

120574 (ℎ) = 12119899 (ℎ)119899(ℎ)sum119894=1

(119911 (119909119894) minus 119911 (119909119894 + ℎ))2 (5)

where 119899(ℎ) is the number of pairs of observation data pointswith lag distance ℎ 119911(119909119894) is the value of the regionalizedvariable at position 119909119894 and 119911(119909119894 + ℎ) is the value of theregionalized variable at a distance ℎ from 119909119894 When the datadistribution is relatively uniform the basic lag distance canbe equal to or slightly larger than the minimum distancebetween the observed data points Alternatively the basiclag distance can be obtained by comparing and analyzingthe variability and stability of the experimental variogram ofseveral candidate basic lag distances

In practice the most important parameter of the radioenvironment map is the signal radiation level in units ofdecibels (dB) If the Kriging algorithm is used directly theexpression of 120574(ℎ) can be simply obtained by (5) in unitsof dB2 However this is not consistent with the dB units ofpropagation loss that are calculated by the radio propagationmodel Hence the variogram is not dimensionally consistent

with the propagationmodelWe believe that the transmissionloss of the propagation model represents the correlationbetween the two radio environment parameters Thereforeto combine the variogram with the propagation modelthe definition of the variation function used in traditionalgeostatistics is modified as follows

120574 (ℎ) = 1119899 (ℎ)radic119899(ℎ)sum119894=1

(119911 (119909119894) minus 119911 (119909119894 + ℎ))2 (6)

The newly defined variogram is called the parameter esti-mation variogram of the radio environment map and thedimensions of the value calculated by the new variogramare consistent with the dimensions of the transmission lossobtained by the propagation model

32 Theoretical Variogram Model Based on PropagationModel It is necessary to use the theoretical variogrammodelto fit the actual variogram The commonly used theoreticalmodels for a variogram are the Gaussian exponential andspherical models In practice the most commonly usedmodel is the spherical model proposed by Pesko et al [11]

In this paper two new theoretical variogram models areproposed based on the LongleyndashRice model one uses theLongleyndashRice to model the theoretical variogram directlyand the other introduces free space transmission loss intothe first model The LongleyndashRice model also called theirregular terrain model [7] is mainly used to predict themedian path loss over irregular terrain The median value ofthe propagation loss in free space for different path lengths iscalculated as follows

119860 ref

= max(0 119860119890119897 + 1198961119889 + 1198962 ln( 119889119889119871119878)) 119889min le 119889 lt 119889119871119878119860119890119889 + 119898119889119889 119889119871119878 le 119889 lt 119889119909119860119890119904 + 119898119904119889 119889 ge 119889119909

(7)

where 119889min le 119889 lt 119889119871119878 is the visual distance spread 119889119871119878 le119889 lt 119889119909 is the diffraction propagation distance and 119889 ge 119889119909 isthe scattering propagation distance In addition119860119890119897119860119890119889 and119860119890119904 are propagation losses for sight diffraction and scatter-ing in free space respectively 1198961 and 1198962 are propagation losscoefficients and119898119889 and119898119904 are loss coefficients for diffractionand scattering respectively If the influence of the free spacetransmission loss is not taken into account the loss on thewhole transmission path can be expressed by (7)

In this paper the loss prediction function of visualdistance spread is used and hence the propagation loss canbe expressed as follows

119871 = 119860119890119897 + 1198961119889 + 1198962log119890 ( 119889119889119871119878) (8)

where all other variables are defined as in (7)For given parameters such as the heights of the trans-

mitting and receiving antennae the value of this function is

4 Wireless Communications and Mobile Computing

only related to distance 119889 Hence the loss prediction can berewritten as follows

120574itm (ℎ) = 1198861 + 1198862119889 + 1198863log119890 (ℎ120579 + 120576) (9)

where ℎ is the distance of two data points and 120576 is a verysmall constant which prevents division by zero Note thatin practice the two data sampling points may be in thesame coordinate position and ℎ is equal to 0 in this caseCoefficients 1198861 1198862 and 1198863 are coefficients to be determinedThe value of 120579 is set to 14000 which is used to simulate thedistance of sight

If the effect of free space propagation loss is taken intoaccount the overall loss across the propagation path is

119871 = 119860 ref + 3245 + 20 lg 119889 + 20 lg119891 (10)

where 3245 + 20 lg 119889 + 20 lg119891 is the loss of free spacepropagation 119889 is the propagation distance and 119891 is theemissive frequency According to the same ideas above (11)can be rewritten as

120574itmf (ℎ) = 1198861 + 1198862119889 + 1198863log119890 (ℎ120579 + 120576)+ 1198864log10 (ℎ + 120576)

(11)

where 1198864 is a coefficient to be determined and the othervariables are defined as in (9)

Equations (9) and (11) are the two theoretical variogrammodels proposed in this paper The new models are moreconsistent with the parameter change behaviors in the radioenvironment map and more accurately reflect the relation-ship between parameter space changes

33 Weighted Fitting Algorithm for theTheoretical VariogramUsing the ground truth data the theoretical variogram isfitted and the undetermined coefficients in the model areobtained In traditional methods the least-squares method ismainly used to fit the function Its fitness function is

119865 (119895) = 119899sum119894=1

[120574 (ℎ119894119895) minus 120574lowast (ℎ119894119895)]2 (12)

where 119865(119895) is the fitness function value of the 119895th variable ℎ119894119895is the 119894th lag of the 119895th variable 120574lowast(ℎ119894119895) is the estimated valueof variogram at position ℎ119894119895 and 120574(ℎ119894119895) is the real value of thevariogram at position ℎ119894119895 The disadvantage of this methodis that it considers the contribution of all data to be equalwithout considering outliers and specific data points as wellas the specificity of the radio environment parameters

In practice because of building occlusion and the effectsof an uneven distribution of sampling nodes abnormal noiseexists To overcome this problem the method proposed inthis paper increases the corresponding weight coefficient ofthe fitness function to strengthen or reduce some environ-mental factors or meet the distribution characteristics of thevariogram To address the problem of uneven sampling pointdistributions of the radio environment parameters the first

weight coefficient 1205821 = 119873119873119894 is introduced where 119873119894 is thenumber of sample point pairs that correspond to a certain lagdistance and119873 is the total number of sample point pairsThesecond weight addresses the inconsistencies and inaccuraciesin the sampled point data which is caused by the electro-magnetic shadowing of buildings and reflections multipathsand radio propagation diffraction For example there couldbe some abnormally large or unusually small sampled valuesTo reduce the impacts of unreasonable sample points on thefitness function the weight coefficient is 1205822 = 120574(ℎ)120574(ℎ119894)where 120574(ℎ) is the mean value of the variogram and 120574(ℎ119894)is the value of the variogram at lag distance ℎ119894 The thirdweight is added because point pairs with smaller lag distancesoften better reflect the degree of variability of regionalizedvariables To increase the contribution of data point pairswith small lag distances the proposed method adds weightcoefficient 1205823 = ℎℎ119894 where ℎ is the mean value of the lagdistance and ℎ119894 is the corresponding lag distance

The final weight coefficient is the product 120582 = 1205821 sdot 1205822 sdot 1205823Then 120582119894 can be computed by

120582119894 = 119873119873119894 lowast 120574 (ℎ)120574 (ℎ119894) lowast ℎℎ119894 (13)

Hence a new fitness function is obtained expressed asfollows

119865 (119895) = 119899sum119894=1

120582119894 [120574 (ℎ119894119895) minus 120574lowast (ℎ119894119895)]2 (14)

For the fitness function defined by (14) the PSO algorithmis used to fit the weighted variogram In the particle swarmthe position of the ith particle can be expressed as 119909119894 = (11990911989411199091198942 119909119894119889) 119894 = 1 119873 where 119889 is the dimension of thesolution space and119873 is the number of particlesThe previousmost optimal position of the 119894th particle is denoted as 119901best119894 =(1199011198941 1199011198942 119901119894119889) and the optimal position of the swarm isdenoted as 119892best = (1199011198921 1199011198922 119901119892119889) Each particle has amoving speed and the moving speed of the 119894th particle isV119894 = (V1198941 V1198942 V119894119889) At each iteration the particle velocityand position changes are updated by the following equation

119881119896+1119894 = 119908 lowast 119881119896119894 + 1198621 lowast rand1 lowast (119901best119896119894 minus 119883119896119894 ) + 1198622lowast rand2 lowast (119892best119896 minus 119883119896119894 )

119883119896+1119894 = 119883119896119894 + 119881119896+1119894 (15)

where 119896 is the number of iterations and C1 and C2 arelearning factors (or acceleration coefficients) that determinethe learning ability of each iteration of the algorithm

34 Radio Environment Map Field Strength Estimation Algo-rithm In this paper an improved Kriging estimation algo-rithm for radio environment map parameters is proposedusing the new variogram in (6) and the modified theoreticalvariogram model in (9) and (11) The algorithm includes thefollowing main steps (i) calculating the value of the vari-ogram by sampling data (ii) fitting the theoretical variogram

Wireless Communications and Mobile Computing 5

Step 1(1) Calculate distance matrix119863[119889119894119895] and variogram value matrix G[119892119894119895] where 119889119894119895 = radic(119909119894 minus 119909119895)2 + (119910119894 minus 119910119895)2 and 119892119894119895 = (119911119894 minus 119911119895)2(2) lag = min(119863) lag max = round (max(119863)2lag) ℎ = 1 lag lag max LAGS = round (119863lag)(3) Calculate experimental variogram value 119877(119894)for 119894 = 1 lag maxh(119894) = 119894 lowast lagSEL = (LAGS == 119894)N(119894) = sum(sum(SEL == 1))R(119894) = sqrt(sum(119866(SEL))(2 lowast 119873(119894)))

end forStep 2The PSO algorithm is used to fit the theoretical variogram models 120574itm and 120574itmf using the theoretical variogram models inEquations (9) and (12)(1) Initialization the position and velocity of a particle in 119889-dimensional problem space is randomly generated(2) Evaluation of particles the fitness value of each particle is calculated using Equation (14)(3) Updating 119892best the particle fitness values are compared with the population optimal value 119892best and if the current value isbetter than 119892best the position of 119892best is set to the current particle position(4) Updating the particle the velocities and positions of all particles are updated using Equations (15)(5) Stop condition return to step (2) for 119878max iterations to obtain optimal parameters 1198861 1198862 1198863 and 1198864 Then use Equations (9)and (11) to obtain theoretical variogram models 120574itm and 120574itmf Step 3(1) 119870 and 120581119905 are calculated using the theoretical variogram model(2) Equation (4) is written in matrix form119870120582 = 120581119905 to get 120582 = 119870minus1120581119905(3)The estimated value is calculated by Equation (2) 119885119905lowast = sum119899119894=1 120582119894 sdot 119885119894

Algorithm 1 Radio environment map field strength estimation

curve equation using PSO and (iii) calculating the test weightparameters using the theoretical variogram curve equationThe complete process is shown in Algorithm 1 The inputsof the algorithm are sample point coordinates 119909119899lowast1 and 119910119899lowast1sampling value 119911119899lowast1 and coordinates (119909119905 119910119905) of the point 119905to be estimated The output of the algorithm is the estimatedvalue 119885119905lowast In the algorithm lag is the basic lag distancelag max is the maximum multiple of the lag distance andmatrix vectors 119870 120582 and 120581119905 are expressed respectively asfollows

119870 = [[[[[[[

12057411 sdot sdot sdot 1205741119899 1 d 1205741198991 sdot sdot sdot 120574119899119899 11 sdot sdot sdot 1 0

]]]]]]]

120582 = [[[[[[[

1205821120582119899120583

]]]]]]]

120581119905 =[[[[[[[

12057411199051205741198991199051

]]]]]]]

(16)

where 120574119894119895 is the value of the variogram between samplingpoints 119909119894 and 119909119895 and 120583 is the Lagrange constant

4 Experimental ClassificationResults and Analysis

In this paper the proposed algorithm was compared withthree kinds of mainstream algorithms which are IDW [14ndash17 20 21 24] Spline [16 20 25] and Kriging [11ndash21] Wetested them on two kinds of data sets and analyzed theperformance of the algorithms through a variety of objectiveevaluation indexes

41 Objective Evaluation Indexes Five kinds of objectiveevaluation indexes are used to compare and analyze theestimation results of the various algorithms for the param-eters of radio environment map which are the maximumerror (MAX ERR) the average error (AVE ERR) the averageestimation error percentage (PAEE) the relativemean squareerror (RMSE) and the root mean square error (RMSPE)

(1) PAEE

PAEE = 1119899 times 119899sum119894=1

(1198851015840119894 minus 119885119894)2 times 100 (17)

where is the mean value of all the sampling points1198851015840119894 is thepredicted value at the position 119894 and119885119894 is the sample value atthe position 119894(2) RMSE

RMSE = 1119899 times 1198782119899sum119894=1

(1198851015840119894 minus 119885119894)2 (18)

where 1198782 is the variance of all sample data

6 Wireless Communications and Mobile Computing

Figure 1 Data sampling position distribution map

(3) RMSPE

RMSPE = radic 1119899119899sum119894=1

(1198851015840119894 minus 119885119894)2 (19)

42 Experimental Data Two sets of data are used to validateall thesemethods One is realmeasured level data of FM radioFM 998MHz and the max level data of bands 87ndash108MHzand 1800ndash1900MHz The measuring terminal is a vehicleradio monitoring receiver and the measurement location islocated in Chengdu The distribution of the sampling pointswas shown in Figure 1 and the specific parameters for realmeasured data were shown in Table 1 Another is radiosignal simulation data which using the free space propagationmodel and the shadow model is a log normal model Thespecific parameters for simulation datawere shown inTable 2

The real data set contains a total of 256 sampling pointsand the simulation data set contains 1024 level datawith rangeof 100 square kilometers In order to compare and analyzethe estimation results of different algorithms at differentsampling granularities we used 12 and 14 of the total dataas the training data and the remaining data as the validationdata That is when we used 14 data as the training data theremaining 34 data was the validation test data

43 Analysis of Experiment Results

(1) 998MHz Real Sampling Data This is the comparativetesting on the actual acquisition level data of frequency998MHz One-half of the data (128 sampling points in total)is used for training the model and the remaining 12 of thedata is used for testing and verification The 5 evaluationresults of the five kinds of algorithms are shown in Table 3

Table 1 Parameters for real measured data

Measurement area 28Km lowast 28KmRadio type FM radio bandBroadcast 998MHz 87ndash108MHzNumber of sources 1 or119873The average vehicle speed About 80Kmh

Table 2 Parameters for simulation data

Calculated area 10Km lowast 10KmNumbers of points 1024Carrier frequency 1017MHzPath loss model Free space modelShadow model Log normal model

Table 3 Estimation results of level values for 998MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 196973 63338 79729 05122 20172Spline 212641 42668 5583 02512 09893Kriging 127859 36714 45996 01705 06714120574itm 126277 36488 45090 01638 06452120574itmf 125643 35610 44359 01586 06244

Table 4 Estimation result of level values for 998Mhz (14 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 262765 63642 81205 05381 20736Spline 578689 49106 77875 04949 19070Kriging 160234 40510 51165 02136 08232120574itm 167655 40749 50926 02116 08155120574itmf 158968 39979 50414 02070 08040

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 4

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms were shown in Figure 2

In the 12 data for training there are 128 sampling pointsin the range of about 784 square kilometers A sampling pointcovers an average of about 6 square kilometers As couldbe seen from Table 3 the results of the prediction of ourtwo methods and the Kriging method are relatively closeand the worst method is the IDW For Spline and IDW theformer is significantly better than the latter on all indexesexcept the maximum errorThe 120574itmf method of our methodshas achieved the best results on all the evaluation indexesCompared with other methods our methods have obviousadvantages both in prediction accuracy and in predictionstability The best average estimation error of our algorithmswas 3561Db According to the research results of [6] it

