research article correction of faulty sensors in phased...
Post on 15-Mar-2018
225 Views
Preview:
TRANSCRIPT
Research ArticleCorrection of Faulty Sensors in Phased ArrayRadars Using Symmetrical Sensor Failure Technique andCultural Algorithm with Differential Evolution
S U Khan1 I M Qureshi23 F Zaman4 B Shoaib4 A Naveed4 and A Basit4
1 School of Engineering amp Applied Sciences ISRA University Islamabad 44000 Pakistan2 Electrical Department Air University Islamabad 44000 Pakistan3 Institute of Signals Systems and Soft Computing (ISSS) Islamabad 44000 Pakistan4 Electronic Engineering Department IIU H-10 Islamabad 44000 Pakistan
Correspondence should be addressed to S U Khan shafqatphyyahoocom
Received 30 August 2013 Accepted 17 November 2013 Published 29 January 2014
Academic Editors Z Cui and X Yang
Copyright copy 2014 S U Khan 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
Three issues regarding sensor failure at any position in the antenna array are discussed We assume that sensor position is knownThe issues include raise in sidelobe levels displacement of nulls from their original positions and diminishing of null depth Therequired null depth is achieved by making the weight of symmetrical complement sensor passive A hybrid method based onmemetic computing algorithm is proposedThe hybridmethod combines the cultural algorithmwith differential evolution (CADE)which is used for the reduction of sidelobe levels and placement of nulls at their original positions Fitness function is used tominimize the error between the desired and estimated beam patterns along with null constraints Simulation results for variousscenarios have been given to exhibit the validity and performance of the proposed algorithm
1 Introduction
In adaptive beamforming null steering and beam steering arehot research areas It has direct application in radar sonarand mobile communication [1ndash3] In the literature variousanalytical and computational methods are available to con-centrate on the issue of null steering [4ndash6] The conditionbecomes more demanding and complicated when a sensorfails in the active antenna array The excitation of thesesensors is to accomplish desired radiation pattern In case ofsensor failure the sidelobe level (SLL) raise and nulls are dis-placedwhich is highly unwanted It is very expensive in termsof time and budget to replace the defective sensor regularlyHence the weights of active sensors in the same array shouldbe recalculated and readjusted to create a new pattern close tothe original one Recently few algorithms have been proposedto correct the damaged pattern of the array [7ndash10]
In the last few decades Radar technology has developedvery rapidly The radar commonly used nowadays is known
as phased array radar In this radar the whole input arraytransmits the same signal with different delay and a beam isformed towards the area of interest [11] The advantages ofbeam include the electronic steering instead of mechanicalsteering and a high processing gain at the transmitter Thephased array radar used the phase shifting in the inputwaveform to steer a beam electronically in the direction of thetarget instead of mechanical steering Array design is one ofthe most active research area in phased array radars in whichthe sensors are arranged together to form an arrayThe phaseshifters adjust the phase in such away that a beam is formed inthe desired direction The width of the beam depends on thenumber of sensors in the array By increasing the number ofsensors in an array the beam becomes sharper and thusmoreefficient in detecting the targets with smaller size Now if oneor more sensors become damaged the radars cannot detectthe target correctly Researchers are still working to recal-culate and adjust the weights of the active array to get thepattern near the original one By recalculating the weights of
Hindawi Publishing Corporatione Scientific World JournalVolume 2014 Article ID 852539 10 pageshttpdxdoiorg1011552014852539
2 The Scientific World Journal
the faulty array the radar will improve its capabilities in sucha way that the radar can perform searching tracking andweapon guidance at the same time
The evolutionary computing technique has been doingwell in solving numerous problems in search and optimiza-tion due to the impartial nature of their operations whichcan still be present in situations with no domain knowledgeThe search method used by evolutionary algorithms (EAs) isimpartial having no domain knowledge to guide the searchmethod Domain knowledge serves as a method to reducethe search space by pruning unnecessary parts of the solutionspace and by promoting required parts Cultural algorithm isbased on the principle to bias the search method with priorknowledge about the domain aswell as the knowledge duringthe evolution method
Among EC techniques differential evolution (DE) isconsidered to be one of the powerful and reliable tools to opti-mize the problems in any engineering field [12ndash14]The DE isa technique based on stochastic searches in which functionparameters are programmed as floating-point variables TheDE algorithmhas a simple structure convergence speed flex-ibility and robustness with only some parameters required tobe put by a user The application of CAs in DE is a differentstrategy to get the performance and local search better Theprevious work on null steering in failed antenna arrays ispresented in [15] The technique tries to restore the previousnulls pattern by using particle swarm optimization (PSO)All the above EC based techniques have discussed the SLLreduction and null steering in failed array but no one is solv-ing the issue of null depth and null steering at their originalpositions using CADE for the correction of faulty arraysAuthors in their previous work [16] have used the symmet-rical element failure technique to achieve the required nulldepth level and first null beamwidth and [17] for fault findingin failed array antenna Memetic computing algorithmsare stochastic population based methods that have beenestablished to be dominant and forceful to solve optimizationproblems The advantages of cultural algorithm (CA) withevolutionary algorithms (EAs) include global search capabil-ity and consistent performance in any field of engineering andtechnology [18ndash20]
In this paper the proposed algorithm developed threeissues in case of sensor failure These are raised in sidelobelevels displacement of nulls from their original positions anddiminishing of null depth We propose a symmetrical sensorfailure (SSF) method that provides better results in terms ofnull depth Moreover the SSF method has deeper first nullwhich is another big improvement over single sensor failureThe first null depth in beamforming is of great importanceTo address the other two issues we have used a culturalalgorithm with differential evolution (CADE) to reducethe sidelobe levels and positions of nulls reverse to theiroriginal positions by adjusting the current weights of activesensors A hybrid method based on the memetic computingalgorithm is proposed which combines the cultural algo-rithmwith differential evolution (CADE) for the reduction ofsidelobes and placement of nulls Different simulation resultsare provided to confirm the performance of the proposedapproach The rest of the paper is organized as follows
The problem formulation is discussed in Section 2 whilein Section 3 the proposed solution is provided Section 4describes the simulations and the results while Section 5concludes the paper and proposes some future work
2 Problem Formulation
Consider a linear array of 17 sensors in which all the sensorsare placed symmetrically about the origin The total numberof sensors is119873 = 2119872 + 1 The array factor in this healthy setup with uniformly spaced sensors nonuniform weight andprogressive phase excitation will be [21]
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp (119895119899 (119896119889 cos 120579
119894+ 120573)) (1)
where 119908119899is the nonuniform weight of 119899th sensor whereas
119899 = 0 plusmn1 plusmn2 plusmn119872 The spacing between the adjacentsensors is 119889 while 120579 is the angle from broadside 119896 = 2120587120582
is the wave number with 120582 as wavelength The progressivephase shift120573 = minus119896119889 cos 120579
119904and 120579119904is steering angle for themain
beam The damage array factor for 7th sensor failure is givenby the expression below
AF (120579119894) =
119872
sum
119899=minus119872119899 = 7
119908119899exp (119895119899 (119896119889 cos 120579
119894+ 120573)) (2)
The nonuniform weights of 17 sensors with 7th symmetrysensor failures are as follows
[119908minus8 119908minus7 119908minus6 119908minus5 119908minus4 119908
minus1 1199080
1199081 119908
4 1199085 1199086 1199087 1199088]
(3)
It is assumed that the 1199087sensor fails in the antenna array
given in (3) One can clearly monitor from Figure 1 that dueto single sensor failure the radiation pattern is damaged interms of sidelobe levels null depth and displacement of thenulls from their original position So the goal of this job isto recover the null depth sidelobe levels and null steeringat their original positions Different methods are available inthe literature to correct the damage pattern of sensor failureshowever none of them is able to achieve the required nulldepth level
3 Proposed Solution
In this section we develop the proposed solution based onSSF As we had assumed the damage of 119908
7sensor we lost the
null depth as given in Figure 1 For SSF method we also forcethe sensor 119908
minus7to be zero as shown in (3) From Figure 2 it is
clear that symmetric sensor failure maintains the null depthalmost as close to that of the original arrayThe damage arrayfactor for 7th symmetrical sensor failure is given by
AF (120579119894) =
119872
sum
119899=minus119872119899 = plusmn7
119908119899exp (119895119899 (119896119889 cos 120579
119894+ 120573)) (4)
The Scientific World Journal 3
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure
120579 (deg)
Figure 1 The original Chebyshev array and the 1199087sensor damage
pattern
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th symmetric sensor failure
120579 (deg)
Figure 2 The original Chebyshev array and the 1199087symmetric
sensor failure
Although we have achieved better null depth level due toSSF but the sidelobe levels and positioning of nulls are still aproblem to be taken into account for which we will use thecultural algorithmwith differential evolution (CADE) for thereduction of sidelobes and placement of nulls in the requiredpositions
31 Differential Evolution (DE) DE is an EA and was devel-oped by Storn and Price which is used to solve real valuedoptimization problems [22] The DE is a method basedon stochastic searches The DE algorithm presents easystructure convergence speed flexibility and robustness withonly some parameters required to be set by a user Howeverthis faster convergence of DE results in a higher possibility ofsearching near a local optimum or getting early convergenceDifferential evolution is based on a mutation operator whichadds an amount obtained by the difference of two randomlychosen individuals of the present populationThe problem to
Adjust
Belief space
Influence function
Fitness evaluationPopulation space
Variate population
Selection
Acceptance function
Figure 3 The flow diagram of the cultural algorithm
Table 1 Parameter used in CADE
CADEParameters SettingPopulation size 300Number of generation 500Value of 119865 05Value of CR 05 le CR le 1
be solved has119873 decision variables 119865 and 119862119877 are parametersgiven by the user and given in Table 1 Computing the differ-ence between two individuals which are selected randomlyfrom the population in fact the algorithm estimating the gra-dient in that region and this technique is a proficient way toself-adapt the mutation operatorThe pseudocode for the DEis given in Pseudocode 1
32 The Cultural Algorithm with Differential Evolution(CADE) Differential evolution is used as a population spacein the cultural algorithm CAs have been developed to modelthe evolution of the cultural component of an evolutionarycomputational system over time as it accumulates experienceAs a result CAs can provide a clear method for globalknowledge and a framework within which to model self-adaptation in an evolutionary system
Cultural algorithms consist of three components a pop-ulation space belief space and a communication protocol asshown in Figure 3 First one is population space that containsthe population to be evolved and the mechanisms for its esti-mate The population space consists of a set of possible solu-tions to the problem in our problem the population space isDE Second one is a belief space that represents the bias thathas been acquired by the population during its problem solv-ing process In CAs the information acquired by a memberof the population can be shared with the entire populationThe third one is the communication protocol that is usedto determine the interface between the population and thebeliefs
CAs model has two levels of evolution One is the popu-lation level and the other is belief space level In addition to apopulation space CA has a belief space in which the beliefsacquired from the populationrsquos evolution can be stored and
4 The Scientific World Journal
Generate the initial population of individualsDo
For each individual 119895 in the populationChoose three numbers 119899
1 1198992 and 119899
3that is 1 le 119899
1 1198992 1198993le 119873 with 119899
1= 1198992= 1198993= 119895
Generate a random integer 119894rand isin (1119873)For each parameter 119894
119910119894119892= 1199091198991 119892 + 119865(119909
1198992 119892 minus 1199091198993 119892)
119911119894119892
119895=
119910119894119892
119895119894119891 rand() le CR 119900119903 119895 = 119895rand
119909119894119892
119895otherwise
End ForReplace 119909119894119892 with the child 119911119894119892 if 119911119894119892 is better
End ForUntil the termination condition is achieved
Pseudocode 1 The pseudocode of the differential evolution algorithm
integrated An acceptance function is used to generate beliefsby gleaning the experience of individuals from the populationspace In return this belief space can bias the evolution of thepopulation component by means of the influence functionThe belief space itself also evolves by the adjust function[23] In the present work the belief space is divided into twoknowledge components
321 Situational Knowledge Situational knowledge storesindividuals from population space which provides the direc-tion for other individuals Situational knowledge consists ofthe best example 119875 found along the evolutionary process Itrepresents a leader for the other individuals to follow Thevariation operators of differential evolution are influenced inthe following way
119910119894119892= 119875119894+ 119865 (119909
1198992119892minus 1199091198993119892) (5)
where 119875119894is the 119894th component of the individual stored in the
situational knowledge This way we use the leader instead ofa randomly chosen individual for the recombination gettingthe children closer to the best point found The update of thesituational knowledge is done by replacing the stored individ-ual 119875 by the best individual found in the current population119909best only if 119909best is better than 119875
322 Normative Knowledge The normative knowledge con-tains the intervals for the decision variables where goodsolutions have been found in order to move new solutionstowards those intervalsThe normative knowledge includes ascaling factor 119889119904
1to influence themutation operator adopted
in differential evolution The following expression shows theinfluence of the normative knowledge of the variation opera-tors
119911119894119892
119895=
1199091198991119892+ 119865 (119909
1198992119892minus 1199091198993119892) if 1199091198991 119892 lt 119897
119894
1199091198991119892minus 119865 (119909
1198992119892minus 1199091198993119892) if 1199091198991 119892 gt 119906
119894
1199091198991119892+ (
119906119894minus 119897119894
119889119904119894
) lowast 119865 (1199091198992119892minus 1199091198993119892) otherwise
(6)
where 119897119894and 119906
119894are the lower and upper bounds respectively
for the 119894th decision variable The update of the normativeknowledge can reduce or expand the intervals stored on itAn extension takes place when the accepted individuals donot fit in the current interval while a reduction occurs whenall the accepted individuals lie in the current interval andthe extreme values have an improved fit and are feasible Thevalues 119889119904
119894are updated with the difference (1199091198992119892minus1199091198993119892) found
of the variation operators of the prior generation Normativeknowledge leads individuals to jump into the good rangeif they are not already there The normative knowledge isupdated as follows let us consider 119909
1198861 1199091198862 1199091198863 119909
119886119899accepted
be the accepted individuals in the current generation and119909min
119894
and 119909max119894
belong to (1198861 1198862 1198863 119899accepted) and theaccepted individualswithminimumandmaximumvalues forthe parameter 119894
119906119894=
119909119894max119894
if 119909119894max119894
gt 119906119894or 119891 (119909max
119894
) lt 119880119894
119906119894
otherwise
119897119894=
119909119894min119894
if 119909119894min119894
lt 119897119894or 119891 (119909min
119894
) lt 119871119894
119897119894
otherwise
(7)
If 119897119894and 119906
119894are updated the values of 119871
119894and 119880
119894will be
done in the same way The 119889119904119894are updated with the greatest
difference of |1199091198941199031minus1199091198941199032| found during the variation operators
at the prior generationThe flow chart and pseudocode for CADE is shown in
Pseudocode 2 and Figure 3
33 Null Constraint (NC) A jamming signal located at a par-ticular angle wants to be eliminated in case of satellite radarand mobile communication applications For a uninformedarray to put a null at a particular angle 120579
119894 we want [24]
AF (120579119894) = w119867s (120579
119894) = 0 (8)
The Scientific World Journal 5
Generate the initial populationCalculate the initial populationInitialize the belief spaceDo
For each individual in the populationApply the variation operator influenced by a randomly knowledge componentCalculate the child generatedReplace the individual with child if the child is better
End forUpdate the belief space with the accepted individuals
Until the termination condition is achieved
Pseudocode 2 The pseudocode of the cultural algorithm
where
s (120579119894) =
[[[[[[[[[[[[[[
[
exp (minus119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
exp (minus119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp(119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp (119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
]]]]]]]]]]]]]]
]119873times1
(9)
and w119867 is119873 times 1 vector which is defined as
w = [119908minus119872 119908minus119872+1
1199080 119908
119872minus1 119908119872]119879 (10)
The null constraint is given as
w119867s (120579119894) = 0 119894 = 1 2 119872
0 (11)
We may define an119873 times1198720constraint matrix C as
C = [s (1205791) s (120579
2) s (120579
1198720
)] (12)
where 120579119894for 119894 = 1 2 119872
0is the direction of null Our
goal is to optimize the squared weighting error subject to thecondition that
w119867C = 0 (13)Our constraint is that the columns of C should be
orthogonal to theweight vectorw Accordinglywemaydefine119866119894 119894 = 1 2 and 119866 as follows
1198661=
119875
sum
119894=1
[1003816100381610038161003816AF119889(120579119894) minus AFCADE(120579119894)
1003816100381610038161003816]2 (14)
1198662=10038171003817100381710038171003817w119867C10038171003817100381710038171003817
2
(15)
119866 = 1198661+ 1198662 (16)
Hence 119866 is the fitness function for the problem givenabove which are to be minimized Best chromosome will givethe minimal value of 119866 The first term in (16) is used forSLL reduction where AF
119889(120579119894) represents the desired pattern
and AFCADE(120579119894) is the pattern obtained by using CADE Thesecond term in (16) is used for jammer suppression and place-ment of nulls at their original positions after sensor failure
4 Simulation Results
In the simulation a classical Dolph-Chebyshev linear arrayof 17 sensors with 1205822 intersensor spacing is used as the testantenna The array factor in this case represents a minus35 dBconstant SLL with the nulls at specific angles Analyticaltechniques are used to find out the nonuniform weights forclassical Dolph-Chebyshev array In case of sensor failurecultural algorithmwith differential evolution (CADE) is usedfor the reduction of sidelobes and placement of nulls in therequired positions
Case a At the first instant the 1199087sensor is assumed to fail
After sensor failure the radiation pattern is destroyed whichresults in an increase of the SLL and displacement of nullpositions In order to regain the symmetry its mirror sensorweight 119908
minus7is forced to zero We achieve the desired null
depth level (NDL) and deeper first null depth level (FNDL)as compared to that of nonsymmetric case The SLL rises tominus3232 dB due to the 119908
7sensor failure while due to SSF of
the 1199087sensor the SLL is minus2653 dB The advantage of SSF is