Wireless Communications and Mobile Computing 7

IDW resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

lsIDW (998Mhz)

Spline resultsMeasurement results

minus200

20406080

100

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Spline (998Mhz)

Kriging resultsMeasurement results

10203040506070

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Kriging (998Mhz)

itm resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itm (998Mhz)

itmf resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itmf (998Mhz)

Figure 2 Estimation result of level values of 998 MHz (14 training data)

shows that our methods are very competitive While in the14 data for training a sampling point covers about 12 squarekilometers From the results in Table 4 the methods basedon Kriging system have better prediction and estimationeffects In particular the prediction errors of Kriging basedmethods are all about 4Db indicating the effectiveness ofthese methods Compared with the 12 training data theincrease of maximum error is more obvious The secondexperiment showed that 120574itmf still has the best predictionresults in all algorithms As could be seen from Figure 2although the IDW had obvious smoothing effect reflectingthe overall trend of the data distribution the predictionaccuracy is the lowest and the estimation errors are very largein the ranges of 40ndash60 and 160ndash180 The prediction of Splinehas two obvious outlier points which indicated that thealgorithm is sensitive to noise data Compared with Krigingbased methods our methods yield significant improvementsin the range of 140ndash180

Table 5 Estimation results of max level values for 87ndash108MHz (12training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 122333 33063 43205 06093 02982Spline 123468 29376 38746 04900 02398Kriging 118977 26554 34731 03937 01927120574itm 108254 25374 32675 03485 01706120574itmf 108099 25368 32658 03481 01704

(2) 87ndash108MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 87ndash108MHz One-half of the data (128sampling points in total) was used for training the modeland the remaining was used for testing and verification The5 evaluation results of the five kinds of algorithms are shownin Table 5

8 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

455055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

itmf (87ndash108Mhz)

itm (87ndash108Mhz)Kriging (87ndash108Mhz)

Spline (87ndash108Mhz)IDW (87ndash108Mhz)

Figure 3 Estimation results of max level values of 87ndash108MHz (14 training data)

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 6

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 3

Themaximum signal strength in the frequency band is animportant parameter of the radio environment map In thelarge scale space many signal sources constitute the spatialdistribution of the maximum signal strength so it is difficultto make estimation by using the radio propagation model

Table 6 Estimation results of max level values for 87ndash108MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 163241 33529 44390 06374 03152Spline 248394 31712 43034 05990 02962Kriging 126690 27459 34564 03864 01911120574itm 102437 26877 34220 03788 01873120574itmf 112699 26453 33709 03675 01817

The spatial interpolation method is more advantageous Theexperimental results of 12 training data are shown in Table 5

Wireless Communications and Mobile Computing 9

Table 7 Estimation results of max level values for 1800ndash1900MHz(12 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 224790 56729 75337 06532 13643Spline 187473 49472 66059 05022 10489Kriging 172293 47758 63212 04598 09605120574itm 182057 46203 61744 04387 09164120574itmf 183114 46199 61344 04331 09046

Table 8 Estimation results of max level values for 1800ndash1900MHz(14 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 282658 59683 79227 07184 15180Spline 301425 67523 90084 09287 19626Kriging 288990 62277 82594 07807 16498120574itm 241963 55533 72744 06056 12797120574itmf 239539 54968 72053 05942 12555

As could be seen from the table all themethods have got goodresults Surprisingly compared to the radiation estimationof single source in experiments (1) the estimation of themaximum signal strength had a better accuracy which wasabout 10Db Furthermore for the average prediction errorthe results of our methods are close to 26Db Similarlyfor all the evaluation indexes the proposed method 120574itmfachieves the best results and our method increases about10 compared to the Kriging For the estimation of themaximum signal strength in frequency band the predictionaccuracy is not significantly reduced with the training datareduction (seen from Table 6) For the maximum error the120574itm algorithm gets the best result and the 120574itmf algorithmachieves the best result on the rest of indexes The Splineand IDW have a large maximum error As could be seenfrom Figure 3 the Spline exhibits a significant error whichis consistent with the previous conclusion that the methodhas a weak ability to overcome noise The proposed methodshave the best prediction and estimation effect

(3) 1800ndash1900MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 1800ndash1900MHz One-half of the data (128sampling points in total) is used for training the modeland the remaining is used for testing and verification The 5evaluation results of the five kinds of algorithms are shown inTable 7

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 8

Same as the above all the five kinds of algorithms use thesame 14 training data and the remaining data as the samemeasured data The comparisons of various algorithms areshown in Figure 4

Themain services in the 1800ndash1900MHz band aremobilecommunications of which band has more complex electro-magnetic environment and the estimation of the parameters

Table 9 Estimation results of level values for 1017MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266984 34255 44763 06184 03720Spline 155874 30751 39084 04715 02836Kriging 121004 27197 33944 03556 02139120574itm 128846 25712 32100 03180 01913120574itmf 135290 25613 31978 03156 01899

Table 10 Estimation results of level values for 1017MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266254 33326 44070 06072 03603Spline 231643 36385 49289 07596 04507Kriging 110104 28034 35230 03881 02303120574itm 115091 27089 33900 03593 02132120574itmf 134562 26326 32835 03371 02000

of this band is more difficult The experimental results of12 training data are shown in Table 7 As could be seenfrom the table all the methods have good results Themethod Kriging has the best performance for MAX ERRindex For the remaining evaluation indexes our method120574itmf obtained the best results In general the results of thethree methods of Kriging 120574itm and 120574itmf are relatively closeand the improved methods based on propagation modelare superior to the traditional Kriging method When thetraining set is reduced by half the performance of allmethodsis significantly reduced (seen from Table 8) Among themthe predication performance of the Kriging based methodsis reduced by nearly 20 This is because the power of themobile communication station is small and the transmissiondistance is close which causes the correlation between thesparse sampling points to be weak However in this case ourapproach is significantly better than the traditional Krigingbased approach with all the indicators increasing by nearly15 It is worth mentioning that the IDW algorithm alsoobtains good results indicating that the algorithm has goodstability As could be seen from Figure 4 the data set isdifficult to predict and in some individual positions allmethods have large errors But the proposed methods havethe best prediction and estimation effect especially in thevicinity of the test point numbered 140 and the proposedmethods are significantly better than the results of theKrigingmethod

(4) 1017MHz Simulation Data This was a comparativetesting on the actual acquisition level data of frequency1017MHz One-half of the data (512 sampling points in total)is used for training the model and the remaining is used fortesting and verification The 5 evaluation results of the fivekinds of algorithm are shown in Table 9

A quarter of the data (256 samples in total) is used to trainthe model and the remaining (768 testing points) is used fortesting and validation The results are shown in Table 10

10 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

itmf (1800ndash1900 Mhz)

itm (1800ndash1900 Mhz)Kriging (1800ndash1900 Mhz)

IDW (1800ndash1900 Mhz) Spline (1800ndash1900 Mhz)

0

10

20

30

40

50

60Le

vels

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

010203040506070

Leve

ls

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Figure 4 Estimation results of max level values of 1800ndash1900MHz (14 training data)

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 5

We use 12 the simulation data for training model in ourexperiment and each sampling point covers about 05 squarekilometers As can be seen from Table 9 the IDW has avery highmaximumprediction error and theKriging obtainsthe best maximum error evaluation while for the rest of theevaluation indexes the 120574itmf is about 10 higher than the

Kriging and about 20 higher than Spline and IDW As canbe seen from Table 10 the Kriging yields the best maximumerror valuation while for the rest of the evaluation indexesthe 120574itmf method obtains the best results In 14 training datasituation the predictive performance of Spline declines moreseverely As can be seen from Figure 5 IDW has a significantprediction error while methods based on Kriging systemhave better prediction accuracy In all compared methodsthe proposed methods based on propagation model haveachieved the highest accuracy Because of the introductionof the shadow model it is difficult to have a high prediction

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

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Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

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Shock and Vibration

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

Wireless Communications and Mobile Computing 3

where 120582119894 is the 119894th weighting coefficient According to theprinciple of optimal unbiased estimation the value of 120582119894should satisfy the following conditions

119864 [119911 (119909119905) minus 1199111015840 (119909119905)] = 0119864 [119911 (119909119905) minus 1199111015840 (119909119905)]2 = min (3)

where 1199111015840(119909119905) is the real sample value Assuming that 119911(119909) sat-isfies the intrinsic hypothesis then according to the Lagrangetheorem the ordinary Kriging equations can be expressed asfollows

119899sum119895=1

120582119895120574 (119909119894 119909119895) + 120583 = 120574 (119909119894 119909119905) 119894 = 1 2 119899119899sum119894=1

120582119894 = 1(4)

where 120574(119909119894 119909119895) is the value of the variogram between sam-pling points 119909119894 and 119909119895 and 120583 is the Lagrange constantWeighting coefficient 120582119894 can be calculated by (4) When 120582119894 issubstituted into (2) the estimation value 119911(119909119905) of grid point119909119905 can be obtained

The process of solving 119911(119909119905) shows that the key of Kriginginterpolation is how to obtain the best estimate of variogram120574(ℎ)3 Proposed Method

31 Improved Variogram for Parameter Estimation of RadioEnvironment Map In geostatistics a variogram is a toolused to study the autocorrelation structure of regionalizedvariables The value of a variogram function is only relatedto the distance between two regionalized variables Largervalues of the variogram indicate smaller autocorrelationThevariogram function is defined as follows [10]

120574 (ℎ) = 12119899 (ℎ)119899(ℎ)sum119894=1

(119911 (119909119894) minus 119911 (119909119894 + ℎ))2 (5)

where 119899(ℎ) is the number of pairs of observation data pointswith lag distance ℎ 119911(119909119894) is the value of the regionalizedvariable at position 119909119894 and 119911(119909119894 + ℎ) is the value of theregionalized variable at a distance ℎ from 119909119894 When the datadistribution is relatively uniform the basic lag distance canbe equal to or slightly larger than the minimum distancebetween the observed data points Alternatively the basiclag distance can be obtained by comparing and analyzingthe variability and stability of the experimental variogram ofseveral candidate basic lag distances

In practice the most important parameter of the radioenvironment map is the signal radiation level in units ofdecibels (dB) If the Kriging algorithm is used directly theexpression of 120574(ℎ) can be simply obtained by (5) in unitsof dB2 However this is not consistent with the dB units ofpropagation loss that are calculated by the radio propagationmodel Hence the variogram is not dimensionally consistent

with the propagationmodelWe believe that the transmissionloss of the propagation model represents the correlationbetween the two radio environment parameters Thereforeto combine the variogram with the propagation modelthe definition of the variation function used in traditionalgeostatistics is modified as follows

120574 (ℎ) = 1119899 (ℎ)radic119899(ℎ)sum119894=1

(119911 (119909119894) minus 119911 (119909119894 + ℎ))2 (6)

The newly defined variogram is called the parameter esti-mation variogram of the radio environment map and thedimensions of the value calculated by the new variogramare consistent with the dimensions of the transmission lossobtained by the propagation model

32 Theoretical Variogram Model Based on PropagationModel It is necessary to use the theoretical variogrammodelto fit the actual variogram The commonly used theoreticalmodels for a variogram are the Gaussian exponential andspherical models In practice the most commonly usedmodel is the spherical model proposed by Pesko et al [11]

In this paper two new theoretical variogram models areproposed based on the LongleyndashRice model one uses theLongleyndashRice to model the theoretical variogram directlyand the other introduces free space transmission loss intothe first model The LongleyndashRice model also called theirregular terrain model [7] is mainly used to predict themedian path loss over irregular terrain The median value ofthe propagation loss in free space for different path lengths iscalculated as follows

119860 ref

= max(0 119860119890119897 + 1198961119889 + 1198962 ln( 119889119889119871119878)) 119889min le 119889 lt 119889119871119878119860119890119889 + 119898119889119889 119889119871119878 le 119889 lt 119889119909119860119890119904 + 119898119904119889 119889 ge 119889119909

(7)

where 119889min le 119889 lt 119889119871119878 is the visual distance spread 119889119871119878 le119889 lt 119889119909 is the diffraction propagation distance and 119889 ge 119889119909 isthe scattering propagation distance In addition119860119890119897119860119890119889 and119860119890119904 are propagation losses for sight diffraction and scatter-ing in free space respectively 1198961 and 1198962 are propagation losscoefficients and119898119889 and119898119904 are loss coefficients for diffractionand scattering respectively If the influence of the free spacetransmission loss is not taken into account the loss on thewhole transmission path can be expressed by (7)

In this paper the loss prediction function of visualdistance spread is used and hence the propagation loss canbe expressed as follows

119871 = 119860119890119897 + 1198961119889 + 1198962log119890 ( 119889119889119871119878) (8)

where all other variables are defined as in (7)For given parameters such as the heights of the trans-

mitting and receiving antennae the value of this function is

4 Wireless Communications and Mobile Computing

only related to distance 119889 Hence the loss prediction can berewritten as follows

120574itm (ℎ) = 1198861 + 1198862119889 + 1198863log119890 (ℎ120579 + 120576) (9)

where ℎ is the distance of two data points and 120576 is a verysmall constant which prevents division by zero Note thatin practice the two data sampling points may be in thesame coordinate position and ℎ is equal to 0 in this caseCoefficients 1198861 1198862 and 1198863 are coefficients to be determinedThe value of 120579 is set to 14000 which is used to simulate thedistance of sight

If the effect of free space propagation loss is taken intoaccount the overall loss across the propagation path is

119871 = 119860 ref + 3245 + 20 lg 119889 + 20 lg119891 (10)

where 3245 + 20 lg 119889 + 20 lg119891 is the loss of free spacepropagation 119889 is the propagation distance and 119891 is theemissive frequency According to the same ideas above (11)can be rewritten as

120574itmf (ℎ) = 1198861 + 1198862119889 + 1198863log119890 (ℎ120579 + 120576)+ 1198864log10 (ℎ + 120576)

(11)

where 1198864 is a coefficient to be determined and the othervariables are defined as in (9)

Equations (9) and (11) are the two theoretical variogrammodels proposed in this paper The new models are moreconsistent with the parameter change behaviors in the radioenvironment map and more accurately reflect the relation-ship between parameter space changes

33 Weighted Fitting Algorithm for theTheoretical VariogramUsing the ground truth data the theoretical variogram isfitted and the undetermined coefficients in the model areobtained In traditional methods the least-squares method ismainly used to fit the function Its fitness function is

119865 (119895) = 119899sum119894=1

[120574 (ℎ119894119895) minus 120574lowast (ℎ119894119895)]2 (12)

where 119865(119895) is the fitness function value of the 119895th variable ℎ119894119895is the 119894th lag of the 119895th variable 120574lowast(ℎ119894119895) is the estimated valueof variogram at position ℎ119894119895 and 120574(ℎ119894119895) is the real value of thevariogram at position ℎ119894119895 The disadvantage of this methodis that it considers the contribution of all data to be equalwithout considering outliers and specific data points as wellas the specificity of the radio environment parameters