deeper nulls especially the first null The SLL and FNDL fora damage array of single sensor failure and SSF are shownin Table 2 It is clear from Figure 2 that SSF maintains betterFNDL as compared to that of single sensor failure
After optimization by a cultural algorithm with differen-tial evolution (CADE) the SLL of the 119908
7sensor failure are
reduced to minus3299 dB while due to SSF the SLL is reduced tominus2835 dB The recovery of one null due to 7th sensor failureand SSF to its original position 120579
1= 1993
∘ is shown inFigures 4 and 5The comparison of recovered patternwith 7thsensor and SSF for one null imposed is given in Table 3 Therecovered NDL of SSF is seven dB deeper than that of 7thsensor failure
Figures 6 and 7 show the recovery of two nulls at anglesof 1205791= 1993
∘ and 1205792= 3488
∘ respectively for 7th sensorfailure and SSF The SLL and NDL for the correspondingnulls are given in Table 4 The NDL of the SSF is deeper ascompared to the 7th sensor failure
Now we check the recovery of three nulls at the requiredpositions Figures 8 and 9 show the recovery of three nullsoriginally at angles of 120579
1= 1993
∘ 1205792= 3488
∘ and 1205793=
4544∘ for 7th sensor failure and SSF The SLL and NDL for
6 The Scientific World Journal
Table 2 Comparison of FNDL and SLL of the damaged pattern
Comparison of FNDL and SLL of damage pattern of 7th sensor and SSF7th sensor failure SSF
FNDL (dB) SLL (dB) FNDL (dB) SLL (dB)minus3232 minus2945 minus8898 minus2653
Table 3 Recovery of one null
Comparison of NDL and SLL of one sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1047 minus3299 minus1115 minus2835 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure1 null recovered
120579 (deg)
Figure 4The original radiation pattern the1199087sensor damage and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF1 nulls recovered
120579 (deg)
Figure 5The original radiation pattern the1199087SSF and recovery of
one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure2 nulls recovered
120579 (deg)
Figure 6The original radiation pattern the1199087sensor damage and
recovery of two nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF2 nulls recovered
120579 (deg)
Figure 7The original radiation pattern the1199087SSF and recovery of
two nulls
The Scientific World Journal 7
Table 4 Recovery of two nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus953 minus2987 minus1151 minus3112 1st null recoveredminus9365 minus3075 minus1014 2707 2nd null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure3 nulls recovered
120579 (deg)
Figure 8The original radiation pattern the1199087sensor damage and
recovery of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF3 nulls recovered
120579 (deg)
Figure 9 The original radiation pattern the 1199087SSF and recovery
of three nulls
the corresponding nulls are given in Table 5 The NDL of allnulls in SSF is deeper than that of 7th sensor failure
Now the recovery of five nulls for 7th sensor failure andSSF originally at positions 1993∘ 3488∘ 4544∘6202∘ and6894∘ is carried out and shown in Figures 10 and 11 A
comparison of SLL and NDL for the recovery of five nullsis given in Table 6 In each case SSF produces deeper nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure5 nulls recovered
120579 (deg)
Figure 10The original radiation pattern the1199087sensor damage and
recovery of five nulls
compared to the 7th sensor failure From simulation it isobserved that we have received deeper depth of nulls in SSFscenarios as compared to 7th sensor failure discussed above
Case b In this case we discuss the failure of 1199084sensor If the
sensor1199084fails due to any reason the whole radiation pattern
became damage After optimization the SLL reduces andnulls are steered back to their original positions as shown inFigure 12Then to create symmetry we also force119908
minus4equal to
zero to achieve the requirednull depth levelThe advantage ofsymmetry sensor failure is to get deeper null depth level Thenumber of nulls achieved in 7th symmetry sensor failure issix and in case of 4th symmetry sensor failure the number ofnulls received are three From the simulation results it is clearthat the number of nulls reduces by one as the sensors getdamage near the centre sensor After optimization by CADEthe SLL reduces and nulls are steered back to their previouspositions at angles 120579
1= 3489
∘ 1205792= 5431
∘ and 1205793= 689
∘ asshown in Figure 13 The null depth level for single and SEF isgiven in Table 7
Case c In this section we discuss the possibility of gettingfailure near the centre sensor if the sensor 119908
1fails due to
unforeseen reason From Figure 14 it is clear that its SLLincreases and nulls are damaged and also lose null depth Tocreate the symmetry we also force its mirror sensor weight119908minus1
equal to zero The one advantage of symmetry sensorfailure is to get the deeper null depth level and on the otherhand due to 119908
1SSF its beamwidth also decreases In case of
8 The Scientific World Journal
Table 5 Recovery of three nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1116 minus3632 minus1185 minus3459 1st null recoveredminus9757 minus3492 minus1056 minus3268 2nd null recoveredminus9501 minus281 minus1033 minus2419 3rd null recovered
Table 6 Recovery of five nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1127 minus3734 minus120 minus378 1st null recoveredminus9816 minus3531 minus1084 minus3493 2nd null recoveredminus9533 minus249 minus1053 minus2291 3rd null recoveredminus946 minus3642 minus1025 minus3227 4th null recoveredminus9739 minus2269 minus9968 minus25832 5th null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF5 nulls recovered
120579 (deg)
Figure 11 The original radiation pattern the 1199087SSF and recovery
of five nulls
7th symmetry sensor failure the nulls are six and in 4th SSFthe achievable nulls are three but we received only one null incase of 119908
1SSF as shown in Figure 15 The null depth level for
single and SEF is given in Table 8
Case d The main beam can be steered at any desired angleIf the user changes their position than the main beam can besteered in the desired direction Figure 16 shows the correctedpattern with recovered nulls at main beam pointing at 120579
119904=
110∘ The main beam can be steered in the direction of the
desired user at any particular angleThe array factor for 2119872+
1 sensors in terms of main beam direction 120579119904is given by
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp 119895119899119896119889 (cos 120579
119894minus cos 120579
119904) (17)
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0N
orm
aliz
ed A
F (d
B)
Original4th element failure3 nulls recovered
120579 (deg)
Figure 12 The original radiation pattern the 1199084sensor failure and
recovery of three nulls
where 120579119904is themain beam direction to which it can be steered
to the desired angles
5 Conclusion and Future Work
We have proposed symmetric sensor failure (SSF) techniquealong cultural algorithm with differential evolution for thecorrection of faulty arrays The null depth of all nullsespecially the first one has been achieved with the help ofSSF technique Null steering at their original positions andsidelobe reduction has been achieved by a cultural algorithmwith differential evolution and using a proper fitness functiondemanding the sidelobe reduction and null constraints Dueto 7th SSF the number of nulls is six and in 4th SSF theachievable nulls are three but in case of 119908
1SSF we received
The Scientific World Journal 9
Table 7 Recovery of three nulls
Comparison of NDL and SLL of 4th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus8756 minus221 minus8624 minus2264 1st null recoveredminus1027 minus237 minus9797 minus1965 2nd null recoveredminus8881 minus2111 minus9401 minus2001 3rd null recovered
Table 8 Recovery of one nulls
Comparison of NDL and SLL of 1199081sensor failure and SSF
Correction of 1199081sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1133 minus2002 minus1151 minus211 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original4th SSF3 nulls recovered
120579 (deg)
Figure 13 The original radiation pattern the 1199084SSF and recovery
of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 element failure
Figure 14 The original radiation pattern the 1199081sensor failure and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 SSF
Figure 15 The original radiation pattern the 1199081SSF and recovery
of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSFRecovered nulls
120579 (deg)
Figure 16 The corrected pattern with main beam pointing at 110∘with recovered nulls
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
2 The Scientific World Journal
the faulty array the radar will improve its capabilities in sucha way that the radar can perform searching tracking andweapon guidance at the same time
The evolutionary computing technique has been doingwell in solving numerous problems in search and optimiza-tion due to the impartial nature of their operations whichcan still be present in situations with no domain knowledgeThe search method used by evolutionary algorithms (EAs) isimpartial having no domain knowledge to guide the searchmethod Domain knowledge serves as a method to reducethe search space by pruning unnecessary parts of the solutionspace and by promoting required parts Cultural algorithm isbased on the principle to bias the search method with priorknowledge about the domain aswell as the knowledge duringthe evolution method
Among EC techniques differential evolution (DE) isconsidered to be one of the powerful and reliable tools to opti-mize the problems in any engineering field [12ndash14]The DE isa technique based on stochastic searches in which functionparameters are programmed as floating-point variables TheDE algorithmhas a simple structure convergence speed flex-ibility and robustness with only some parameters required tobe put by a user The application of CAs in DE is a differentstrategy to get the performance and local search better Theprevious work on null steering in failed antenna arrays ispresented in [15] The technique tries to restore the previousnulls pattern by using particle swarm optimization (PSO)All the above EC based techniques have discussed the SLLreduction and null steering in failed array but no one is solv-ing the issue of null depth and null steering at their originalpositions using CADE for the correction of faulty arraysAuthors in their previous work [16] have used the symmet-rical element failure technique to achieve the required nulldepth level and first null beamwidth and [17] for fault findingin failed array antenna Memetic computing algorithmsare stochastic population based methods that have beenestablished to be dominant and forceful to solve optimizationproblems The advantages of cultural algorithm (CA) withevolutionary algorithms (EAs) include global search capabil-ity and consistent performance in any field of engineering andtechnology [18ndash20]
In this paper the proposed algorithm developed threeissues in case of sensor failure These are raised in sidelobelevels displacement of nulls from their original positions anddiminishing of null depth We propose a symmetrical sensorfailure (SSF) method that provides better results in terms ofnull depth Moreover the SSF method has deeper first nullwhich is another big improvement over single sensor failureThe first null depth in beamforming is of great importanceTo address the other two issues we have used a culturalalgorithm with differential evolution (CADE) to reducethe sidelobe levels and positions of nulls reverse to theiroriginal positions by adjusting the current weights of activesensors A hybrid method based on the memetic computingalgorithm is proposed which combines the cultural algo-rithmwith differential evolution (CADE) for the reduction ofsidelobes and placement of nulls Different simulation resultsare provided to confirm the performance of the proposedapproach The rest of the paper is organized as follows
The problem formulation is discussed in Section 2 whilein Section 3 the proposed solution is provided Section 4describes the simulations and the results while Section 5concludes the paper and proposes some future work
2 Problem Formulation
Consider a linear array of 17 sensors in which all the sensorsare placed symmetrically about the origin The total numberof sensors is119873 = 2119872 + 1 The array factor in this healthy setup with uniformly spaced sensors nonuniform weight andprogressive phase excitation will be [21]
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp (119895119899 (119896119889 cos 120579
119894+ 120573)) (1)
where 119908119899is the nonuniform weight of 119899th sensor whereas
119899 = 0 plusmn1 plusmn2 plusmn119872 The spacing between the adjacentsensors is 119889 while 120579 is the angle from broadside 119896 = 2120587120582
is the wave number with 120582 as wavelength The progressivephase shift120573 = minus119896119889 cos 120579
119904and 120579119904is steering angle for themain
beam The damage array factor for 7th sensor failure is givenby the expression below
AF (120579119894) =
119872
sum
119899=minus119872119899 = 7
119908119899exp (119895119899 (119896119889 cos 120579
119894+ 120573)) (2)
The nonuniform weights of 17 sensors with 7th symmetrysensor failures are as follows
[119908minus8 119908minus7 119908minus6 119908minus5 119908minus4 119908
minus1 1199080
1199081 119908
4 1199085 1199086 1199087 1199088]
(3)
It is assumed that the 1199087sensor fails in the antenna array
given in (3) One can clearly monitor from Figure 1 that dueto single sensor failure the radiation pattern is damaged interms of sidelobe levels null depth and displacement of thenulls from their original position So the goal of this job isto recover the null depth sidelobe levels and null steeringat their original positions Different methods are available inthe literature to correct the damage pattern of sensor failureshowever none of them is able to achieve the required nulldepth level
3 Proposed Solution
In this section we develop the proposed solution based onSSF As we had assumed the damage of 119908
7sensor we lost the
null depth as given in Figure 1 For SSF method we also forcethe sensor 119908
minus7to be zero as shown in (3) From Figure 2 it is
clear that symmetric sensor failure maintains the null depthalmost as close to that of the original arrayThe damage arrayfactor for 7th symmetrical sensor failure is given by
AF (120579119894) =
119872
sum
119899=minus119872119899 = plusmn7
119908119899exp (119895119899 (119896119889 cos 120579
119894+ 120573)) (4)
The Scientific World Journal 3
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure
120579 (deg)
Figure 1 The original Chebyshev array and the 1199087sensor damage
pattern
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th symmetric sensor failure
120579 (deg)
Figure 2 The original Chebyshev array and the 1199087symmetric
sensor failure
Although we have achieved better null depth level due toSSF but the sidelobe levels and positioning of nulls are still aproblem to be taken into account for which we will use thecultural algorithmwith differential evolution (CADE) for thereduction of sidelobes and placement of nulls in the requiredpositions
31 Differential Evolution (DE) DE is an EA and was devel-oped by Storn and Price which is used to solve real valuedoptimization problems [22] The DE is a method basedon stochastic searches The DE algorithm presents easystructure convergence speed flexibility and robustness withonly some parameters required to be set by a user Howeverthis faster convergence of DE results in a higher possibility ofsearching near a local optimum or getting early convergenceDifferential evolution is based on a mutation operator whichadds an amount obtained by the difference of two randomlychosen individuals of the present populationThe problem to
Adjust
Belief space
Influence function
Fitness evaluationPopulation space
Variate population
Selection
Acceptance function
Figure 3 The flow diagram of the cultural algorithm
Table 1 Parameter used in CADE
CADEParameters SettingPopulation size 300Number of generation 500Value of 119865 05Value of CR 05 le CR le 1
be solved has119873 decision variables 119865 and 119862119877 are parametersgiven by the user and given in Table 1 Computing the differ-ence between two individuals which are selected randomlyfrom the population in fact the algorithm estimating the gra-dient in that region and this technique is a proficient way toself-adapt the mutation operatorThe pseudocode for the DEis given in Pseudocode 1
32 The Cultural Algorithm with Differential Evolution(CADE) Differential evolution is used as a population spacein the cultural algorithm CAs have been developed to modelthe evolution of the cultural component of an evolutionarycomputational system over time as it accumulates experienceAs a result CAs can provide a clear method for globalknowledge and a framework within which to model self-adaptation in an evolutionary system
Cultural algorithms consist of three components a pop-ulation space belief space and a communication protocol asshown in Figure 3 First one is population space that containsthe population to be evolved and the mechanisms for its esti-mate The population space consists of a set of possible solu-tions to the problem in our problem the population space isDE Second one is a belief space that represents the bias thathas been acquired by the population during its problem solv-ing process In CAs the information acquired by a memberof the population can be shared with the entire populationThe third one is the communication protocol that is usedto determine the interface between the population and thebeliefs
CAs model has two levels of evolution One is the popu-lation level and the other is belief space level In addition to apopulation space CA has a belief space in which the beliefsacquired from the populationrsquos evolution can be stored and
4 The Scientific World Journal
Generate the initial population of individualsDo
For each individual 119895 in the populationChoose three numbers 119899
1 1198992 and 119899
3that is 1 le 119899
1 1198992 1198993le 119873 with 119899
1= 1198992= 1198993= 119895
Generate a random integer 119894rand isin (1119873)For each parameter 119894
119910119894119892= 1199091198991 119892 + 119865(119909
1198992 119892 minus 1199091198993 119892)
119911119894119892
119895=
119910119894119892
119895119894119891 rand() le CR 119900119903 119895 = 119895rand
119909119894119892
119895otherwise
End ForReplace 119909119894119892 with the child 119911119894119892 if 119911119894119892 is better
End ForUntil the termination condition is achieved
Pseudocode 1 The pseudocode of the differential evolution algorithm
integrated An acceptance function is used to generate beliefsby gleaning the experience of individuals from the populationspace In return this belief space can bias the evolution of thepopulation component by means of the influence functionThe belief space itself also evolves by the adjust function[23] In the present work the belief space is divided into twoknowledge components
321 Situational Knowledge Situational knowledge storesindividuals from population space which provides the direc-tion for other individuals Situational knowledge consists ofthe best example 119875 found along the evolutionary process Itrepresents a leader for the other individuals to follow Thevariation operators of differential evolution are influenced inthe following way
119910119894119892= 119875119894+ 119865 (119909
1198992119892minus 1199091198993119892) (5)
where 119875119894is the 119894th component of the individual stored in the
situational knowledge This way we use the leader instead ofa randomly chosen individual for the recombination gettingthe children closer to the best point found The update of thesituational knowledge is done by replacing the stored individ-ual 119875 by the best individual found in the current population119909best only if 119909best is better than 119875
322 Normative Knowledge The normative knowledge con-tains the intervals for the decision variables where goodsolutions have been found in order to move new solutionstowards those intervalsThe normative knowledge includes ascaling factor 119889119904
1to influence themutation operator adopted
in differential evolution The following expression shows theinfluence of the normative knowledge of the variation opera-tors
119911119894119892
119895=
1199091198991119892+ 119865 (119909
1198992119892minus 1199091198993119892) if 1199091198991 119892 lt 119897
119894
1199091198991119892minus 119865 (119909
1198992119892minus 1199091198993119892) if 1199091198991 119892 gt 119906
119894
1199091198991119892+ (
119906119894minus 119897119894
119889119904119894
) lowast 119865 (1199091198992119892minus 1199091198993119892) otherwise
(6)
where 119897119894and 119906
119894are the lower and upper bounds respectively
for the 119894th decision variable The update of the normativeknowledge can reduce or expand the intervals stored on itAn extension takes place when the accepted individuals donot fit in the current interval while a reduction occurs whenall the accepted individuals lie in the current interval andthe extreme values have an improved fit and are feasible Thevalues 119889119904
119894are updated with the difference (1199091198992119892minus1199091198993119892) found
of the variation operators of the prior generation Normativeknowledge leads individuals to jump into the good rangeif they are not already there The normative knowledge isupdated as follows let us consider 119909