In practice because of building occlusion and the effectsof an uneven distribution of sampling nodes abnormal noiseexists To overcome this problem the method proposed inthis paper increases the corresponding weight coefficient ofthe fitness function to strengthen or reduce some environ-mental factors or meet the distribution characteristics of thevariogram To address the problem of uneven sampling pointdistributions of the radio environment parameters the first

weight coefficient 1205821 = 119873119873119894 is introduced where 119873119894 is thenumber of sample point pairs that correspond to a certain lagdistance and119873 is the total number of sample point pairsThesecond weight addresses the inconsistencies and inaccuraciesin the sampled point data which is caused by the electro-magnetic shadowing of buildings and reflections multipathsand radio propagation diffraction For example there couldbe some abnormally large or unusually small sampled valuesTo reduce the impacts of unreasonable sample points on thefitness function the weight coefficient is 1205822 = 120574(ℎ)120574(ℎ119894)where 120574(ℎ) is the mean value of the variogram and 120574(ℎ119894)is the value of the variogram at lag distance ℎ119894 The thirdweight is added because point pairs with smaller lag distancesoften better reflect the degree of variability of regionalizedvariables To increase the contribution of data point pairswith small lag distances the proposed method adds weightcoefficient 1205823 = ℎℎ119894 where ℎ is the mean value of the lagdistance and ℎ119894 is the corresponding lag distance

The final weight coefficient is the product 120582 = 1205821 sdot 1205822 sdot 1205823Then 120582119894 can be computed by

120582119894 = 119873119873119894 lowast 120574 (ℎ)120574 (ℎ119894) lowast ℎℎ119894 (13)

Hence a new fitness function is obtained expressed asfollows

119865 (119895) = 119899sum119894=1

120582119894 [120574 (ℎ119894119895) minus 120574lowast (ℎ119894119895)]2 (14)

For the fitness function defined by (14) the PSO algorithmis used to fit the weighted variogram In the particle swarmthe position of the ith particle can be expressed as 119909119894 = (11990911989411199091198942 119909119894119889) 119894 = 1 119873 where 119889 is the dimension of thesolution space and119873 is the number of particlesThe previousmost optimal position of the 119894th particle is denoted as 119901best119894 =(1199011198941 1199011198942 119901119894119889) and the optimal position of the swarm isdenoted as 119892best = (1199011198921 1199011198922 119901119892119889) Each particle has amoving speed and the moving speed of the 119894th particle isV119894 = (V1198941 V1198942 V119894119889) At each iteration the particle velocityand position changes are updated by the following equation

119881119896+1119894 = 119908 lowast 119881119896119894 + 1198621 lowast rand1 lowast (119901best119896119894 minus 119883119896119894 ) + 1198622lowast rand2 lowast (119892best119896 minus 119883119896119894 )

119883119896+1119894 = 119883119896119894 + 119881119896+1119894 (15)

where 119896 is the number of iterations and C1 and C2 arelearning factors (or acceleration coefficients) that determinethe learning ability of each iteration of the algorithm

34 Radio Environment Map Field Strength Estimation Algo-rithm In this paper an improved Kriging estimation algo-rithm for radio environment map parameters is proposedusing the new variogram in (6) and the modified theoreticalvariogram model in (9) and (11) The algorithm includes thefollowing main steps (i) calculating the value of the vari-ogram by sampling data (ii) fitting the theoretical variogram

Wireless Communications and Mobile Computing 5

Step 1(1) Calculate distance matrix119863[119889119894119895] and variogram value matrix G[119892119894119895] where 119889119894119895 = radic(119909119894 minus 119909119895)2 + (119910119894 minus 119910119895)2 and 119892119894119895 = (119911119894 minus 119911119895)2(2) lag = min(119863) lag max = round (max(119863)2lag) ℎ = 1 lag lag max LAGS = round (119863lag)(3) Calculate experimental variogram value 119877(119894)for 119894 = 1 lag maxh(119894) = 119894 lowast lagSEL = (LAGS == 119894)N(119894) = sum(sum(SEL == 1))R(119894) = sqrt(sum(119866(SEL))(2 lowast 119873(119894)))

end forStep 2The PSO algorithm is used to fit the theoretical variogram models 120574itm and 120574itmf using the theoretical variogram models inEquations (9) and (12)(1) Initialization the position and velocity of a particle in 119889-dimensional problem space is randomly generated(2) Evaluation of particles the fitness value of each particle is calculated using Equation (14)(3) Updating 119892best the particle fitness values are compared with the population optimal value 119892best and if the current value isbetter than 119892best the position of 119892best is set to the current particle position(4) Updating the particle the velocities and positions of all particles are updated using Equations (15)(5) Stop condition return to step (2) for 119878max iterations to obtain optimal parameters 1198861 1198862 1198863 and 1198864 Then use Equations (9)and (11) to obtain theoretical variogram models 120574itm and 120574itmf Step 3(1) 119870 and 120581119905 are calculated using the theoretical variogram model(2) Equation (4) is written in matrix form119870120582 = 120581119905 to get 120582 = 119870minus1120581119905(3)The estimated value is calculated by Equation (2) 119885119905lowast = sum119899119894=1 120582119894 sdot 119885119894

Algorithm 1 Radio environment map field strength estimation

curve equation using PSO and (iii) calculating the test weightparameters using the theoretical variogram curve equationThe complete process is shown in Algorithm 1 The inputsof the algorithm are sample point coordinates 119909119899lowast1 and 119910119899lowast1sampling value 119911119899lowast1 and coordinates (119909119905 119910119905) of the point 119905to be estimated The output of the algorithm is the estimatedvalue 119885119905lowast In the algorithm lag is the basic lag distancelag max is the maximum multiple of the lag distance andmatrix vectors 119870 120582 and 120581119905 are expressed respectively asfollows

119870 = [[[[[[[

12057411 sdot sdot sdot 1205741119899 1 d 1205741198991 sdot sdot sdot 120574119899119899 11 sdot sdot sdot 1 0

]]]]]]]

120582 = [[[[[[[

1205821120582119899120583

]]]]]]]

120581119905 =[[[[[[[

12057411199051205741198991199051

]]]]]]]

(16)

where 120574119894119895 is the value of the variogram between samplingpoints 119909119894 and 119909119895 and 120583 is the Lagrange constant

4 Experimental ClassificationResults and Analysis

In this paper the proposed algorithm was compared withthree kinds of mainstream algorithms which are IDW [14ndash17 20 21 24] Spline [16 20 25] and Kriging [11ndash21] Wetested them on two kinds of data sets and analyzed theperformance of the algorithms through a variety of objectiveevaluation indexes

41 Objective Evaluation Indexes Five kinds of objectiveevaluation indexes are used to compare and analyze theestimation results of the various algorithms for the param-eters of radio environment map which are the maximumerror (MAX ERR) the average error (AVE ERR) the averageestimation error percentage (PAEE) the relativemean squareerror (RMSE) and the root mean square error (RMSPE)

(1) PAEE

PAEE = 1119899 times 119899sum119894=1

(1198851015840119894 minus 119885119894)2 times 100 (17)

where is the mean value of all the sampling points1198851015840119894 is thepredicted value at the position 119894 and119885119894 is the sample value atthe position 119894(2) RMSE

RMSE = 1119899 times 1198782119899sum119894=1

(1198851015840119894 minus 119885119894)2 (18)

where 1198782 is the variance of all sample data

6 Wireless Communications and Mobile Computing

Figure 1 Data sampling position distribution map

(3) RMSPE

RMSPE = radic 1119899119899sum119894=1

(1198851015840119894 minus 119885119894)2 (19)

42 Experimental Data Two sets of data are used to validateall thesemethods One is realmeasured level data of FM radioFM 998MHz and the max level data of bands 87ndash108MHzand 1800ndash1900MHz The measuring terminal is a vehicleradio monitoring receiver and the measurement location islocated in Chengdu The distribution of the sampling pointswas shown in Figure 1 and the specific parameters for realmeasured data were shown in Table 1 Another is radiosignal simulation data which using the free space propagationmodel and the shadow model is a log normal model Thespecific parameters for simulation datawere shown inTable 2

The real data set contains a total of 256 sampling pointsand the simulation data set contains 1024 level datawith rangeof 100 square kilometers In order to compare and analyzethe estimation results of different algorithms at differentsampling granularities we used 12 and 14 of the total dataas the training data and the remaining data as the validationdata That is when we used 14 data as the training data theremaining 34 data was the validation test data

43 Analysis of Experiment Results

(1) 998MHz Real Sampling Data This is the comparativetesting on the actual acquisition level data of frequency998MHz One-half of the data (128 sampling points in total)is used for training the model and the remaining 12 of thedata is used for testing and verification The 5 evaluationresults of the five kinds of algorithms are shown in Table 3

Table 1 Parameters for real measured data

Measurement area 28Km lowast 28KmRadio type FM radio bandBroadcast 998MHz 87ndash108MHzNumber of sources 1 or119873The average vehicle speed About 80Kmh

Table 2 Parameters for simulation data

Calculated area 10Km lowast 10KmNumbers of points 1024Carrier frequency 1017MHzPath loss model Free space modelShadow model Log normal model

Table 3 Estimation results of level values for 998MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 196973 63338 79729 05122 20172Spline 212641 42668 5583 02512 09893Kriging 127859 36714 45996 01705 06714120574itm 126277 36488 45090 01638 06452120574itmf 125643 35610 44359 01586 06244

Table 4 Estimation result of level values for 998Mhz (14 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 262765 63642 81205 05381 20736Spline 578689 49106 77875 04949 19070Kriging 160234 40510 51165 02136 08232120574itm 167655 40749 50926 02116 08155120574itmf 158968 39979 50414 02070 08040

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 4

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms were shown in Figure 2

In the 12 data for training there are 128 sampling pointsin the range of about 784 square kilometers A sampling pointcovers an average of about 6 square kilometers As couldbe seen from Table 3 the results of the prediction of ourtwo methods and the Kriging method are relatively closeand the worst method is the IDW For Spline and IDW theformer is significantly better than the latter on all indexesexcept the maximum errorThe 120574itmf method of our methodshas achieved the best results on all the evaluation indexesCompared with other methods our methods have obviousadvantages both in prediction accuracy and in predictionstability The best average estimation error of our algorithmswas 3561Db According to the research results of [6] it

Wireless Communications and Mobile Computing 7

IDW resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

lsIDW (998Mhz)

Spline resultsMeasurement results

minus200

20406080

100

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Spline (998Mhz)

Kriging resultsMeasurement results

10203040506070

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Kriging (998Mhz)

itm resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itm (998Mhz)

itmf resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itmf (998Mhz)

Figure 2 Estimation result of level values of 998 MHz (14 training data)

shows that our methods are very competitive While in the14 data for training a sampling point covers about 12 squarekilometers From the results in Table 4 the methods basedon Kriging system have better prediction and estimationeffects In particular the prediction errors of Kriging basedmethods are all about 4Db indicating the effectiveness ofthese methods Compared with the 12 training data theincrease of maximum error is more obvious The secondexperiment showed that 120574itmf still has the best predictionresults in all algorithms As could be seen from Figure 2although the IDW had obvious smoothing effect reflectingthe overall trend of the data distribution the predictionaccuracy is the lowest and the estimation errors are very largein the ranges of 40ndash60 and 160ndash180 The prediction of Splinehas two obvious outlier points which indicated that thealgorithm is sensitive to noise data Compared with Krigingbased methods our methods yield significant improvementsin the range of 140ndash180

Table 5 Estimation results of max level values for 87ndash108MHz (12training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 122333 33063 43205 06093 02982Spline 123468 29376 38746 04900 02398Kriging 118977 26554 34731 03937 01927120574itm 108254 25374 32675 03485 01706120574itmf 108099 25368 32658 03481 01704

(2) 87ndash108MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 87ndash108MHz One-half of the data (128sampling points in total) was used for training the modeland the remaining was used for testing and verification The5 evaluation results of the five kinds of algorithms are shownin Table 5

8 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

455055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

itmf (87ndash108Mhz)

itm (87ndash108Mhz)Kriging (87ndash108Mhz)

Spline (87ndash108Mhz)IDW (87ndash108Mhz)

Figure 3 Estimation results of max level values of 87ndash108MHz (14 training data)

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 6

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 3

Themaximum signal strength in the frequency band is animportant parameter of the radio environment map In thelarge scale space many signal sources constitute the spatialdistribution of the maximum signal strength so it is difficultto make estimation by using the radio propagation model

Table 6 Estimation results of max level values for 87ndash108MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 163241 33529 44390 06374 03152Spline 248394 31712 43034 05990 02962Kriging 126690 27459 34564 03864 01911120574itm 102437 26877 34220 03788 01873120574itmf 112699 26453 33709 03675 01817

The spatial interpolation method is more advantageous Theexperimental results of 12 training data are shown in Table 5

Wireless Communications and Mobile Computing 9

Table 7 Estimation results of max level values for 1800ndash1900MHz(12 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 224790 56729 75337 06532 13643Spline 187473 49472 66059 05022 10489Kriging 172293 47758 63212 04598 09605120574itm 182057 46203 61744 04387 09164120574itmf 183114 46199 61344 04331 09046

Table 8 Estimation results of max level values for 1800ndash1900MHz(14 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 282658 59683 79227 07184 15180Spline 301425 67523 90084 09287 19626Kriging 288990 62277 82594 07807 16498120574itm 241963 55533 72744 06056 12797120574itmf 239539 54968 72053 05942 12555

As could be seen from the table all themethods have got goodresults Surprisingly compared to the radiation estimationof single source in experiments (1) the estimation of themaximum signal strength had a better accuracy which wasabout 10Db Furthermore for the average prediction errorthe results of our methods are close to 26Db Similarlyfor all the evaluation indexes the proposed method 120574itmfachieves the best results and our method increases about10 compared to the Kriging For the estimation of themaximum signal strength in frequency band the predictionaccuracy is not significantly reduced with the training datareduction (seen from Table 6) For the maximum error the120574itm algorithm gets the best result and the 120574itmf algorithmachieves the best result on the rest of indexes The Splineand IDW have a large maximum error As could be seenfrom Figure 3 the Spline exhibits a significant error whichis consistent with the previous conclusion that the methodhas a weak ability to overcome noise The proposed methodshave the best prediction and estimation effect

(3) 1800ndash1900MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 1800ndash1900MHz One-half of the data (128sampling points in total) is used for training the modeland the remaining is used for testing and verification The 5evaluation results of the five kinds of algorithms are shown inTable 7

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 8

Same as the above all the five kinds of algorithms use thesame 14 training data and the remaining data as the samemeasured data The comparisons of various algorithms areshown in Figure 4

Themain services in the 1800ndash1900MHz band aremobilecommunications of which band has more complex electro-magnetic environment and the estimation of the parameters

Table 9 Estimation results of level values for 1017MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266984 34255 44763 06184 03720Spline 155874 30751 39084 04715 02836Kriging 121004 27197 33944 03556 02139120574itm 128846 25712 32100 03180 01913120574itmf 135290 25613 31978 03156 01899

Table 10 Estimation results of level values for 1017MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266254 33326 44070 06072 03603Spline 231643 36385 49289 07596 04507Kriging 110104 28034 35230 03881 02303120574itm 115091 27089 33900 03593 02132120574itmf 134562 26326 32835 03371 02000

of this band is more difficult The experimental results of12 training data are shown in Table 7 As could be seenfrom the table all the methods have good results Themethod Kriging has the best performance for MAX ERRindex For the remaining evaluation indexes our method120574itmf obtained the best results In general the results of thethree methods of Kriging 120574itm and 120574itmf are relatively closeand the improved methods based on propagation modelare superior to the traditional Kriging method When thetraining set is reduced by half the performance of allmethodsis significantly reduced (seen from Table 8) Among themthe predication performance of the Kriging based methodsis reduced by nearly 20 This is because the power of themobile communication station is small and the transmissiondistance is close which causes the correlation between thesparse sampling points to be weak However in this case ourapproach is significantly better than the traditional Krigingbased approach with all the indicators increasing by nearly15 It is worth mentioning that the IDW algorithm alsoobtains good results indicating that the algorithm has goodstability As could be seen from Figure 4 the data set isdifficult to predict and in some individual positions allmethods have large errors But the proposed methods havethe best prediction and estimation effect especially in thevicinity of the test point numbered 140 and the proposedmethods are significantly better than the results of theKrigingmethod