1198861 1199091198862 1199091198863 119909
119886119899accepted
be the accepted individuals in the current generation and119909min
119894
and 119909max119894
belong to (1198861 1198862 1198863 119899accepted) and theaccepted individualswithminimumandmaximumvalues forthe parameter 119894
119906119894=
119909119894max119894
if 119909119894max119894
gt 119906119894or 119891 (119909max
119894
) lt 119880119894
119906119894
otherwise
119897119894=
119909119894min119894
if 119909119894min119894
lt 119897119894or 119891 (119909min
119894
) lt 119871119894
119897119894
otherwise
(7)
If 119897119894and 119906
119894are updated the values of 119871
119894and 119880
119894will be
done in the same way The 119889119904119894are updated with the greatest
difference of |1199091198941199031minus1199091198941199032| found during the variation operators
at the prior generationThe flow chart and pseudocode for CADE is shown in
Pseudocode 2 and Figure 3
33 Null Constraint (NC) A jamming signal located at a par-ticular angle wants to be eliminated in case of satellite radarand mobile communication applications For a uninformedarray to put a null at a particular angle 120579
119894 we want [24]
AF (120579119894) = w119867s (120579
119894) = 0 (8)
The Scientific World Journal 5
Generate the initial populationCalculate the initial populationInitialize the belief spaceDo
For each individual in the populationApply the variation operator influenced by a randomly knowledge componentCalculate the child generatedReplace the individual with child if the child is better
End forUpdate the belief space with the accepted individuals
Until the termination condition is achieved
Pseudocode 2 The pseudocode of the cultural algorithm
where
s (120579119894) =
[[[[[[[[[[[[[[
[
exp (minus119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
exp (minus119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp(119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp (119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
]]]]]]]]]]]]]]
]119873times1
(9)
and w119867 is119873 times 1 vector which is defined as
w = [119908minus119872 119908minus119872+1
1199080 119908
119872minus1 119908119872]119879 (10)
The null constraint is given as
w119867s (120579119894) = 0 119894 = 1 2 119872
0 (11)
We may define an119873 times1198720constraint matrix C as
C = [s (1205791) s (120579
2) s (120579
1198720
)] (12)
where 120579119894for 119894 = 1 2 119872
0is the direction of null Our
goal is to optimize the squared weighting error subject to thecondition that
w119867C = 0 (13)Our constraint is that the columns of C should be
orthogonal to theweight vectorw Accordinglywemaydefine119866119894 119894 = 1 2 and 119866 as follows
1198661=
119875
sum
119894=1
[1003816100381610038161003816AF119889(120579119894) minus AFCADE(120579119894)
1003816100381610038161003816]2 (14)
1198662=10038171003817100381710038171003817w119867C10038171003817100381710038171003817
2
(15)
119866 = 1198661+ 1198662 (16)
Hence 119866 is the fitness function for the problem givenabove which are to be minimized Best chromosome will givethe minimal value of 119866 The first term in (16) is used forSLL reduction where AF
119889(120579119894) represents the desired pattern
and AFCADE(120579119894) is the pattern obtained by using CADE Thesecond term in (16) is used for jammer suppression and place-ment of nulls at their original positions after sensor failure
4 Simulation Results
In the simulation a classical Dolph-Chebyshev linear arrayof 17 sensors with 1205822 intersensor spacing is used as the testantenna The array factor in this case represents a minus35 dBconstant SLL with the nulls at specific angles Analyticaltechniques are used to find out the nonuniform weights forclassical Dolph-Chebyshev array In case of sensor failurecultural algorithmwith differential evolution (CADE) is usedfor the reduction of sidelobes and placement of nulls in therequired positions
Case a At the first instant the 1199087sensor is assumed to fail
After sensor failure the radiation pattern is destroyed whichresults in an increase of the SLL and displacement of nullpositions In order to regain the symmetry its mirror sensorweight 119908
minus7is forced to zero We achieve the desired null
depth level (NDL) and deeper first null depth level (FNDL)as compared to that of nonsymmetric case The SLL rises tominus3232 dB due to the 119908
7sensor failure while due to SSF of
the 1199087sensor the SLL is minus2653 dB The advantage of SSF is
deeper nulls especially the first null The SLL and FNDL fora damage array of single sensor failure and SSF are shownin Table 2 It is clear from Figure 2 that SSF maintains betterFNDL as compared to that of single sensor failure
After optimization by a cultural algorithm with differen-tial evolution (CADE) the SLL of the 119908
7sensor failure are
reduced to minus3299 dB while due to SSF the SLL is reduced tominus2835 dB The recovery of one null due to 7th sensor failureand SSF to its original position 120579
1= 1993
∘ is shown inFigures 4 and 5The comparison of recovered patternwith 7thsensor and SSF for one null imposed is given in Table 3 Therecovered NDL of SSF is seven dB deeper than that of 7thsensor failure
Figures 6 and 7 show the recovery of two nulls at anglesof 1205791= 1993
∘ and 1205792= 3488
∘ respectively for 7th sensorfailure and SSF The SLL and NDL for the correspondingnulls are given in Table 4 The NDL of the SSF is deeper ascompared to the 7th sensor failure
Now we check the recovery of three nulls at the requiredpositions Figures 8 and 9 show the recovery of three nullsoriginally at angles of 120579
1= 1993
∘ 1205792= 3488
∘ and 1205793=
4544∘ for 7th sensor failure and SSF The SLL and NDL for
6 The Scientific World Journal
Table 2 Comparison of FNDL and SLL of the damaged pattern
Comparison of FNDL and SLL of damage pattern of 7th sensor and SSF7th sensor failure SSF
FNDL (dB) SLL (dB) FNDL (dB) SLL (dB)minus3232 minus2945 minus8898 minus2653
Table 3 Recovery of one null
Comparison of NDL and SLL of one sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1047 minus3299 minus1115 minus2835 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure1 null recovered
120579 (deg)
Figure 4The original radiation pattern the1199087sensor damage and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF1 nulls recovered
120579 (deg)
Figure 5The original radiation pattern the1199087SSF and recovery of
one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure2 nulls recovered
120579 (deg)
Figure 6The original radiation pattern the1199087sensor damage and
recovery of two nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF2 nulls recovered
120579 (deg)
Figure 7The original radiation pattern the1199087SSF and recovery of
two nulls
The Scientific World Journal 7
Table 4 Recovery of two nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus953 minus2987 minus1151 minus3112 1st null recoveredminus9365 minus3075 minus1014 2707 2nd null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure3 nulls recovered
120579 (deg)
Figure 8The original radiation pattern the1199087sensor damage and
recovery of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF3 nulls recovered
120579 (deg)
Figure 9 The original radiation pattern the 1199087SSF and recovery
of three nulls
the corresponding nulls are given in Table 5 The NDL of allnulls in SSF is deeper than that of 7th sensor failure
Now the recovery of five nulls for 7th sensor failure andSSF originally at positions 1993∘ 3488∘ 4544∘6202∘ and6894∘ is carried out and shown in Figures 10 and 11 A
comparison of SLL and NDL for the recovery of five nullsis given in Table 6 In each case SSF produces deeper nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure5 nulls recovered
120579 (deg)
Figure 10The original radiation pattern the1199087sensor damage and
recovery of five nulls
compared to the 7th sensor failure From simulation it isobserved that we have received deeper depth of nulls in SSFscenarios as compared to 7th sensor failure discussed above
Case b In this case we discuss the failure of 1199084sensor If the
sensor1199084fails due to any reason the whole radiation pattern
became damage After optimization the SLL reduces andnulls are steered back to their original positions as shown inFigure 12Then to create symmetry we also force119908
minus4equal to
zero to achieve the requirednull depth levelThe advantage ofsymmetry sensor failure is to get deeper null depth level Thenumber of nulls achieved in 7th symmetry sensor failure issix and in case of 4th symmetry sensor failure the number ofnulls received are three From the simulation results it is clearthat the number of nulls reduces by one as the sensors getdamage near the centre sensor After optimization by CADEthe SLL reduces and nulls are steered back to their previouspositions at angles 120579
1= 3489
∘ 1205792= 5431
∘ and 1205793= 689
∘ asshown in Figure 13 The null depth level for single and SEF isgiven in Table 7
Case c In this section we discuss the possibility of gettingfailure near the centre sensor if the sensor 119908
1fails due to
unforeseen reason From Figure 14 it is clear that its SLLincreases and nulls are damaged and also lose null depth Tocreate the symmetry we also force its mirror sensor weight119908minus1
equal to zero The one advantage of symmetry sensorfailure is to get the deeper null depth level and on the otherhand due to 119908
1SSF its beamwidth also decreases In case of
8 The Scientific World Journal
Table 5 Recovery of three nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1116 minus3632 minus1185 minus3459 1st null recoveredminus9757 minus3492 minus1056 minus3268 2nd null recoveredminus9501 minus281 minus1033 minus2419 3rd null recovered
Table 6 Recovery of five nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1127 minus3734 minus120 minus378 1st null recoveredminus9816 minus3531 minus1084 minus3493 2nd null recoveredminus9533 minus249 minus1053 minus2291 3rd null recoveredminus946 minus3642 minus1025 minus3227 4th null recoveredminus9739 minus2269 minus9968 minus25832 5th null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF5 nulls recovered
120579 (deg)
Figure 11 The original radiation pattern the 1199087SSF and recovery
of five nulls
7th symmetry sensor failure the nulls are six and in 4th SSFthe achievable nulls are three but we received only one null incase of 119908
1SSF as shown in Figure 15 The null depth level for
single and SEF is given in Table 8
Case d The main beam can be steered at any desired angleIf the user changes their position than the main beam can besteered in the desired direction Figure 16 shows the correctedpattern with recovered nulls at main beam pointing at 120579
119904=
110∘ The main beam can be steered in the direction of the
desired user at any particular angleThe array factor for 2119872+
1 sensors in terms of main beam direction 120579119904is given by
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp 119895119899119896119889 (cos 120579
119894minus cos 120579
119904) (17)
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0N
orm
aliz
ed A
F (d
B)
Original4th element failure3 nulls recovered
120579 (deg)
Figure 12 The original radiation pattern the 1199084sensor failure and
recovery of three nulls
where 120579119904is themain beam direction to which it can be steered
to the desired angles
5 Conclusion and Future Work
We have proposed symmetric sensor failure (SSF) techniquealong cultural algorithm with differential evolution for thecorrection of faulty arrays The null depth of all nullsespecially the first one has been achieved with the help ofSSF technique Null steering at their original positions andsidelobe reduction has been achieved by a cultural algorithmwith differential evolution and using a proper fitness functiondemanding the sidelobe reduction and null constraints Dueto 7th SSF the number of nulls is six and in 4th SSF theachievable nulls are three but in case of 119908
1SSF we received
The Scientific World Journal 9
Table 7 Recovery of three nulls
Comparison of NDL and SLL of 4th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus8756 minus221 minus8624 minus2264 1st null recoveredminus1027 minus237 minus9797 minus1965 2nd null recoveredminus8881 minus2111 minus9401 minus2001 3rd null recovered
Table 8 Recovery of one nulls
Comparison of NDL and SLL of 1199081sensor failure and SSF
Correction of 1199081sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1133 minus2002 minus1151 minus211 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original4th SSF3 nulls recovered
120579 (deg)
Figure 13 The original radiation pattern the 1199084SSF and recovery
of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 element failure
Figure 14 The original radiation pattern the 1199081sensor failure and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 SSF
Figure 15 The original radiation pattern the 1199081SSF and recovery
of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSFRecovered nulls
120579 (deg)
Figure 16 The corrected pattern with main beam pointing at 110∘with recovered nulls
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World Journal 3
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure
120579 (deg)
Figure 1 The original Chebyshev array and the 1199087sensor damage
pattern
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th symmetric sensor failure
120579 (deg)
Figure 2 The original Chebyshev array and the 1199087symmetric
sensor failure
Although we have achieved better null depth level due toSSF but the sidelobe levels and positioning of nulls are still aproblem to be taken into account for which we will use thecultural algorithmwith differential evolution (CADE) for thereduction of sidelobes and placement of nulls in the requiredpositions
31 Differential Evolution (DE) DE is an EA and was devel-oped by Storn and Price which is used to solve real valuedoptimization problems [22] The DE is a method basedon stochastic searches The DE algorithm presents easystructure convergence speed flexibility and robustness withonly some parameters required to be set by a user Howeverthis faster convergence of DE results in a higher possibility ofsearching near a local optimum or getting early convergenceDifferential evolution is based on a mutation operator whichadds an amount obtained by the difference of two randomlychosen individuals of the present populationThe problem to
Adjust
Belief space
Influence function
Fitness evaluationPopulation space
Variate population
Selection
Acceptance function
Figure 3 The flow diagram of the cultural algorithm
Table 1 Parameter used in CADE
CADEParameters SettingPopulation size 300Number of generation 500Value of 119865 05Value of CR 05 le CR le 1
be solved has119873 decision variables 119865 and 119862119877 are parametersgiven by the user and given in Table 1 Computing the differ-ence between two individuals which are selected randomlyfrom the population in fact the algorithm estimating the gra-dient in that region and this technique is a proficient way toself-adapt the mutation operatorThe pseudocode for the DEis given in Pseudocode 1
32 The Cultural Algorithm with Differential Evolution(CADE) Differential evolution is used as a population spacein the cultural algorithm CAs have been developed to modelthe evolution of the cultural component of an evolutionarycomputational system over time as it accumulates experienceAs a result CAs can provide a clear method for globalknowledge and a framework within which to model self-adaptation in an evolutionary system
Cultural algorithms consist of three components a pop-ulation space belief space and a communication protocol asshown in Figure 3 First one is population space that containsthe population to be evolved and the mechanisms for its esti-mate The population space consists of a set of possible solu-tions to the problem in our problem the population space isDE Second one is a belief space that represents the bias thathas been acquired by the population during its problem solv-ing process In CAs the information acquired by a memberof the population can be shared with the entire populationThe third one is the communication protocol that is usedto determine the interface between the population and thebeliefs
CAs model has two levels of evolution One is the popu-lation level and the other is belief space level In addition to apopulation space CA has a belief space in which the beliefsacquired from the populationrsquos evolution can be stored and
4 The Scientific World Journal
Generate the initial population of individualsDo
For each individual 119895 in the populationChoose three numbers 119899
1 1198992 and 119899
3that is 1 le 119899
1 1198992 1198993le 119873 with 119899
1= 1198992= 1198993= 119895
Generate a random integer 119894rand isin (1119873)For each parameter 119894
119910119894119892= 1199091198991 119892 + 119865(119909
1198992 119892 minus 1199091198993 119892)
119911119894119892
119895=
119910119894119892
119895119894119891 rand() le CR 119900119903 119895 = 119895rand
119909119894119892
119895otherwise
End ForReplace 119909119894119892 with the child 119911119894119892 if 119911119894119892 is better
End ForUntil the termination condition is achieved
Pseudocode 1 The pseudocode of the differential evolution algorithm
integrated An acceptance function is used to generate beliefsby gleaning the experience of individuals from the populationspace In return this belief space can bias the evolution of thepopulation component by means of the influence functionThe belief space itself also evolves by the adjust function[23] In the present work the belief space is divided into twoknowledge components
321 Situational Knowledge Situational knowledge storesindividuals from population space which provides the direc-tion for other individuals Situational knowledge consists ofthe best example 119875 found along the evolutionary process Itrepresents a leader for the other individuals to follow Thevariation operators of differential evolution are influenced inthe following way
119910119894119892= 119875119894+ 119865 (119909
1198992119892minus 1199091198993119892) (5)
where 119875119894is the 119894th component of the individual stored in the
situational knowledge This way we use the leader instead ofa randomly chosen individual for the recombination gettingthe children closer to the best point found The update of thesituational knowledge is done by replacing the stored individ-ual 119875 by the best individual found in the current population119909best only if 119909best is better than 119875
322 Normative Knowledge The normative knowledge con-tains the intervals for the decision variables where goodsolutions have been found in order to move new solutionstowards those intervalsThe normative knowledge includes ascaling factor 119889119904
1to influence themutation operator adopted
in differential evolution The following expression shows theinfluence of the normative knowledge of the variation opera-tors
119911119894119892
119895=
1199091198991119892+ 119865 (119909
1198992119892minus 1199091198993119892) if 1199091198991 119892 lt 119897
119894
1199091198991119892minus 119865 (119909
1198992119892minus 1199091198993119892) if 1199091198991 119892 gt 119906
119894
1199091198991119892+ (
119906119894minus 119897119894
119889119904119894
) lowast 119865 (1199091198992119892minus 1199091198993119892) otherwise
(6)
where 119897119894and 119906
119894are the lower and upper bounds respectively
for the 119894th decision variable The update of the normativeknowledge can reduce or expand the intervals stored on itAn extension takes place when the accepted individuals donot fit in the current interval while a reduction occurs whenall the accepted individuals lie in the current interval andthe extreme values have an improved fit and are feasible Thevalues 119889119904
119894are updated with the difference (1199091198992119892minus1199091198993119892) found
of the variation operators of the prior generation Normativeknowledge leads individuals to jump into the good rangeif they are not already there The normative knowledge isupdated as follows let us consider 119909
1198861 1199091198862 1199091198863 119909
119886119899accepted
be the accepted individuals in the current generation and119909min
119894
and 119909max119894
belong to (1198861 1198862 1198863 119899accepted) and theaccepted individualswithminimumandmaximumvalues forthe parameter 119894
119906119894=
119909119894max119894
if 119909119894max119894
gt 119906119894or 119891 (119909max
119894
) lt 119880119894
119906119894
otherwise
119897119894=
119909119894min119894
if 119909119894min119894
lt 119897119894or 119891 (119909min
119894
) lt 119871119894
119897119894
otherwise
(7)
If 119897119894and 119906
119894are updated the values of 119871
119894and 119880
119894will be
done in the same way The 119889119904119894are updated with the greatest
difference of |1199091198941199031minus1199091198941199032| found during the variation operators
at the prior generationThe flow chart and pseudocode for CADE is shown in
Pseudocode 2 and Figure 3
33 Null Constraint (NC) A jamming signal located at a par-ticular angle wants to be eliminated in case of satellite radarand mobile communication applications For a uninformedarray to put a null at a particular angle 120579
119894 we want [24]
AF (120579119894) = w119867s (120579