(4) 1017MHz Simulation Data This was a comparativetesting on the actual acquisition level data of frequency1017MHz One-half of the data (512 sampling points in total)is used for training the model and the remaining is used fortesting and verification The 5 evaluation results of the fivekinds of algorithm are shown in Table 9

A quarter of the data (256 samples in total) is used to trainthe model and the remaining (768 testing points) is used fortesting and validation The results are shown in Table 10

10 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

itmf (1800ndash1900 Mhz)

itm (1800ndash1900 Mhz)Kriging (1800ndash1900 Mhz)

IDW (1800ndash1900 Mhz) Spline (1800ndash1900 Mhz)

0

10

20

30

40

50

60Le

vels

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

010203040506070

Leve

ls

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Figure 4 Estimation results of max level values of 1800ndash1900MHz (14 training data)

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 5

We use 12 the simulation data for training model in ourexperiment and each sampling point covers about 05 squarekilometers As can be seen from Table 9 the IDW has avery highmaximumprediction error and theKriging obtainsthe best maximum error evaluation while for the rest of theevaluation indexes the 120574itmf is about 10 higher than the

Kriging and about 20 higher than Spline and IDW As canbe seen from Table 10 the Kriging yields the best maximumerror valuation while for the rest of the evaluation indexesthe 120574itmf method obtains the best results In 14 training datasituation the predictive performance of Spline declines moreseverely As can be seen from Figure 5 IDW has a significantprediction error while methods based on Kriging systemhave better prediction accuracy In all compared methodsthe proposed methods based on propagation model haveachieved the highest accuracy Because of the introductionof the shadow model it is difficult to have a high prediction

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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RotatingMachinery

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Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

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Electrical and Computer Engineering

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Advances inOptoElectronics

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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DistributedSensor Networks

International Journal of

4 Wireless Communications and Mobile Computing

only related to distance 119889 Hence the loss prediction can berewritten as follows

120574itm (ℎ) = 1198861 + 1198862119889 + 1198863log119890 (ℎ120579 + 120576) (9)

where ℎ is the distance of two data points and 120576 is a verysmall constant which prevents division by zero Note thatin practice the two data sampling points may be in thesame coordinate position and ℎ is equal to 0 in this caseCoefficients 1198861 1198862 and 1198863 are coefficients to be determinedThe value of 120579 is set to 14000 which is used to simulate thedistance of sight

If the effect of free space propagation loss is taken intoaccount the overall loss across the propagation path is

119871 = 119860 ref + 3245 + 20 lg 119889 + 20 lg119891 (10)

where 3245 + 20 lg 119889 + 20 lg119891 is the loss of free spacepropagation 119889 is the propagation distance and 119891 is theemissive frequency According to the same ideas above (11)can be rewritten as

120574itmf (ℎ) = 1198861 + 1198862119889 + 1198863log119890 (ℎ120579 + 120576)+ 1198864log10 (ℎ + 120576)

(11)

where 1198864 is a coefficient to be determined and the othervariables are defined as in (9)

Equations (9) and (11) are the two theoretical variogrammodels proposed in this paper The new models are moreconsistent with the parameter change behaviors in the radioenvironment map and more accurately reflect the relation-ship between parameter space changes

33 Weighted Fitting Algorithm for theTheoretical VariogramUsing the ground truth data the theoretical variogram isfitted and the undetermined coefficients in the model areobtained In traditional methods the least-squares method ismainly used to fit the function Its fitness function is

119865 (119895) = 119899sum119894=1

[120574 (ℎ119894119895) minus 120574lowast (ℎ119894119895)]2 (12)

where 119865(119895) is the fitness function value of the 119895th variable ℎ119894119895is the 119894th lag of the 119895th variable 120574lowast(ℎ119894119895) is the estimated valueof variogram at position ℎ119894119895 and 120574(ℎ119894119895) is the real value of thevariogram at position ℎ119894119895 The disadvantage of this methodis that it considers the contribution of all data to be equalwithout considering outliers and specific data points as wellas the specificity of the radio environment parameters

In practice because of building occlusion and the effectsof an uneven distribution of sampling nodes abnormal noiseexists To overcome this problem the method proposed inthis paper increases the corresponding weight coefficient ofthe fitness function to strengthen or reduce some environ-mental factors or meet the distribution characteristics of thevariogram To address the problem of uneven sampling pointdistributions of the radio environment parameters the first

weight coefficient 1205821 = 119873119873119894 is introduced where 119873119894 is thenumber of sample point pairs that correspond to a certain lagdistance and119873 is the total number of sample point pairsThesecond weight addresses the inconsistencies and inaccuraciesin the sampled point data which is caused by the electro-magnetic shadowing of buildings and reflections multipathsand radio propagation diffraction For example there couldbe some abnormally large or unusually small sampled valuesTo reduce the impacts of unreasonable sample points on thefitness function the weight coefficient is 1205822 = 120574(ℎ)120574(ℎ119894)where 120574(ℎ) is the mean value of the variogram and 120574(ℎ119894)is the value of the variogram at lag distance ℎ119894 The thirdweight is added because point pairs with smaller lag distancesoften better reflect the degree of variability of regionalizedvariables To increase the contribution of data point pairswith small lag distances the proposed method adds weightcoefficient 1205823 = ℎℎ119894 where ℎ is the mean value of the lagdistance and ℎ119894 is the corresponding lag distance

The final weight coefficient is the product 120582 = 1205821 sdot 1205822 sdot 1205823Then 120582119894 can be computed by

120582119894 = 119873119873119894 lowast 120574 (ℎ)120574 (ℎ119894) lowast ℎℎ119894 (13)

Hence a new fitness function is obtained expressed asfollows

119865 (119895) = 119899sum119894=1

120582119894 [120574 (ℎ119894119895) minus 120574lowast (ℎ119894119895)]2 (14)

For the fitness function defined by (14) the PSO algorithmis used to fit the weighted variogram In the particle swarmthe position of the ith particle can be expressed as 119909119894 = (11990911989411199091198942 119909119894119889) 119894 = 1 119873 where 119889 is the dimension of thesolution space and119873 is the number of particlesThe previousmost optimal position of the 119894th particle is denoted as 119901best119894 =(1199011198941 1199011198942 119901119894119889) and the optimal position of the swarm isdenoted as 119892best = (1199011198921 1199011198922 119901119892119889) Each particle has amoving speed and the moving speed of the 119894th particle isV119894 = (V1198941 V1198942 V119894119889) At each iteration the particle velocityand position changes are updated by the following equation

119881119896+1119894 = 119908 lowast 119881119896119894 + 1198621 lowast rand1 lowast (119901best119896119894 minus 119883119896119894 ) + 1198622lowast rand2 lowast (119892best119896 minus 119883119896119894 )

119883119896+1119894 = 119883119896119894 + 119881119896+1119894 (15)

where 119896 is the number of iterations and C1 and C2 arelearning factors (or acceleration coefficients) that determinethe learning ability of each iteration of the algorithm

34 Radio Environment Map Field Strength Estimation Algo-rithm In this paper an improved Kriging estimation algo-rithm for radio environment map parameters is proposedusing the new variogram in (6) and the modified theoreticalvariogram model in (9) and (11) The algorithm includes thefollowing main steps (i) calculating the value of the vari-ogram by sampling data (ii) fitting the theoretical variogram

Wireless Communications and Mobile Computing 5

Step 1(1) Calculate distance matrix119863[119889119894119895] and variogram value matrix G[119892119894119895] where 119889119894119895 = radic(119909119894 minus 119909119895)2 + (119910119894 minus 119910119895)2 and 119892119894119895 = (119911119894 minus 119911119895)2(2) lag = min(119863) lag max = round (max(119863)2lag) ℎ = 1 lag lag max LAGS = round (119863lag)(3) Calculate experimental variogram value 119877(119894)for 119894 = 1 lag maxh(119894) = 119894 lowast lagSEL = (LAGS == 119894)N(119894) = sum(sum(SEL == 1))R(119894) = sqrt(sum(119866(SEL))(2 lowast 119873(119894)))

end forStep 2The PSO algorithm is used to fit the theoretical variogram models 120574itm and 120574itmf using the theoretical variogram models inEquations (9) and (12)(1) Initialization the position and velocity of a particle in 119889-dimensional problem space is randomly generated(2) Evaluation of particles the fitness value of each particle is calculated using Equation (14)(3) Updating 119892best the particle fitness values are compared with the population optimal value 119892best and if the current value isbetter than 119892best the position of 119892best is set to the current particle position(4) Updating the particle the velocities and positions of all particles are updated using Equations (15)(5) Stop condition return to step (2) for 119878max iterations to obtain optimal parameters 1198861 1198862 1198863 and 1198864 Then use Equations (9)and (11) to obtain theoretical variogram models 120574itm and 120574itmf Step 3(1) 119870 and 120581119905 are calculated using the theoretical variogram model(2) Equation (4) is written in matrix form119870120582 = 120581119905 to get 120582 = 119870minus1120581119905(3)The estimated value is calculated by Equation (2) 119885119905lowast = sum119899119894=1 120582119894 sdot 119885119894

Algorithm 1 Radio environment map field strength estimation

curve equation using PSO and (iii) calculating the test weightparameters using the theoretical variogram curve equationThe complete process is shown in Algorithm 1 The inputsof the algorithm are sample point coordinates 119909119899lowast1 and 119910119899lowast1sampling value 119911119899lowast1 and coordinates (119909119905 119910119905) of the point 119905to be estimated The output of the algorithm is the estimatedvalue 119885119905lowast In the algorithm lag is the basic lag distancelag max is the maximum multiple of the lag distance andmatrix vectors 119870 120582 and 120581119905 are expressed respectively asfollows

119870 = [[[[[[[

12057411 sdot sdot sdot 1205741119899 1 d 1205741198991 sdot sdot sdot 120574119899119899 11 sdot sdot sdot 1 0

]]]]]]]

120582 = [[[[[[[

1205821120582119899120583

]]]]]]]

120581119905 =[[[[[[[

12057411199051205741198991199051

]]]]]]]

(16)

where 120574119894119895 is the value of the variogram between samplingpoints 119909119894 and 119909119895 and 120583 is the Lagrange constant

4 Experimental ClassificationResults and Analysis

In this paper the proposed algorithm was compared withthree kinds of mainstream algorithms which are IDW [14ndash17 20 21 24] Spline [16 20 25] and Kriging [11ndash21] Wetested them on two kinds of data sets and analyzed theperformance of the algorithms through a variety of objectiveevaluation indexes

41 Objective Evaluation Indexes Five kinds of objectiveevaluation indexes are used to compare and analyze theestimation results of the various algorithms for the param-eters of radio environment map which are the maximumerror (MAX ERR) the average error (AVE ERR) the averageestimation error percentage (PAEE) the relativemean squareerror (RMSE) and the root mean square error (RMSPE)

(1) PAEE

PAEE = 1119899 times 119899sum119894=1

(1198851015840119894 minus 119885119894)2 times 100 (17)

where is the mean value of all the sampling points1198851015840119894 is thepredicted value at the position 119894 and119885119894 is the sample value atthe position 119894(2) RMSE

RMSE = 1119899 times 1198782119899sum119894=1

(1198851015840119894 minus 119885119894)2 (18)

where 1198782 is the variance of all sample data

6 Wireless Communications and Mobile Computing

Figure 1 Data sampling position distribution map

(3) RMSPE

RMSPE = radic 1119899119899sum119894=1

(1198851015840119894 minus 119885119894)2 (19)

42 Experimental Data Two sets of data are used to validateall thesemethods One is realmeasured level data of FM radioFM 998MHz and the max level data of bands 87ndash108MHzand 1800ndash1900MHz The measuring terminal is a vehicleradio monitoring receiver and the measurement location islocated in Chengdu The distribution of the sampling pointswas shown in Figure 1 and the specific parameters for realmeasured data were shown in Table 1 Another is radiosignal simulation data which using the free space propagationmodel and the shadow model is a log normal model Thespecific parameters for simulation datawere shown inTable 2

The real data set contains a total of 256 sampling pointsand the simulation data set contains 1024 level datawith rangeof 100 square kilometers In order to compare and analyzethe estimation results of different algorithms at differentsampling granularities we used 12 and 14 of the total dataas the training data and the remaining data as the validationdata That is when we used 14 data as the training data theremaining 34 data was the validation test data

43 Analysis of Experiment Results

(1) 998MHz Real Sampling Data This is the comparativetesting on the actual acquisition level data of frequency998MHz One-half of the data (128 sampling points in total)is used for training the model and the remaining 12 of thedata is used for testing and verification The 5 evaluationresults of the five kinds of algorithms are shown in Table 3

Table 1 Parameters for real measured data

Measurement area 28Km lowast 28KmRadio type FM radio bandBroadcast 998MHz 87ndash108MHzNumber of sources 1 or119873The average vehicle speed About 80Kmh

Table 2 Parameters for simulation data

Calculated area 10Km lowast 10KmNumbers of points 1024Carrier frequency 1017MHzPath loss model Free space modelShadow model Log normal model

Table 3 Estimation results of level values for 998MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 196973 63338 79729 05122 20172Spline 212641 42668 5583 02512 09893Kriging 127859 36714 45996 01705 06714120574itm 126277 36488 45090 01638 06452120574itmf 125643 35610 44359 01586 06244

Table 4 Estimation result of level values for 998Mhz (14 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 262765 63642 81205 05381 20736Spline 578689 49106 77875 04949 19070Kriging 160234 40510 51165 02136 08232120574itm 167655 40749 50926 02116 08155120574itmf 158968 39979 50414 02070 08040

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 4

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms were shown in Figure 2

In the 12 data for training there are 128 sampling pointsin the range of about 784 square kilometers A sampling pointcovers an average of about 6 square kilometers As couldbe seen from Table 3 the results of the prediction of ourtwo methods and the Kriging method are relatively closeand the worst method is the IDW For Spline and IDW theformer is significantly better than the latter on all indexesexcept the maximum errorThe 120574itmf method of our methodshas achieved the best results on all the evaluation indexesCompared with other methods our methods have obviousadvantages both in prediction accuracy and in predictionstability The best average estimation error of our algorithmswas 3561Db According to the research results of [6] it

Wireless Communications and Mobile Computing 7

IDW resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

lsIDW (998Mhz)

Spline resultsMeasurement results

minus200

20406080

100

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Spline (998Mhz)

Kriging resultsMeasurement results

10203040506070

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Kriging (998Mhz)

itm resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itm (998Mhz)

itmf resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itmf (998Mhz)

Figure 2 Estimation result of level values of 998 MHz (14 training data)

shows that our methods are very competitive While in the14 data for training a sampling point covers about 12 squarekilometers From the results in Table 4 the methods basedon Kriging system have better prediction and estimationeffects In particular the prediction errors of Kriging basedmethods are all about 4Db indicating the effectiveness ofthese methods Compared with the 12 training data theincrease of maximum error is more obvious The secondexperiment showed that 120574itmf still has the best predictionresults in all algorithms As could be seen from Figure 2although the IDW had obvious smoothing effect reflectingthe overall trend of the data distribution the predictionaccuracy is the lowest and the estimation errors are very largein the ranges of 40ndash60 and 160ndash180 The prediction of Splinehas two obvious outlier points which indicated that thealgorithm is sensitive to noise data Compared with Krigingbased methods our methods yield significant improvementsin the range of 140ndash180

Table 5 Estimation results of max level values for 87ndash108MHz (12training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 122333 33063 43205 06093 02982Spline 123468 29376 38746 04900 02398Kriging 118977 26554 34731 03937 01927120574itm 108254 25374 32675 03485 01706120574itmf 108099 25368 32658 03481 01704

(2) 87ndash108MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 87ndash108MHz One-half of the data (128sampling points in total) was used for training the modeland the remaining was used for testing and verification The5 evaluation results of the five kinds of algorithms are shownin Table 5

8 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

455055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

itmf (87ndash108Mhz)

itm (87ndash108Mhz)Kriging (87ndash108Mhz)

Spline (87ndash108Mhz)IDW (87ndash108Mhz)

Figure 3 Estimation results of max level values of 87ndash108MHz (14 training data)

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 6

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 3

Themaximum signal strength in the frequency band is animportant parameter of the radio environment map In thelarge scale space many signal sources constitute the spatialdistribution of the maximum signal strength so it is difficultto make estimation by using the radio propagation model

Table 6 Estimation results of max level values for 87ndash108MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 163241 33529 44390 06374 03152Spline 248394 31712 43034 05990 02962Kriging 126690 27459 34564 03864 01911120574itm 102437 26877 34220 03788 01873120574itmf 112699 26453 33709 03675 01817

The spatial interpolation method is more advantageous Theexperimental results of 12 training data are shown in Table 5

Wireless Communications and Mobile Computing 9

Table 7 Estimation results of max level values for 1800ndash1900MHz(12 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 224790 56729 75337 06532 13643Spline 187473 49472 66059 05022 10489Kriging 172293 47758 63212 04598 09605120574itm 182057 46203 61744 04387 09164120574itmf 183114 46199 61344 04331 09046

Table 8 Estimation results of max level values for 1800ndash1900MHz(14 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 282658 59683 79227 07184 15180Spline 301425 67523 90084 09287 19626Kriging 288990 62277 82594 07807 16498120574itm 241963 55533 72744 06056 12797120574itmf 239539 54968 72053 05942 12555

As could be seen from the table all themethods have got goodresults Surprisingly compared to the radiation estimationof single source in experiments (1) the estimation of themaximum signal strength had a better accuracy which wasabout 10Db Furthermore for the average prediction errorthe results of our methods are close to 26Db Similarlyfor all the evaluation indexes the proposed method 120574itmfachieves the best results and our method increases about10 compared to the Kriging For the estimation of themaximum signal strength in frequency band the predictionaccuracy is not significantly reduced with the training datareduction (seen from Table 6) For the maximum error the120574itm algorithm gets the best result and the 120574itmf algorithmachieves the best result on the rest of indexes The Splineand IDW have a large maximum error As could be seenfrom Figure 3 the Spline exhibits a significant error whichis consistent with the previous conclusion that the methodhas a weak ability to overcome noise The proposed methodshave the best prediction and estimation effect

(3) 1800ndash1900MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 1800ndash1900MHz One-half of the data (128sampling points in total) is used for training the modeland the remaining is used for testing and verification The 5evaluation results of the five kinds of algorithms are shown inTable 7

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 8

Same as the above all the five kinds of algorithms use thesame 14 training data and the remaining data as the samemeasured data The comparisons of various algorithms areshown in Figure 4

Themain services in the 1800ndash1900MHz band aremobilecommunications of which band has more complex electro-magnetic environment and the estimation of the parameters

Table 9 Estimation results of level values for 1017MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266984 34255 44763 06184 03720Spline 155874 30751 39084 04715 02836Kriging 121004 27197 33944 03556 02139120574itm 128846 25712 32100 03180 01913120574itmf 135290 25613 31978 03156 01899

Table 10 Estimation results of level values for 1017MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266254 33326 44070 06072 03603Spline 231643 36385 49289 07596 04507Kriging 110104 28034 35230 03881 02303120574itm 115091 27089 33900 03593 02132120574itmf 134562 26326 32835 03371 02000

of this band is more difficult The experimental results of12 training data are shown in Table 7 As could be seenfrom the table all the methods have good results Themethod Kriging has the best performance for MAX ERRindex For the remaining evaluation indexes our method120574itmf obtained the best results In general the results of thethree methods of Kriging 120574itm and 120574itmf are relatively closeand the improved methods based on propagation modelare superior to the traditional Kriging method When thetraining set is reduced by half the performance of allmethodsis significantly reduced (seen from Table 8) Among themthe predication performance of the Kriging based methodsis reduced by nearly 20 This is because the power of themobile communication station is small and the transmissiondistance is close which causes the correlation between thesparse sampling points to be weak However in this case ourapproach is significantly better than the traditional Krigingbased approach with all the indicators increasing by nearly15 It is worth mentioning that the IDW algorithm alsoobtains good results indicating that the algorithm has goodstability As could be seen from Figure 4 the data set isdifficult to predict and in some individual positions allmethods have large errors But the proposed methods havethe best prediction and estimation effect especially in thevicinity of the test point numbered 140 and the proposedmethods are significantly better than the results of theKrigingmethod

(4) 1017MHz Simulation Data This was a comparativetesting on the actual acquisition level data of frequency1017MHz One-half of the data (512 sampling points in total)is used for training the model and the remaining is used fortesting and verification The 5 evaluation results of the fivekinds of algorithm are shown in Table 9

A quarter of the data (256 samples in total) is used to trainthe model and the remaining (768 testing points) is used fortesting and validation The results are shown in Table 10

10 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

itmf (1800ndash1900 Mhz)

itm (1800ndash1900 Mhz)Kriging (1800ndash1900 Mhz)

IDW (1800ndash1900 Mhz) Spline (1800ndash1900 Mhz)

0

10

20

30

40

50

60Le

vels

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

010203040506070

Leve

ls

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Figure 4 Estimation results of max level values of 1800ndash1900MHz (14 training data)

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 5

We use 12 the simulation data for training model in ourexperiment and each sampling point covers about 05 squarekilometers As can be seen from Table 9 the IDW has avery highmaximumprediction error and theKriging obtainsthe best maximum error evaluation while for the rest of theevaluation indexes the 120574itmf is about 10 higher than the

Kriging and about 20 higher than Spline and IDW As canbe seen from Table 10 the Kriging yields the best maximumerror valuation while for the rest of the evaluation indexesthe 120574itmf method obtains the best results In 14 training datasituation the predictive performance of Spline declines moreseverely As can be seen from Figure 5 IDW has a significantprediction error while methods based on Kriging systemhave better prediction accuracy In all compared methodsthe proposed methods based on propagation model haveachieved the highest accuracy Because of the introductionof the shadow model it is difficult to have a high prediction

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Wireless Communications and Mobile Computing 5

Step 1(1) Calculate distance matrix119863[119889119894119895] and variogram value matrix G[119892119894119895] where 119889119894119895 = radic(119909119894 minus 119909119895)2 + (119910119894 minus 119910119895)2 and 119892119894119895 = (119911119894 minus 119911119895)2(2) lag = min(119863) lag max = round (max(119863)2lag) ℎ = 1 lag lag max LAGS = round (119863lag)(3) Calculate experimental variogram value 119877(119894)for 119894 = 1 lag maxh(119894) = 119894 lowast lagSEL = (LAGS == 119894)N(119894) = sum(sum(SEL == 1))R(119894) = sqrt(sum(119866(SEL))(2 lowast 119873(119894)))

end forStep 2The PSO algorithm is used to fit the theoretical variogram models 120574itm and 120574itmf using the theoretical variogram models inEquations (9) and (12)(1) Initialization the position and velocity of a particle in 119889-dimensional problem space is randomly generated(2) Evaluation of particles the fitness value of each particle is calculated using Equation (14)(3) Updating 119892best the particle fitness values are compared with the population optimal value 119892best and if the current value isbetter than 119892best the position of 119892best is set to the current particle position(4) Updating the particle the velocities and positions of all particles are updated using Equations (15)(5) Stop condition return to step (2) for 119878max iterations to obtain optimal parameters 1198861 1198862 1198863 and 1198864 Then use Equations (9)and (11) to obtain theoretical variogram models 120574itm and 120574itmf Step 3(1) 119870 and 120581119905 are calculated using the theoretical variogram model(2) Equation (4) is written in matrix form119870120582 = 120581119905 to get 120582 = 119870minus1120581119905(3)The estimated value is calculated by Equation (2) 119885119905lowast = sum119899119894=1 120582119894 sdot 119885119894

Algorithm 1 Radio environment map field strength estimation

curve equation using PSO and (iii) calculating the test weightparameters using the theoretical variogram curve equationThe complete process is shown in Algorithm 1 The inputsof the algorithm are sample point coordinates 119909119899lowast1 and 119910119899lowast1sampling value 119911119899lowast1 and coordinates (119909119905 119910119905) of the point 119905to be estimated The output of the algorithm is the estimatedvalue 119885119905lowast In the algorithm lag is the basic lag distancelag max is the maximum multiple of the lag distance andmatrix vectors 119870 120582 and 120581119905 are expressed respectively asfollows

119870 = [[[[[[[

12057411 sdot sdot sdot 1205741119899 1 d 1205741198991 sdot sdot sdot 120574119899119899 11 sdot sdot sdot 1 0

]]]]]]]

120582 = [[[[[[[

1205821120582119899120583

]]]]]]]

120581119905 =[[[[[[[

12057411199051205741198991199051

]]]]]]]

(16)

where 120574119894119895 is the value of the variogram between samplingpoints 119909119894 and 119909119895 and 120583 is the Lagrange constant

4 Experimental ClassificationResults and Analysis

In this paper the proposed algorithm was compared withthree kinds of mainstream algorithms which are IDW [14ndash17 20 21 24] Spline [16 20 25] and Kriging [11ndash21] Wetested them on two kinds of data sets and analyzed theperformance of the algorithms through a variety of objectiveevaluation indexes

41 Objective Evaluation Indexes Five kinds of objectiveevaluation indexes are used to compare and analyze theestimation results of the various algorithms for the param-eters of radio environment map which are the maximumerror (MAX ERR) the average error (AVE ERR) the averageestimation error percentage (PAEE) the relativemean squareerror (RMSE) and the root mean square error (RMSPE)

(1) PAEE

PAEE = 1119899 times 119899sum119894=1

(1198851015840119894 minus 119885119894)2 times 100 (17)

where is the mean value of all the sampling points1198851015840119894 is thepredicted value at the position 119894 and119885119894 is the sample value atthe position 119894(2) RMSE

RMSE = 1119899 times 1198782119899sum119894=1

(1198851015840119894 minus 119885119894)2 (18)

where 1198782 is the variance of all sample data

6 Wireless Communications and Mobile Computing

Figure 1 Data sampling position distribution map

(3) RMSPE

RMSPE = radic 1119899119899sum119894=1

(1198851015840119894 minus 119885119894)2 (19)

42 Experimental Data Two sets of data are used to validateall thesemethods One is realmeasured level data of FM radioFM 998MHz and the max level data of bands 87ndash108MHzand 1800ndash1900MHz The measuring terminal is a vehicleradio monitoring receiver and the measurement location islocated in Chengdu The distribution of the sampling pointswas shown in Figure 1 and the specific parameters for realmeasured data were shown in Table 1 Another is radiosignal simulation data which using the free space propagationmodel and the shadow model is a log normal model Thespecific parameters for simulation datawere shown inTable 2

The real data set contains a total of 256 sampling pointsand the simulation data set contains 1024 level datawith rangeof 100 square kilometers In order to compare and analyzethe estimation results of different algorithms at differentsampling granularities we used 12 and 14 of the total dataas the training data and the remaining data as the validationdata That is when we used 14 data as the training data theremaining 34 data was the validation test data

43 Analysis of Experiment Results

(1) 998MHz Real Sampling Data This is the comparativetesting on the actual acquisition level data of frequency998MHz One-half of the data (128 sampling points in total)is used for training the model and the remaining 12 of thedata is used for testing and verification The 5 evaluationresults of the five kinds of algorithms are shown in Table 3

Table 1 Parameters for real measured data

Measurement area 28Km lowast 28KmRadio type FM radio bandBroadcast 998MHz 87ndash108MHzNumber of sources 1 or119873The average vehicle speed About 80Kmh

Table 2 Parameters for simulation data

Calculated area 10Km lowast 10KmNumbers of points 1024Carrier frequency 1017MHzPath loss model Free space modelShadow model Log normal model

Table 3 Estimation results of level values for 998MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 196973 63338 79729 05122 20172Spline 212641 42668 5583 02512 09893Kriging 127859 36714 45996 01705 06714120574itm 126277 36488 45090 01638 06452120574itmf 125643 35610 44359 01586 06244

Table 4 Estimation result of level values for 998Mhz (14 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 262765 63642 81205 05381 20736Spline 578689 49106 77875 04949 19070Kriging 160234 40510 51165 02136 08232120574itm 167655 40749 50926 02116 08155120574itmf 158968 39979 50414 02070 08040

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 4

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms were shown in Figure 2

In the 12 data for training there are 128 sampling pointsin the range of about 784 square kilometers A sampling pointcovers an average of about 6 square kilometers As couldbe seen from Table 3 the results of the prediction of ourtwo methods and the Kriging method are relatively closeand the worst method is the IDW For Spline and IDW theformer is significantly better than the latter on all indexesexcept the maximum errorThe 120574itmf method of our methodshas achieved the best results on all the evaluation indexesCompared with other methods our methods have obviousadvantages both in prediction accuracy and in predictionstability The best average estimation error of our algorithmswas 3561Db According to the research results of [6] it

Wireless Communications and Mobile Computing 7

IDW resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

lsIDW (998Mhz)

Spline resultsMeasurement results

minus200

20406080

100

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Spline (998Mhz)

Kriging resultsMeasurement results

10203040506070

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Kriging (998Mhz)

itm resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itm (998Mhz)

itmf resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itmf (998Mhz)

Figure 2 Estimation result of level values of 998 MHz (14 training data)

shows that our methods are very competitive While in the14 data for training a sampling point covers about 12 squarekilometers From the results in Table 4 the methods basedon Kriging system have better prediction and estimationeffects In particular the prediction errors of Kriging basedmethods are all about 4Db indicating the effectiveness ofthese methods Compared with the 12 training data theincrease of maximum error is more obvious The secondexperiment showed that 120574itmf still has the best predictionresults in all algorithms As could be seen from Figure 2although the IDW had obvious smoothing effect reflectingthe overall trend of the data distribution the predictionaccuracy is the lowest and the estimation errors are very largein the ranges of 40ndash60 and 160ndash180 The prediction of Splinehas two obvious outlier points which indicated that thealgorithm is sensitive to noise data Compared with Krigingbased methods our methods yield significant improvementsin the range of 140ndash180

Table 5 Estimation results of max level values for 87ndash108MHz (12training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 122333 33063 43205 06093 02982Spline 123468 29376 38746 04900 02398Kriging 118977 26554 34731 03937 01927120574itm 108254 25374 32675 03485 01706120574itmf 108099 25368 32658 03481 01704

(2) 87ndash108MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 87ndash108MHz One-half of the data (128sampling points in total) was used for training the modeland the remaining was used for testing and verification The5 evaluation results of the five kinds of algorithms are shownin Table 5

8 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

455055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

itmf (87ndash108Mhz)

itm (87ndash108Mhz)Kriging (87ndash108Mhz)

Spline (87ndash108Mhz)IDW (87ndash108Mhz)

Figure 3 Estimation results of max level values of 87ndash108MHz (14 training data)

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 6

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 3

Themaximum signal strength in the frequency band is animportant parameter of the radio environment map In thelarge scale space many signal sources constitute the spatialdistribution of the maximum signal strength so it is difficultto make estimation by using the radio propagation model