119894) = 0 (8)
The Scientific World Journal 5
Generate the initial populationCalculate the initial populationInitialize the belief spaceDo
For each individual in the populationApply the variation operator influenced by a randomly knowledge componentCalculate the child generatedReplace the individual with child if the child is better
End forUpdate the belief space with the accepted individuals
Until the termination condition is achieved
Pseudocode 2 The pseudocode of the cultural algorithm
where
s (120579119894) =
[[[[[[[[[[[[[[
[
exp (minus119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
exp (minus119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp(119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp (119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
]]]]]]]]]]]]]]
]119873times1
(9)
and w119867 is119873 times 1 vector which is defined as
w = [119908minus119872 119908minus119872+1
1199080 119908
119872minus1 119908119872]119879 (10)
The null constraint is given as
w119867s (120579119894) = 0 119894 = 1 2 119872
0 (11)
We may define an119873 times1198720constraint matrix C as
C = [s (1205791) s (120579
2) s (120579
1198720
)] (12)
where 120579119894for 119894 = 1 2 119872
0is the direction of null Our
goal is to optimize the squared weighting error subject to thecondition that
w119867C = 0 (13)Our constraint is that the columns of C should be
orthogonal to theweight vectorw Accordinglywemaydefine119866119894 119894 = 1 2 and 119866 as follows
1198661=
119875
sum
119894=1
[1003816100381610038161003816AF119889(120579119894) minus AFCADE(120579119894)
1003816100381610038161003816]2 (14)
1198662=10038171003817100381710038171003817w119867C10038171003817100381710038171003817
2
(15)
119866 = 1198661+ 1198662 (16)
Hence 119866 is the fitness function for the problem givenabove which are to be minimized Best chromosome will givethe minimal value of 119866 The first term in (16) is used forSLL reduction where AF
119889(120579119894) represents the desired pattern
and AFCADE(120579119894) is the pattern obtained by using CADE Thesecond term in (16) is used for jammer suppression and place-ment of nulls at their original positions after sensor failure
4 Simulation Results
In the simulation a classical Dolph-Chebyshev linear arrayof 17 sensors with 1205822 intersensor spacing is used as the testantenna The array factor in this case represents a minus35 dBconstant SLL with the nulls at specific angles Analyticaltechniques are used to find out the nonuniform weights forclassical Dolph-Chebyshev array In case of sensor failurecultural algorithmwith differential evolution (CADE) is usedfor the reduction of sidelobes and placement of nulls in therequired positions
Case a At the first instant the 1199087sensor is assumed to fail
After sensor failure the radiation pattern is destroyed whichresults in an increase of the SLL and displacement of nullpositions In order to regain the symmetry its mirror sensorweight 119908
minus7is forced to zero We achieve the desired null
depth level (NDL) and deeper first null depth level (FNDL)as compared to that of nonsymmetric case The SLL rises tominus3232 dB due to the 119908
7sensor failure while due to SSF of
the 1199087sensor the SLL is minus2653 dB The advantage of SSF is
deeper nulls especially the first null The SLL and FNDL fora damage array of single sensor failure and SSF are shownin Table 2 It is clear from Figure 2 that SSF maintains betterFNDL as compared to that of single sensor failure
After optimization by a cultural algorithm with differen-tial evolution (CADE) the SLL of the 119908
7sensor failure are
reduced to minus3299 dB while due to SSF the SLL is reduced tominus2835 dB The recovery of one null due to 7th sensor failureand SSF to its original position 120579
1= 1993
∘ is shown inFigures 4 and 5The comparison of recovered patternwith 7thsensor and SSF for one null imposed is given in Table 3 Therecovered NDL of SSF is seven dB deeper than that of 7thsensor failure
Figures 6 and 7 show the recovery of two nulls at anglesof 1205791= 1993
∘ and 1205792= 3488
∘ respectively for 7th sensorfailure and SSF The SLL and NDL for the correspondingnulls are given in Table 4 The NDL of the SSF is deeper ascompared to the 7th sensor failure
Now we check the recovery of three nulls at the requiredpositions Figures 8 and 9 show the recovery of three nullsoriginally at angles of 120579
1= 1993
∘ 1205792= 3488
∘ and 1205793=
4544∘ for 7th sensor failure and SSF The SLL and NDL for
6 The Scientific World Journal
Table 2 Comparison of FNDL and SLL of the damaged pattern
Comparison of FNDL and SLL of damage pattern of 7th sensor and SSF7th sensor failure SSF
FNDL (dB) SLL (dB) FNDL (dB) SLL (dB)minus3232 minus2945 minus8898 minus2653
Table 3 Recovery of one null
Comparison of NDL and SLL of one sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1047 minus3299 minus1115 minus2835 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure1 null recovered
120579 (deg)
Figure 4The original radiation pattern the1199087sensor damage and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF1 nulls recovered
120579 (deg)
Figure 5The original radiation pattern the1199087SSF and recovery of
one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure2 nulls recovered
120579 (deg)
Figure 6The original radiation pattern the1199087sensor damage and
recovery of two nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF2 nulls recovered
120579 (deg)
Figure 7The original radiation pattern the1199087SSF and recovery of
two nulls
The Scientific World Journal 7
Table 4 Recovery of two nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus953 minus2987 minus1151 minus3112 1st null recoveredminus9365 minus3075 minus1014 2707 2nd null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure3 nulls recovered
120579 (deg)
Figure 8The original radiation pattern the1199087sensor damage and
recovery of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF3 nulls recovered
120579 (deg)
Figure 9 The original radiation pattern the 1199087SSF and recovery
of three nulls
the corresponding nulls are given in Table 5 The NDL of allnulls in SSF is deeper than that of 7th sensor failure
Now the recovery of five nulls for 7th sensor failure andSSF originally at positions 1993∘ 3488∘ 4544∘6202∘ and6894∘ is carried out and shown in Figures 10 and 11 A
comparison of SLL and NDL for the recovery of five nullsis given in Table 6 In each case SSF produces deeper nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure5 nulls recovered
120579 (deg)
Figure 10The original radiation pattern the1199087sensor damage and
recovery of five nulls
compared to the 7th sensor failure From simulation it isobserved that we have received deeper depth of nulls in SSFscenarios as compared to 7th sensor failure discussed above
Case b In this case we discuss the failure of 1199084sensor If the
sensor1199084fails due to any reason the whole radiation pattern
became damage After optimization the SLL reduces andnulls are steered back to their original positions as shown inFigure 12Then to create symmetry we also force119908
minus4equal to
zero to achieve the requirednull depth levelThe advantage ofsymmetry sensor failure is to get deeper null depth level Thenumber of nulls achieved in 7th symmetry sensor failure issix and in case of 4th symmetry sensor failure the number ofnulls received are three From the simulation results it is clearthat the number of nulls reduces by one as the sensors getdamage near the centre sensor After optimization by CADEthe SLL reduces and nulls are steered back to their previouspositions at angles 120579
1= 3489
∘ 1205792= 5431
∘ and 1205793= 689
∘ asshown in Figure 13 The null depth level for single and SEF isgiven in Table 7
Case c In this section we discuss the possibility of gettingfailure near the centre sensor if the sensor 119908
1fails due to
unforeseen reason From Figure 14 it is clear that its SLLincreases and nulls are damaged and also lose null depth Tocreate the symmetry we also force its mirror sensor weight119908minus1
equal to zero The one advantage of symmetry sensorfailure is to get the deeper null depth level and on the otherhand due to 119908
1SSF its beamwidth also decreases In case of
8 The Scientific World Journal
Table 5 Recovery of three nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1116 minus3632 minus1185 minus3459 1st null recoveredminus9757 minus3492 minus1056 minus3268 2nd null recoveredminus9501 minus281 minus1033 minus2419 3rd null recovered
Table 6 Recovery of five nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1127 minus3734 minus120 minus378 1st null recoveredminus9816 minus3531 minus1084 minus3493 2nd null recoveredminus9533 minus249 minus1053 minus2291 3rd null recoveredminus946 minus3642 minus1025 minus3227 4th null recoveredminus9739 minus2269 minus9968 minus25832 5th null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF5 nulls recovered
120579 (deg)
Figure 11 The original radiation pattern the 1199087SSF and recovery
of five nulls
7th symmetry sensor failure the nulls are six and in 4th SSFthe achievable nulls are three but we received only one null incase of 119908
1SSF as shown in Figure 15 The null depth level for
single and SEF is given in Table 8
Case d The main beam can be steered at any desired angleIf the user changes their position than the main beam can besteered in the desired direction Figure 16 shows the correctedpattern with recovered nulls at main beam pointing at 120579
119904=
110∘ The main beam can be steered in the direction of the
desired user at any particular angleThe array factor for 2119872+
1 sensors in terms of main beam direction 120579119904is given by
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp 119895119899119896119889 (cos 120579
119894minus cos 120579
119904) (17)
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0N
orm
aliz
ed A
F (d
B)
Original4th element failure3 nulls recovered
120579 (deg)
Figure 12 The original radiation pattern the 1199084sensor failure and
recovery of three nulls
where 120579119904is themain beam direction to which it can be steered
to the desired angles
5 Conclusion and Future Work
We have proposed symmetric sensor failure (SSF) techniquealong cultural algorithm with differential evolution for thecorrection of faulty arrays The null depth of all nullsespecially the first one has been achieved with the help ofSSF technique Null steering at their original positions andsidelobe reduction has been achieved by a cultural algorithmwith differential evolution and using a proper fitness functiondemanding the sidelobe reduction and null constraints Dueto 7th SSF the number of nulls is six and in 4th SSF theachievable nulls are three but in case of 119908