Table 6 Estimation results of max level values for 87ndash108MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 163241 33529 44390 06374 03152Spline 248394 31712 43034 05990 02962Kriging 126690 27459 34564 03864 01911120574itm 102437 26877 34220 03788 01873120574itmf 112699 26453 33709 03675 01817

The spatial interpolation method is more advantageous Theexperimental results of 12 training data are shown in Table 5

Wireless Communications and Mobile Computing 9

Table 7 Estimation results of max level values for 1800ndash1900MHz(12 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 224790 56729 75337 06532 13643Spline 187473 49472 66059 05022 10489Kriging 172293 47758 63212 04598 09605120574itm 182057 46203 61744 04387 09164120574itmf 183114 46199 61344 04331 09046

Table 8 Estimation results of max level values for 1800ndash1900MHz(14 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 282658 59683 79227 07184 15180Spline 301425 67523 90084 09287 19626Kriging 288990 62277 82594 07807 16498120574itm 241963 55533 72744 06056 12797120574itmf 239539 54968 72053 05942 12555

As could be seen from the table all themethods have got goodresults Surprisingly compared to the radiation estimationof single source in experiments (1) the estimation of themaximum signal strength had a better accuracy which wasabout 10Db Furthermore for the average prediction errorthe results of our methods are close to 26Db Similarlyfor all the evaluation indexes the proposed method 120574itmfachieves the best results and our method increases about10 compared to the Kriging For the estimation of themaximum signal strength in frequency band the predictionaccuracy is not significantly reduced with the training datareduction (seen from Table 6) For the maximum error the120574itm algorithm gets the best result and the 120574itmf algorithmachieves the best result on the rest of indexes The Splineand IDW have a large maximum error As could be seenfrom Figure 3 the Spline exhibits a significant error whichis consistent with the previous conclusion that the methodhas a weak ability to overcome noise The proposed methodshave the best prediction and estimation effect

(3) 1800ndash1900MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 1800ndash1900MHz One-half of the data (128sampling points in total) is used for training the modeland the remaining is used for testing and verification The 5evaluation results of the five kinds of algorithms are shown inTable 7

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 8

Same as the above all the five kinds of algorithms use thesame 14 training data and the remaining data as the samemeasured data The comparisons of various algorithms areshown in Figure 4

Themain services in the 1800ndash1900MHz band aremobilecommunications of which band has more complex electro-magnetic environment and the estimation of the parameters

Table 9 Estimation results of level values for 1017MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266984 34255 44763 06184 03720Spline 155874 30751 39084 04715 02836Kriging 121004 27197 33944 03556 02139120574itm 128846 25712 32100 03180 01913120574itmf 135290 25613 31978 03156 01899

Table 10 Estimation results of level values for 1017MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266254 33326 44070 06072 03603Spline 231643 36385 49289 07596 04507Kriging 110104 28034 35230 03881 02303120574itm 115091 27089 33900 03593 02132120574itmf 134562 26326 32835 03371 02000

of this band is more difficult The experimental results of12 training data are shown in Table 7 As could be seenfrom the table all the methods have good results Themethod Kriging has the best performance for MAX ERRindex For the remaining evaluation indexes our method120574itmf obtained the best results In general the results of thethree methods of Kriging 120574itm and 120574itmf are relatively closeand the improved methods based on propagation modelare superior to the traditional Kriging method When thetraining set is reduced by half the performance of allmethodsis significantly reduced (seen from Table 8) Among themthe predication performance of the Kriging based methodsis reduced by nearly 20 This is because the power of themobile communication station is small and the transmissiondistance is close which causes the correlation between thesparse sampling points to be weak However in this case ourapproach is significantly better than the traditional Krigingbased approach with all the indicators increasing by nearly15 It is worth mentioning that the IDW algorithm alsoobtains good results indicating that the algorithm has goodstability As could be seen from Figure 4 the data set isdifficult to predict and in some individual positions allmethods have large errors But the proposed methods havethe best prediction and estimation effect especially in thevicinity of the test point numbered 140 and the proposedmethods are significantly better than the results of theKrigingmethod

(4) 1017MHz Simulation Data This was a comparativetesting on the actual acquisition level data of frequency1017MHz One-half of the data (512 sampling points in total)is used for training the model and the remaining is used fortesting and verification The 5 evaluation results of the fivekinds of algorithm are shown in Table 9

A quarter of the data (256 samples in total) is used to trainthe model and the remaining (768 testing points) is used fortesting and validation The results are shown in Table 10

10 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

itmf (1800ndash1900 Mhz)

itm (1800ndash1900 Mhz)Kriging (1800ndash1900 Mhz)

IDW (1800ndash1900 Mhz) Spline (1800ndash1900 Mhz)

0

10

20

30

40

50

60Le

vels

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

010203040506070

Leve

ls

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Figure 4 Estimation results of max level values of 1800ndash1900MHz (14 training data)

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 5

We use 12 the simulation data for training model in ourexperiment and each sampling point covers about 05 squarekilometers As can be seen from Table 9 the IDW has avery highmaximumprediction error and theKriging obtainsthe best maximum error evaluation while for the rest of theevaluation indexes the 120574itmf is about 10 higher than the

Kriging and about 20 higher than Spline and IDW As canbe seen from Table 10 the Kriging yields the best maximumerror valuation while for the rest of the evaluation indexesthe 120574itmf method obtains the best results In 14 training datasituation the predictive performance of Spline declines moreseverely As can be seen from Figure 5 IDW has a significantprediction error while methods based on Kriging systemhave better prediction accuracy In all compared methodsthe proposed methods based on propagation model haveachieved the highest accuracy Because of the introductionof the shadow model it is difficult to have a high prediction

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Wireless Communications and Mobile Computing

Figure 1 Data sampling position distribution map

(3) RMSPE

RMSPE = radic 1119899119899sum119894=1

(1198851015840119894 minus 119885119894)2 (19)

42 Experimental Data Two sets of data are used to validateall thesemethods One is realmeasured level data of FM radioFM 998MHz and the max level data of bands 87ndash108MHzand 1800ndash1900MHz The measuring terminal is a vehicleradio monitoring receiver and the measurement location islocated in Chengdu The distribution of the sampling pointswas shown in Figure 1 and the specific parameters for realmeasured data were shown in Table 1 Another is radiosignal simulation data which using the free space propagationmodel and the shadow model is a log normal model Thespecific parameters for simulation datawere shown inTable 2

The real data set contains a total of 256 sampling pointsand the simulation data set contains 1024 level datawith rangeof 100 square kilometers In order to compare and analyzethe estimation results of different algorithms at differentsampling granularities we used 12 and 14 of the total dataas the training data and the remaining data as the validationdata That is when we used 14 data as the training data theremaining 34 data was the validation test data

43 Analysis of Experiment Results

(1) 998MHz Real Sampling Data This is the comparativetesting on the actual acquisition level data of frequency998MHz One-half of the data (128 sampling points in total)is used for training the model and the remaining 12 of thedata is used for testing and verification The 5 evaluationresults of the five kinds of algorithms are shown in Table 3

Table 1 Parameters for real measured data

Measurement area 28Km lowast 28KmRadio type FM radio bandBroadcast 998MHz 87ndash108MHzNumber of sources 1 or119873The average vehicle speed About 80Kmh

Table 2 Parameters for simulation data

Calculated area 10Km lowast 10KmNumbers of points 1024Carrier frequency 1017MHzPath loss model Free space modelShadow model Log normal model

Table 3 Estimation results of level values for 998MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 196973 63338 79729 05122 20172Spline 212641 42668 5583 02512 09893Kriging 127859 36714 45996 01705 06714120574itm 126277 36488 45090 01638 06452120574itmf 125643 35610 44359 01586 06244

Table 4 Estimation result of level values for 998Mhz (14 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 262765 63642 81205 05381 20736Spline 578689 49106 77875 04949 19070Kriging 160234 40510 51165 02136 08232120574itm 167655 40749 50926 02116 08155120574itmf 158968 39979 50414 02070 08040

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 4

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms were shown in Figure 2

In the 12 data for training there are 128 sampling pointsin the range of about 784 square kilometers A sampling pointcovers an average of about 6 square kilometers As couldbe seen from Table 3 the results of the prediction of ourtwo methods and the Kriging method are relatively closeand the worst method is the IDW For Spline and IDW theformer is significantly better than the latter on all indexesexcept the maximum errorThe 120574itmf method of our methodshas achieved the best results on all the evaluation indexesCompared with other methods our methods have obviousadvantages both in prediction accuracy and in predictionstability The best average estimation error of our algorithmswas 3561Db According to the research results of [6] it

Wireless Communications and Mobile Computing 7

IDW resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

lsIDW (998Mhz)

Spline resultsMeasurement results

minus200

20406080

100

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Spline (998Mhz)

Kriging resultsMeasurement results

10203040506070

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Kriging (998Mhz)

itm resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itm (998Mhz)

itmf resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itmf (998Mhz)

Figure 2 Estimation result of level values of 998 MHz (14 training data)

shows that our methods are very competitive While in the14 data for training a sampling point covers about 12 squarekilometers From the results in Table 4 the methods basedon Kriging system have better prediction and estimationeffects In particular the prediction errors of Kriging basedmethods are all about 4Db indicating the effectiveness ofthese methods Compared with the 12 training data theincrease of maximum error is more obvious The secondexperiment showed that 120574itmf still has the best predictionresults in all algorithms As could be seen from Figure 2although the IDW had obvious smoothing effect reflectingthe overall trend of the data distribution the predictionaccuracy is the lowest and the estimation errors are very largein the ranges of 40ndash60 and 160ndash180 The prediction of Splinehas two obvious outlier points which indicated that thealgorithm is sensitive to noise data Compared with Krigingbased methods our methods yield significant improvementsin the range of 140ndash180

Table 5 Estimation results of max level values for 87ndash108MHz (12training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 122333 33063 43205 06093 02982Spline 123468 29376 38746 04900 02398Kriging 118977 26554 34731 03937 01927120574itm 108254 25374 32675 03485 01706120574itmf 108099 25368 32658 03481 01704

(2) 87ndash108MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 87ndash108MHz One-half of the data (128sampling points in total) was used for training the modeland the remaining was used for testing and verification The5 evaluation results of the five kinds of algorithms are shownin Table 5

8 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

455055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

itmf (87ndash108Mhz)

itm (87ndash108Mhz)Kriging (87ndash108Mhz)

Spline (87ndash108Mhz)IDW (87ndash108Mhz)

Figure 3 Estimation results of max level values of 87ndash108MHz (14 training data)

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 6

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 3

Themaximum signal strength in the frequency band is animportant parameter of the radio environment map In thelarge scale space many signal sources constitute the spatialdistribution of the maximum signal strength so it is difficultto make estimation by using the radio propagation model

Table 6 Estimation results of max level values for 87ndash108MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 163241 33529 44390 06374 03152Spline 248394 31712 43034 05990 02962Kriging 126690 27459 34564 03864 01911120574itm 102437 26877 34220 03788 01873120574itmf 112699 26453 33709 03675 01817

The spatial interpolation method is more advantageous Theexperimental results of 12 training data are shown in Table 5

Wireless Communications and Mobile Computing 9

Table 7 Estimation results of max level values for 1800ndash1900MHz(12 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 224790 56729 75337 06532 13643Spline 187473 49472 66059 05022 10489Kriging 172293 47758 63212 04598 09605120574itm 182057 46203 61744 04387 09164120574itmf 183114 46199 61344 04331 09046

Table 8 Estimation results of max level values for 1800ndash1900MHz(14 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 282658 59683 79227 07184 15180Spline 301425 67523 90084 09287 19626Kriging 288990 62277 82594 07807 16498120574itm 241963 55533 72744 06056 12797120574itmf 239539 54968 72053 05942 12555

As could be seen from the table all themethods have got goodresults Surprisingly compared to the radiation estimationof single source in experiments (1) the estimation of themaximum signal strength had a better accuracy which wasabout 10Db Furthermore for the average prediction errorthe results of our methods are close to 26Db Similarlyfor all the evaluation indexes the proposed method 120574itmfachieves the best results and our method increases about10 compared to the Kriging For the estimation of themaximum signal strength in frequency band the predictionaccuracy is not significantly reduced with the training datareduction (seen from Table 6) For the maximum error the120574itm algorithm gets the best result and the 120574itmf algorithmachieves the best result on the rest of indexes The Splineand IDW have a large maximum error As could be seenfrom Figure 3 the Spline exhibits a significant error whichis consistent with the previous conclusion that the methodhas a weak ability to overcome noise The proposed methodshave the best prediction and estimation effect

(3) 1800ndash1900MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 1800ndash1900MHz One-half of the data (128sampling points in total) is used for training the modeland the remaining is used for testing and verification The 5evaluation results of the five kinds of algorithms are shown inTable 7

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 8

Same as the above all the five kinds of algorithms use thesame 14 training data and the remaining data as the samemeasured data The comparisons of various algorithms areshown in Figure 4

Themain services in the 1800ndash1900MHz band aremobilecommunications of which band has more complex electro-magnetic environment and the estimation of the parameters

Table 9 Estimation results of level values for 1017MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266984 34255 44763 06184 03720Spline 155874 30751 39084 04715 02836Kriging 121004 27197 33944 03556 02139120574itm 128846 25712 32100 03180 01913120574itmf 135290 25613 31978 03156 01899

Table 10 Estimation results of level values for 1017MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266254 33326 44070 06072 03603Spline 231643 36385 49289 07596 04507Kriging 110104 28034 35230 03881 02303120574itm 115091 27089 33900 03593 02132120574itmf 134562 26326 32835 03371 02000

of this band is more difficult The experimental results of12 training data are shown in Table 7 As could be seenfrom the table all the methods have good results Themethod Kriging has the best performance for MAX ERRindex For the remaining evaluation indexes our method120574itmf obtained the best results In general the results of thethree methods of Kriging 120574itm and 120574itmf are relatively closeand the improved methods based on propagation modelare superior to the traditional Kriging method When thetraining set is reduced by half the performance of allmethodsis significantly reduced (seen from Table 8) Among themthe predication performance of the Kriging based methodsis reduced by nearly 20 This is because the power of themobile communication station is small and the transmissiondistance is close which causes the correlation between thesparse sampling points to be weak However in this case ourapproach is significantly better than the traditional Krigingbased approach with all the indicators increasing by nearly15 It is worth mentioning that the IDW algorithm alsoobtains good results indicating that the algorithm has goodstability As could be seen from Figure 4 the data set isdifficult to predict and in some individual positions allmethods have large errors But the proposed methods havethe best prediction and estimation effect especially in thevicinity of the test point numbered 140 and the proposedmethods are significantly better than the results of theKrigingmethod

(4) 1017MHz Simulation Data This was a comparativetesting on the actual acquisition level data of frequency1017MHz One-half of the data (512 sampling points in total)is used for training the model and the remaining is used fortesting and verification The 5 evaluation results of the fivekinds of algorithm are shown in Table 9

A quarter of the data (256 samples in total) is used to trainthe model and the remaining (768 testing points) is used fortesting and validation The results are shown in Table 10

10 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

itmf (1800ndash1900 Mhz)

itm (1800ndash1900 Mhz)Kriging (1800ndash1900 Mhz)

IDW (1800ndash1900 Mhz) Spline (1800ndash1900 Mhz)

0

10

20

30

40

50

60Le

vels

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

010203040506070

Leve

ls

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Figure 4 Estimation results of max level values of 1800ndash1900MHz (14 training data)

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 5

We use 12 the simulation data for training model in ourexperiment and each sampling point covers about 05 squarekilometers As can be seen from Table 9 the IDW has avery highmaximumprediction error and theKriging obtainsthe best maximum error evaluation while for the rest of theevaluation indexes the 120574itmf is about 10 higher than the

Kriging and about 20 higher than Spline and IDW As canbe seen from Table 10 the Kriging yields the best maximumerror valuation while for the rest of the evaluation indexesthe 120574itmf method obtains the best results In 14 training datasituation the predictive performance of Spline declines moreseverely As can be seen from Figure 5 IDW has a significantprediction error while methods based on Kriging systemhave better prediction accuracy In all compared methodsthe proposed methods based on propagation model haveachieved the highest accuracy Because of the introductionof the shadow model it is difficult to have a high prediction

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Wireless Communications and Mobile Computing 7

IDW resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

lsIDW (998Mhz)

Spline resultsMeasurement results

minus200

20406080

100

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Spline (998Mhz)

Kriging resultsMeasurement results

10203040506070

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Kriging (998Mhz)

itm resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itm (998Mhz)

itmf resultsMeasurement results

20 40 60 80 100 120 140 160 180 2000Test points

10203040506070

Leve

ls

itmf (998Mhz)

Figure 2 Estimation result of level values of 998 MHz (14 training data)

shows that our methods are very competitive While in the14 data for training a sampling point covers about 12 squarekilometers From the results in Table 4 the methods basedon Kriging system have better prediction and estimationeffects In particular the prediction errors of Kriging basedmethods are all about 4Db indicating the effectiveness ofthese methods Compared with the 12 training data theincrease of maximum error is more obvious The secondexperiment showed that 120574itmf still has the best predictionresults in all algorithms As could be seen from Figure 2although the IDW had obvious smoothing effect reflectingthe overall trend of the data distribution the predictionaccuracy is the lowest and the estimation errors are very largein the ranges of 40ndash60 and 160ndash180 The prediction of Splinehas two obvious outlier points which indicated that thealgorithm is sensitive to noise data Compared with Krigingbased methods our methods yield significant improvementsin the range of 140ndash180

Table 5 Estimation results of max level values for 87ndash108MHz (12training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 122333 33063 43205 06093 02982Spline 123468 29376 38746 04900 02398Kriging 118977 26554 34731 03937 01927120574itm 108254 25374 32675 03485 01706120574itmf 108099 25368 32658 03481 01704

(2) 87ndash108MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 87ndash108MHz One-half of the data (128sampling points in total) was used for training the modeland the remaining was used for testing and verification The5 evaluation results of the five kinds of algorithms are shownin Table 5

8 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

455055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

itmf (87ndash108Mhz)

itm (87ndash108Mhz)Kriging (87ndash108Mhz)

Spline (87ndash108Mhz)IDW (87ndash108Mhz)

Figure 3 Estimation results of max level values of 87ndash108MHz (14 training data)

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 6

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 3

Themaximum signal strength in the frequency band is animportant parameter of the radio environment map In thelarge scale space many signal sources constitute the spatialdistribution of the maximum signal strength so it is difficultto make estimation by using the radio propagation model

Table 6 Estimation results of max level values for 87ndash108MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 163241 33529 44390 06374 03152Spline 248394 31712 43034 05990 02962Kriging 126690 27459 34564 03864 01911120574itm 102437 26877 34220 03788 01873120574itmf 112699 26453 33709 03675 01817

The spatial interpolation method is more advantageous Theexperimental results of 12 training data are shown in Table 5

Wireless Communications and Mobile Computing 9

Table 7 Estimation results of max level values for 1800ndash1900MHz(12 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 224790 56729 75337 06532 13643Spline 187473 49472 66059 05022 10489Kriging 172293 47758 63212 04598 09605120574itm 182057 46203 61744 04387 09164120574itmf 183114 46199 61344 04331 09046

Table 8 Estimation results of max level values for 1800ndash1900MHz(14 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 282658 59683 79227 07184 15180Spline 301425 67523 90084 09287 19626Kriging 288990 62277 82594 07807 16498120574itm 241963 55533 72744 06056 12797120574itmf 239539 54968 72053 05942 12555

As could be seen from the table all themethods have got goodresults Surprisingly compared to the radiation estimationof single source in experiments (1) the estimation of themaximum signal strength had a better accuracy which wasabout 10Db Furthermore for the average prediction errorthe results of our methods are close to 26Db Similarlyfor all the evaluation indexes the proposed method 120574itmfachieves the best results and our method increases about10 compared to the Kriging For the estimation of themaximum signal strength in frequency band the predictionaccuracy is not significantly reduced with the training datareduction (seen from Table 6) For the maximum error the120574itm algorithm gets the best result and the 120574itmf algorithmachieves the best result on the rest of indexes The Splineand IDW have a large maximum error As could be seenfrom Figure 3 the Spline exhibits a significant error whichis consistent with the previous conclusion that the methodhas a weak ability to overcome noise The proposed methodshave the best prediction and estimation effect

(3) 1800ndash1900MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 1800ndash1900MHz One-half of the data (128sampling points in total) is used for training the modeland the remaining is used for testing and verification The 5evaluation results of the five kinds of algorithms are shown inTable 7

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 8

Same as the above all the five kinds of algorithms use thesame 14 training data and the remaining data as the samemeasured data The comparisons of various algorithms areshown in Figure 4

Themain services in the 1800ndash1900MHz band aremobilecommunications of which band has more complex electro-magnetic environment and the estimation of the parameters

Table 9 Estimation results of level values for 1017MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266984 34255 44763 06184 03720Spline 155874 30751 39084 04715 02836Kriging 121004 27197 33944 03556 02139120574itm 128846 25712 32100 03180 01913120574itmf 135290 25613 31978 03156 01899

Table 10 Estimation results of level values for 1017MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266254 33326 44070 06072 03603Spline 231643 36385 49289 07596 04507Kriging 110104 28034 35230 03881 02303120574itm 115091 27089 33900 03593 02132120574itmf 134562 26326 32835 03371 02000

of this band is more difficult The experimental results of12 training data are shown in Table 7 As could be seenfrom the table all the methods have good results Themethod Kriging has the best performance for MAX ERRindex For the remaining evaluation indexes our method120574itmf obtained the best results In general the results of thethree methods of Kriging 120574itm and 120574itmf are relatively closeand the improved methods based on propagation modelare superior to the traditional Kriging method When thetraining set is reduced by half the performance of allmethodsis significantly reduced (seen from Table 8) Among themthe predication performance of the Kriging based methodsis reduced by nearly 20 This is because the power of themobile communication station is small and the transmissiondistance is close which causes the correlation between thesparse sampling points to be weak However in this case ourapproach is significantly better than the traditional Krigingbased approach with all the indicators increasing by nearly15 It is worth mentioning that the IDW algorithm alsoobtains good results indicating that the algorithm has goodstability As could be seen from Figure 4 the data set isdifficult to predict and in some individual positions allmethods have large errors But the proposed methods havethe best prediction and estimation effect especially in thevicinity of the test point numbered 140 and the proposedmethods are significantly better than the results of theKrigingmethod

(4) 1017MHz Simulation Data This was a comparativetesting on the actual acquisition level data of frequency1017MHz One-half of the data (512 sampling points in total)is used for training the model and the remaining is used fortesting and verification The 5 evaluation results of the fivekinds of algorithm are shown in Table 9

A quarter of the data (256 samples in total) is used to trainthe model and the remaining (768 testing points) is used fortesting and validation The results are shown in Table 10

10 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

itmf (1800ndash1900 Mhz)

itm (1800ndash1900 Mhz)Kriging (1800ndash1900 Mhz)

IDW (1800ndash1900 Mhz) Spline (1800ndash1900 Mhz)

0

10

20

30

40

50

60Le

vels

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

010203040506070

Leve

ls

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Figure 4 Estimation results of max level values of 1800ndash1900MHz (14 training data)

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 5

We use 12 the simulation data for training model in ourexperiment and each sampling point covers about 05 squarekilometers As can be seen from Table 9 the IDW has avery highmaximumprediction error and theKriging obtainsthe best maximum error evaluation while for the rest of theevaluation indexes the 120574itmf is about 10 higher than the

Kriging and about 20 higher than Spline and IDW As canbe seen from Table 10 the Kriging yields the best maximumerror valuation while for the rest of the evaluation indexesthe 120574itmf method obtains the best results In 14 training datasituation the predictive performance of Spline declines moreseverely As can be seen from Figure 5 IDW has a significantprediction error while methods based on Kriging systemhave better prediction accuracy In all compared methodsthe proposed methods based on propagation model haveachieved the highest accuracy Because of the introductionof the shadow model it is difficult to have a high prediction

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

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International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

8 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

5055606570758085

Leve

ls

455055606570758085

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

itmf (87ndash108Mhz)

itm (87ndash108Mhz)Kriging (87ndash108Mhz)

Spline (87ndash108Mhz)IDW (87ndash108Mhz)

Figure 3 Estimation results of max level values of 87ndash108MHz (14 training data)

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 6

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 3

Themaximum signal strength in the frequency band is animportant parameter of the radio environment map In thelarge scale space many signal sources constitute the spatialdistribution of the maximum signal strength so it is difficultto make estimation by using the radio propagation model

Table 6 Estimation results of max level values for 87ndash108MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 163241 33529 44390 06374 03152Spline 248394 31712 43034 05990 02962Kriging 126690 27459 34564 03864 01911120574itm 102437 26877 34220 03788 01873120574itmf 112699 26453 33709 03675 01817

The spatial interpolation method is more advantageous Theexperimental results of 12 training data are shown in Table 5

Wireless Communications and Mobile Computing 9

Table 7 Estimation results of max level values for 1800ndash1900MHz(12 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 224790 56729 75337 06532 13643Spline 187473 49472 66059 05022 10489Kriging 172293 47758 63212 04598 09605120574itm 182057 46203 61744 04387 09164120574itmf 183114 46199 61344 04331 09046

Table 8 Estimation results of max level values for 1800ndash1900MHz(14 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 282658 59683 79227 07184 15180Spline 301425 67523 90084 09287 19626Kriging 288990 62277 82594 07807 16498120574itm 241963 55533 72744 06056 12797120574itmf 239539 54968 72053 05942 12555

As could be seen from the table all themethods have got goodresults Surprisingly compared to the radiation estimationof single source in experiments (1) the estimation of themaximum signal strength had a better accuracy which wasabout 10Db Furthermore for the average prediction errorthe results of our methods are close to 26Db Similarlyfor all the evaluation indexes the proposed method 120574itmfachieves the best results and our method increases about10 compared to the Kriging For the estimation of themaximum signal strength in frequency band the predictionaccuracy is not significantly reduced with the training datareduction (seen from Table 6) For the maximum error the120574itm algorithm gets the best result and the 120574itmf algorithmachieves the best result on the rest of indexes The Splineand IDW have a large maximum error As could be seenfrom Figure 3 the Spline exhibits a significant error whichis consistent with the previous conclusion that the methodhas a weak ability to overcome noise The proposed methodshave the best prediction and estimation effect

(3) 1800ndash1900MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 1800ndash1900MHz One-half of the data (128sampling points in total) is used for training the modeland the remaining is used for testing and verification The 5evaluation results of the five kinds of algorithms are shown inTable 7

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 8

Same as the above all the five kinds of algorithms use thesame 14 training data and the remaining data as the samemeasured data The comparisons of various algorithms areshown in Figure 4

Themain services in the 1800ndash1900MHz band aremobilecommunications of which band has more complex electro-magnetic environment and the estimation of the parameters

Table 9 Estimation results of level values for 1017MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266984 34255 44763 06184 03720Spline 155874 30751 39084 04715 02836Kriging 121004 27197 33944 03556 02139120574itm 128846 25712 32100 03180 01913120574itmf 135290 25613 31978 03156 01899

Table 10 Estimation results of level values for 1017MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266254 33326 44070 06072 03603Spline 231643 36385 49289 07596 04507Kriging 110104 28034 35230 03881 02303120574itm 115091 27089 33900 03593 02132120574itmf 134562 26326 32835 03371 02000

of this band is more difficult The experimental results of12 training data are shown in Table 7 As could be seenfrom the table all the methods have good results Themethod Kriging has the best performance for MAX ERRindex For the remaining evaluation indexes our method120574itmf obtained the best results In general the results of thethree methods of Kriging 120574itm and 120574itmf are relatively closeand the improved methods based on propagation modelare superior to the traditional Kriging method When thetraining set is reduced by half the performance of allmethodsis significantly reduced (seen from Table 8) Among themthe predication performance of the Kriging based methodsis reduced by nearly 20 This is because the power of themobile communication station is small and the transmissiondistance is close which causes the correlation between thesparse sampling points to be weak However in this case ourapproach is significantly better than the traditional Krigingbased approach with all the indicators increasing by nearly15 It is worth mentioning that the IDW algorithm alsoobtains good results indicating that the algorithm has goodstability As could be seen from Figure 4 the data set isdifficult to predict and in some individual positions allmethods have large errors But the proposed methods havethe best prediction and estimation effect especially in thevicinity of the test point numbered 140 and the proposedmethods are significantly better than the results of theKrigingmethod

(4) 1017MHz Simulation Data This was a comparativetesting on the actual acquisition level data of frequency1017MHz One-half of the data (512 sampling points in total)is used for training the model and the remaining is used fortesting and verification The 5 evaluation results of the fivekinds of algorithm are shown in Table 9

A quarter of the data (256 samples in total) is used to trainthe model and the remaining (768 testing points) is used fortesting and validation The results are shown in Table 10

10 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

itmf (1800ndash1900 Mhz)

itm (1800ndash1900 Mhz)Kriging (1800ndash1900 Mhz)

IDW (1800ndash1900 Mhz) Spline (1800ndash1900 Mhz)

0

10

20

30

40

50

60Le

vels

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

010203040506070

Leve

ls

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Figure 4 Estimation results of max level values of 1800ndash1900MHz (14 training data)

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 5

We use 12 the simulation data for training model in ourexperiment and each sampling point covers about 05 squarekilometers As can be seen from Table 9 the IDW has avery highmaximumprediction error and theKriging obtainsthe best maximum error evaluation while for the rest of theevaluation indexes the 120574itmf is about 10 higher than the

Kriging and about 20 higher than Spline and IDW As canbe seen from Table 10 the Kriging yields the best maximumerror valuation while for the rest of the evaluation indexesthe 120574itmf method obtains the best results In 14 training datasituation the predictive performance of Spline declines moreseverely As can be seen from Figure 5 IDW has a significantprediction error while methods based on Kriging systemhave better prediction accuracy In all compared methodsthe proposed methods based on propagation model haveachieved the highest accuracy Because of the introductionof the shadow model it is difficult to have a high prediction

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Wireless Communications and Mobile Computing 9

Table 7 Estimation results of max level values for 1800ndash1900MHz(12 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 224790 56729 75337 06532 13643Spline 187473 49472 66059 05022 10489Kriging 172293 47758 63212 04598 09605120574itm 182057 46203 61744 04387 09164120574itmf 183114 46199 61344 04331 09046

Table 8 Estimation results of max level values for 1800ndash1900MHz(14 training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 282658 59683 79227 07184 15180Spline 301425 67523 90084 09287 19626Kriging 288990 62277 82594 07807 16498120574itm 241963 55533 72744 06056 12797120574itmf 239539 54968 72053 05942 12555

As could be seen from the table all themethods have got goodresults Surprisingly compared to the radiation estimationof single source in experiments (1) the estimation of themaximum signal strength had a better accuracy which wasabout 10Db Furthermore for the average prediction errorthe results of our methods are close to 26Db Similarlyfor all the evaluation indexes the proposed method 120574itmfachieves the best results and our method increases about10 compared to the Kriging For the estimation of themaximum signal strength in frequency band the predictionaccuracy is not significantly reduced with the training datareduction (seen from Table 6) For the maximum error the120574itm algorithm gets the best result and the 120574itmf algorithmachieves the best result on the rest of indexes The Splineand IDW have a large maximum error As could be seenfrom Figure 3 the Spline exhibits a significant error whichis consistent with the previous conclusion that the methodhas a weak ability to overcome noise The proposed methodshave the best prediction and estimation effect

(3) 1800ndash1900MHz Maximum Level of Real Sampling DataThis is a comparative testing on the actual acquisition maxlevel data of band 1800ndash1900MHz One-half of the data (128sampling points in total) is used for training the modeland the remaining is used for testing and verification The 5evaluation results of the five kinds of algorithms are shown inTable 7

A quarter of the data (64 samples in total) is used to trainthe model and the remaining 34 of the data is used for testvalidation The results are shown in Table 8

Same as the above all the five kinds of algorithms use thesame 14 training data and the remaining data as the samemeasured data The comparisons of various algorithms areshown in Figure 4

Themain services in the 1800ndash1900MHz band aremobilecommunications of which band has more complex electro-magnetic environment and the estimation of the parameters

Table 9 Estimation results of level values for 1017MHz (12 trainingdata)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266984 34255 44763 06184 03720Spline 155874 30751 39084 04715 02836Kriging 121004 27197 33944 03556 02139120574itm 128846 25712 32100 03180 01913120574itmf 135290 25613 31978 03156 01899

Table 10 Estimation results of level values for 1017MHz (14training data)

MAX ERR AVE ERR RMSPE RMSE PAEEIDW 266254 33326 44070 06072 03603Spline 231643 36385 49289 07596 04507Kriging 110104 28034 35230 03881 02303120574itm 115091 27089 33900 03593 02132120574itmf 134562 26326 32835 03371 02000

of this band is more difficult The experimental results of12 training data are shown in Table 7 As could be seenfrom the table all the methods have good results Themethod Kriging has the best performance for MAX ERRindex For the remaining evaluation indexes our method120574itmf obtained the best results In general the results of thethree methods of Kriging 120574itm and 120574itmf are relatively closeand the improved methods based on propagation modelare superior to the traditional Kriging method When thetraining set is reduced by half the performance of allmethodsis significantly reduced (seen from Table 8) Among themthe predication performance of the Kriging based methodsis reduced by nearly 20 This is because the power of themobile communication station is small and the transmissiondistance is close which causes the correlation between thesparse sampling points to be weak However in this case ourapproach is significantly better than the traditional Krigingbased approach with all the indicators increasing by nearly15 It is worth mentioning that the IDW algorithm alsoobtains good results indicating that the algorithm has goodstability As could be seen from Figure 4 the data set isdifficult to predict and in some individual positions allmethods have large errors But the proposed methods havethe best prediction and estimation effect especially in thevicinity of the test point numbered 140 and the proposedmethods are significantly better than the results of theKrigingmethod

(4) 1017MHz Simulation Data This was a comparativetesting on the actual acquisition level data of frequency1017MHz One-half of the data (512 sampling points in total)is used for training the model and the remaining is used fortesting and verification The 5 evaluation results of the fivekinds of algorithm are shown in Table 9

A quarter of the data (256 samples in total) is used to trainthe model and the remaining (768 testing points) is used fortesting and validation The results are shown in Table 10

10 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

itmf (1800ndash1900 Mhz)

itm (1800ndash1900 Mhz)Kriging (1800ndash1900 Mhz)

IDW (1800ndash1900 Mhz) Spline (1800ndash1900 Mhz)

0

10

20

30

40

50

60Le

vels

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

010203040506070

Leve

ls

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Figure 4 Estimation results of max level values of 1800ndash1900MHz (14 training data)

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 5

We use 12 the simulation data for training model in ourexperiment and each sampling point covers about 05 squarekilometers As can be seen from Table 9 the IDW has avery highmaximumprediction error and theKriging obtainsthe best maximum error evaluation while for the rest of theevaluation indexes the 120574itmf is about 10 higher than the

Kriging and about 20 higher than Spline and IDW As canbe seen from Table 10 the Kriging yields the best maximumerror valuation while for the rest of the evaluation indexesthe 120574itmf method obtains the best results In 14 training datasituation the predictive performance of Spline declines moreseverely As can be seen from Figure 5 IDW has a significantprediction error while methods based on Kriging systemhave better prediction accuracy In all compared methodsthe proposed methods based on propagation model haveachieved the highest accuracy Because of the introductionof the shadow model it is difficult to have a high prediction

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Wireless Communications and Mobile Computing

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

itmf (1800ndash1900 Mhz)

itm (1800ndash1900 Mhz)Kriging (1800ndash1900 Mhz)

IDW (1800ndash1900 Mhz) Spline (1800ndash1900 Mhz)

0

10

20

30

40

50

60Le

vels

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

20 40 60 80 100 120 140 160 180 2000Test points

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

010203040506070

Leve

ls

0

10

20

30

40

50

60

Leve

ls

20 40 60 80 100 120 140 160 180 2000Test points

Figure 4 Estimation results of max level values of 1800ndash1900MHz (14 training data)

In order to reflect the estimation results of variousalgorithms directly all the five kinds of algorithms use thesame 14 training data the results of which are comparedwith the same measured data The comparisons of variousalgorithms are shown in Figure 5

We use 12 the simulation data for training model in ourexperiment and each sampling point covers about 05 squarekilometers As can be seen from Table 9 the IDW has avery highmaximumprediction error and theKriging obtainsthe best maximum error evaluation while for the rest of theevaluation indexes the 120574itmf is about 10 higher than the

Kriging and about 20 higher than Spline and IDW As canbe seen from Table 10 the Kriging yields the best maximumerror valuation while for the rest of the evaluation indexesthe 120574itmf method obtains the best results In 14 training datasituation the predictive performance of Spline declines moreseverely As can be seen from Figure 5 IDW has a significantprediction error while methods based on Kriging systemhave better prediction accuracy In all compared methodsthe proposed methods based on propagation model haveachieved the highest accuracy Because of the introductionof the shadow model it is difficult to have a high prediction

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Wireless Communications and Mobile Computing 11

IDW resultsMeasurement results

Spline resultsMeasurement results

Kriging resultsMeasurement results

itm resultsMeasurement results

itmf resultsMeasurement results

IDW (1017 Mhz) Spline (1017 Mhz)

Kriging (1017 Mhz)

itmf (1017 Mhz)

itm (1017 Mhz)

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

500200 300 400100 600 700 8000Test points

3035404550556065707580

Leve

ls

3035404550556065707580

Leve

ls

100 200 300 400 500 600 700 8000Test points

100 200 300 400 500 600 700 8000Test points

3035404550556065707580

Leve

ls

Figure 5 Estimation results of level values of 1017MHz (14 training data)

and estimation on the simulated data It can be seen that theprediction accuracy of the simulation data is equivalent tothat of the maximum signal strength of the frequency band

5 Conclusion

In this paper we proposed a spatial distribution predictionmethod for radio environment map parameters It wasshown that the IDW Spline and Kriging methods are themost effective methods to solve this problem and of theseKriging is the best method The main parameters of theradio environment map are the signal strength and otherparameters are affected by it In this study based on the

Kriging approach the definition of a variogramwas improvedbased on the loss characteristics of radio propagation A newvariogram theoretical model was proposed in combinationwith a radio propagation model Based on the characteristicsof data sampling and signal propagation a new weightedfitting method for variograms was also proposed The newmethod is more suitable for the actual characteristics ofradio environment map parameter prediction Moreover theproposed model is better adapted to the spatial correlationof radio environment parameters and has better predictionaccuracy Experiments on the signal strength data of asingle frequency and the maximum signal strength data of afrequency band and simulation data prove these conclusions

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Wireless Communications and Mobile Computing

The evaluation indexes of our method are improved by about10 on average compared with those of the conventionalKriging method

Radio signal propagation in space is a complex pro-cess There are some intractable problems such as buildingshadows same-frequency adjacent channel interference andmultipath propagationTherefore to obtain better predictionaccuracy the terrain and station information to the modelwill be taken into consideration in our future research

Conflicts of Interest

The authors declare that they have no conflicts of interest

Authorsrsquo Contributions

Zhisheng Gao proposed the original idea Yaoshun Li wrotethe paper under the guidance of Zhisheng Gao Yaoshun Liand Chunzhi Xie designed the experiment and provided allthe figures and Chunzhi Xie checked the manuscript Allauthors read and approved the final manuscript

Acknowledgments

This work has been partially supported by the Major Projectof Education Department of Sichuan (Grant no 14ZA0118)the Ministry of Education Chunhui project (Grant noZ2016149) the Xihua University Key Laboratory Develop-ment Program (Grant nos szjj2017-065 s2jj2014-050) andthe Graduate Innovation Foundation of Xihua University(ycjj2017070)

References

[1] Y Zhao L Morales J Gaeddert K K Bae J-S Um and J HReed ldquoApplying radio environment maps to cognitive wirelessregional area networksrdquo in Proceedings of the 2nd IEEE Interna-tional Symposium onNew Frontiers in Dynamic SpectrumAccessNetworks vol 1 pp 115ndash118 April 2007

[2] H Yilmaz Birkan T Tugcu F Alagoz and S Bayhan ldquoRadioenvironment map as enabler for practical cognitive radio net-worksrdquo IEEE CommunicationsMagazine vol 51 no 12 pp 162ndash169 2013

[3] S Sodagari ldquoA Secure Radio Environment Map Database toShare Spectrumrdquo IEEE Journal of Selected Topics in SignalProcessing vol 9 no 7 pp 1298ndash1305 2015

[4] N Ezzati H Taheri and T Tugcu ldquoOptimised sensor networkfor transmitter localisation and radio environment mappingrdquoIET Communications vol 10 no 16 pp 2170ndash2178 2016

[5] J Perez-Romero A Zalonis L Boukhatem et al ldquoOn the useof radio environment maps for interference management inheterogeneous networksrdquo IEEECommunicationsMagazine vol53 no 8 pp 184ndash191 2015

[6] A Galindo-Serrano B Sayrac S Ben Jemaa J Riihijarvi andP Mahonen ldquoAutomated coverage hole detection for cellularnetworks using radio environment mapsrdquo in Proceedings of the11th International Symposium and Workshops on Modeling andOptimization in Mobile Ad Hoc and Wireless Networks WiOpt2013 vol 1 pp 35ndash40 May 2013

[7] V Atanasovski J Van De Beek A Dejonghe et al ldquoConstruct-ing radio environment maps with heterogeneous spectrum

sensorsrdquo in Proceedings of the IEEE International Symposium onDynamic Spectrum Access Networks DySPAN 2011 vol 3 pp660-661 May 2011

[8] F Paisana Z Khan J Lehtomaki L A Dasilva and RVuohtoniemi ldquoExploring radio environment map architecturesfor spectrum sharing in the radar bandsrdquo in Proceedings of the23rd International Conference on Telecommunications ICT 2016vol 1 May 2016

[9] S Subramani T Farnham and M Sooriyabandara ldquoDeploy-ment and interface design considerations for radio environmentmapsrdquo in Proceedings of the IEEE 8th International Conferenceon Wireless and Mobile Computing Networking and Communi-cations WiMob 2012 vol 1 pp 480ndash487 October 2012

[10] J Ojaniemi J Kalliovaara A Alam J Poikonen and R Wich-man ldquoOptimal field measurement design for radio environ-ment mappingrdquo in Proceedings of the 47th Annual Conferenceon Information Sciences and Systems CISS 2013 March 2013

[11] M Pesko T Javornik A Kosir M Stular and M MohorcicldquoRadio environment maps The survey of construction meth-odsrdquoKSII Transactions on Internet and Information Systems vol8 no 11 pp 3789ndash3809 2014

[12] M Pesko T Javornik L Vidmar A Kosir M Stular and MMohorcic ldquoThe indirect self-tuning method for constructingradio environment map using omnidirectional or directionaltransmitter antennardquo EURASIP Journal on Wireless Communi-cations and Networking vol 2015 no 1 pp 1ndash12 2015

[13] H B Yilmaz and T T Bogazici ldquoLocation estimation-basedradio environmentmap construction in fading channelsrdquoWire-less Communications and Mobile Computing vol 15 no 3 pp561ndash570 2015

[14] S Ulaganathan D Deschrijver M Pakparvar et al ldquoBuildingaccurate radio environment maps frommulti-fidelity spectrumsensing datardquo Wireless Networks vol 22 no 8 pp 2551ndash25622016

[15] G Zou K Xue D Huang C Su and J Sun ldquoThe comparisonand study of small sample data spatial interpolation accuracyrdquoin Proceedings of the 6th International Conference on NaturalComputation ICNCrsquo10 vol 4 pp 1897ndash1900 August 2010

[16] M Azpurua and K dos Ramos ldquoA comparison of spatial inter-polation methods for estimation of average electromagneticfield magnituderdquo Progress in Electromagnetics Research M vol14 pp 135ndash145 2010

[17] M Angjelicinoski V Atanasovski and L Gavrilovska ldquoCom-parative analysis of spatial interpolation methods for creatingradio environmentmapsrdquo in Proceedings of the 19th Telecommu-nications Forum TELFOR 2011 vol 1 pp 334ndash337 November2011

[18] K Sato and T Fujii ldquoKriging-Based Interference Power Con-straint Integrated Design of the Radio Environment Map andTransmission Powerrdquo IEEE Transactions on Cognitive Commu-nications and Networking vol 3 no 1 pp 13ndash25 2017

[19] J Riihijarvi P Mahonen M Wellens and M Gordziel ldquoChar-acterization and modelling of spectrum for dynamic spectrumaccesswith spatial statistics and randomfieldsrdquo inProceedings ofthe IEEE 19th International Symposium on Personal Indoor andMobile Radio Communications PIMRC 2008 vol 1 September2008

[20] D Denkovski V Atanasovski L Gavrilovska J Riihijarvi andP Mahonen ldquoReliability of a radio environment map Caseof spatial interpolation techniquesrdquo in Proceedings of the 7thInternational ICST Conference on Cognitive Radio Oriented

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Wireless Communications and Mobile Computing 13

Wireless Networks and Communications CROWNCOM 2012vol 1 pp 248ndash253 June 2012

[21] C PhillipsM Ton D Sicker andD Grunwald ldquoPractical radioenvironment mapping with geostatisticsrdquo in Proceedings of theIEEE International Symposium on Dynamic Spectrum AccessNetworks DYSPAN 2012 vol 1 pp 422ndash433 October 2012

[22] Z Wei Q Zhang Z Feng W Li and T A Gulliver ldquoOn theconstruction of Radio Environment Maps for Cognitive RadioNetworksrdquo in Proceedings of the IEEEWireless Communicationsand Networking Conference WCNC 2013 vol 1 pp 4504ndash4509April 2013

[23] X H Li F Yuan C Jia M M Zhang and T F ZhouldquoComparison of Geostatistical Interpolation Methods for LocalSingularity Exponent Calculationrdquo Scientia Geographica Sinicavol 32 no 2 pp 136ndash142 2012

[24] H B Yılmaz Cooperative spectrum sensing and radio envi-ronment map construction in cognitive radio networks DissBogazici University 2012

[25] G Mateos J-A Bazerque and G B Giannakis ldquoSpline-basedspectrum cartography for cognitive radiosrdquo in Proceedings ofthe Conference Record of the Forty-Third Asilomar Conference onSignals Systems andComputers vol 1 pp 1025ndash1029 November2009

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal of

Volume 201

Submit your manuscripts athttpswwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 201

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

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DistributedSensor Networks

International Journal of

RoboticsJournal of

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

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RotatingMachinery

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VLSI Design

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

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Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of