1SSF we received
The Scientific World Journal 9
Table 7 Recovery of three nulls
Comparison of NDL and SLL of 4th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus8756 minus221 minus8624 minus2264 1st null recoveredminus1027 minus237 minus9797 minus1965 2nd null recoveredminus8881 minus2111 minus9401 minus2001 3rd null recovered
Table 8 Recovery of one nulls
Comparison of NDL and SLL of 1199081sensor failure and SSF
Correction of 1199081sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1133 minus2002 minus1151 minus211 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original4th SSF3 nulls recovered
120579 (deg)
Figure 13 The original radiation pattern the 1199084SSF and recovery
of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 element failure
Figure 14 The original radiation pattern the 1199081sensor failure and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 SSF
Figure 15 The original radiation pattern the 1199081SSF and recovery
of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSFRecovered nulls
120579 (deg)
Figure 16 The corrected pattern with main beam pointing at 110∘with recovered nulls
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
4 The Scientific World Journal
Generate the initial population of individualsDo
For each individual 119895 in the populationChoose three numbers 119899
1 1198992 and 119899
3that is 1 le 119899
1 1198992 1198993le 119873 with 119899
1= 1198992= 1198993= 119895
Generate a random integer 119894rand isin (1119873)For each parameter 119894
119910119894119892= 1199091198991 119892 + 119865(119909
1198992 119892 minus 1199091198993 119892)
119911119894119892
119895=
119910119894119892
119895119894119891 rand() le CR 119900119903 119895 = 119895rand
119909119894119892
119895otherwise
End ForReplace 119909119894119892 with the child 119911119894119892 if 119911119894119892 is better
End ForUntil the termination condition is achieved
Pseudocode 1 The pseudocode of the differential evolution algorithm
integrated An acceptance function is used to generate beliefsby gleaning the experience of individuals from the populationspace In return this belief space can bias the evolution of thepopulation component by means of the influence functionThe belief space itself also evolves by the adjust function[23] In the present work the belief space is divided into twoknowledge components
321 Situational Knowledge Situational knowledge storesindividuals from population space which provides the direc-tion for other individuals Situational knowledge consists ofthe best example 119875 found along the evolutionary process Itrepresents a leader for the other individuals to follow Thevariation operators of differential evolution are influenced inthe following way
119910119894119892= 119875119894+ 119865 (119909
1198992119892minus 1199091198993119892) (5)
where 119875119894is the 119894th component of the individual stored in the
situational knowledge This way we use the leader instead ofa randomly chosen individual for the recombination gettingthe children closer to the best point found The update of thesituational knowledge is done by replacing the stored individ-ual 119875 by the best individual found in the current population119909best only if 119909best is better than 119875
322 Normative Knowledge The normative knowledge con-tains the intervals for the decision variables where goodsolutions have been found in order to move new solutionstowards those intervalsThe normative knowledge includes ascaling factor 119889119904
1to influence themutation operator adopted
in differential evolution The following expression shows theinfluence of the normative knowledge of the variation opera-tors
119911119894119892
119895=
1199091198991119892+ 119865 (119909
1198992119892minus 1199091198993119892) if 1199091198991 119892 lt 119897
119894
1199091198991119892minus 119865 (119909
1198992119892minus 1199091198993119892) if 1199091198991 119892 gt 119906
119894
1199091198991119892+ (
119906119894minus 119897119894
119889119904119894
) lowast 119865 (1199091198992119892minus 1199091198993119892) otherwise
(6)
where 119897119894and 119906
119894are the lower and upper bounds respectively
for the 119894th decision variable The update of the normativeknowledge can reduce or expand the intervals stored on itAn extension takes place when the accepted individuals donot fit in the current interval while a reduction occurs whenall the accepted individuals lie in the current interval andthe extreme values have an improved fit and are feasible Thevalues 119889119904
119894are updated with the difference (1199091198992119892minus1199091198993119892) found
of the variation operators of the prior generation Normativeknowledge leads individuals to jump into the good rangeif they are not already there The normative knowledge isupdated as follows let us consider 119909
1198861 1199091198862 1199091198863 119909
119886119899accepted
be the accepted individuals in the current generation and119909min
119894
and 119909max119894
belong to (1198861 1198862 1198863 119899accepted) and theaccepted individualswithminimumandmaximumvalues forthe parameter 119894
119906119894=
119909119894max119894
if 119909119894max119894
gt 119906119894or 119891 (119909max
119894
) lt 119880119894
119906119894
otherwise
119897119894=
119909119894min119894
if 119909119894min119894
lt 119897119894or 119891 (119909min
119894
) lt 119871119894
119897119894
otherwise
(7)
If 119897119894and 119906
119894are updated the values of 119871
119894and 119880
119894will be
done in the same way The 119889119904119894are updated with the greatest
difference of |1199091198941199031minus1199091198941199032| found during the variation operators
at the prior generationThe flow chart and pseudocode for CADE is shown in
Pseudocode 2 and Figure 3
33 Null Constraint (NC) A jamming signal located at a par-ticular angle wants to be eliminated in case of satellite radarand mobile communication applications For a uninformedarray to put a null at a particular angle 120579
119894 we want [24]
AF (120579119894) = w119867s (120579
119894) = 0 (8)
The Scientific World Journal 5
Generate the initial populationCalculate the initial populationInitialize the belief spaceDo
For each individual in the populationApply the variation operator influenced by a randomly knowledge componentCalculate the child generatedReplace the individual with child if the child is better
End forUpdate the belief space with the accepted individuals
Until the termination condition is achieved
Pseudocode 2 The pseudocode of the cultural algorithm
where
s (120579119894) =
[[[[[[[[[[[[[[
[
exp (minus119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
exp (minus119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp(119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp (119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
]]]]]]]]]]]]]]
]119873times1
(9)
and w119867 is119873 times 1 vector which is defined as
w = [119908minus119872 119908minus119872+1
1199080 119908
119872minus1 119908119872]119879 (10)
The null constraint is given as
w119867s (120579119894) = 0 119894 = 1 2 119872
0 (11)
We may define an119873 times1198720constraint matrix C as
C = [s (1205791) s (120579
2) s (120579
1198720
)] (12)
where 120579119894for 119894 = 1 2 119872
0is the direction of null Our
goal is to optimize the squared weighting error subject to thecondition that
w119867C = 0 (13)Our constraint is that the columns of C should be
orthogonal to theweight vectorw Accordinglywemaydefine119866119894 119894 = 1 2 and 119866 as follows
1198661=
119875
sum
119894=1
[1003816100381610038161003816AF119889(120579119894) minus AFCADE(120579119894)
1003816100381610038161003816]2 (14)
1198662=10038171003817100381710038171003817w119867C10038171003817100381710038171003817
2
(15)
119866 = 1198661+ 1198662 (16)
Hence 119866 is the fitness function for the problem givenabove which are to be minimized Best chromosome will givethe minimal value of 119866 The first term in (16) is used forSLL reduction where AF
119889(120579119894) represents the desired pattern
and AFCADE(120579119894) is the pattern obtained by using CADE Thesecond term in (16) is used for jammer suppression and place-ment of nulls at their original positions after sensor failure
4 Simulation Results
In the simulation a classical Dolph-Chebyshev linear arrayof 17 sensors with 1205822 intersensor spacing is used as the testantenna The array factor in this case represents a minus35 dBconstant SLL with the nulls at specific angles Analyticaltechniques are used to find out the nonuniform weights forclassical Dolph-Chebyshev array In case of sensor failurecultural algorithmwith differential evolution (CADE) is usedfor the reduction of sidelobes and placement of nulls in therequired positions
Case a At the first instant the 1199087sensor is assumed to fail
After sensor failure the radiation pattern is destroyed whichresults in an increase of the SLL and displacement of nullpositions In order to regain the symmetry its mirror sensorweight 119908
minus7is forced to zero We achieve the desired null
depth level (NDL) and deeper first null depth level (FNDL)as compared to that of nonsymmetric case The SLL rises tominus3232 dB due to the 119908
7sensor failure while due to SSF of
the 1199087sensor the SLL is minus2653 dB The advantage of SSF is
deeper nulls especially the first null The SLL and FNDL fora damage array of single sensor failure and SSF are shownin Table 2 It is clear from Figure 2 that SSF maintains betterFNDL as compared to that of single sensor failure
After optimization by a cultural algorithm with differen-tial evolution (CADE) the SLL of the 119908
7sensor failure are
reduced to minus3299 dB while due to SSF the SLL is reduced tominus2835 dB The recovery of one null due to 7th sensor failureand SSF to its original position 120579
1= 1993
∘ is shown inFigures 4 and 5The comparison of recovered patternwith 7thsensor and SSF for one null imposed is given in Table 3 Therecovered NDL of SSF is seven dB deeper than that of 7thsensor failure
Figures 6 and 7 show the recovery of two nulls at anglesof 1205791= 1993
∘ and 1205792= 3488
∘ respectively for 7th sensorfailure and SSF The SLL and NDL for the correspondingnulls are given in Table 4 The NDL of the SSF is deeper ascompared to the 7th sensor failure
Now we check the recovery of three nulls at the requiredpositions Figures 8 and 9 show the recovery of three nullsoriginally at angles of 120579
1= 1993
∘ 1205792= 3488
∘ and 1205793=
4544∘ for 7th sensor failure and SSF The SLL and NDL for
6 The Scientific World Journal
Table 2 Comparison of FNDL and SLL of the damaged pattern
Comparison of FNDL and SLL of damage pattern of 7th sensor and SSF7th sensor failure SSF
FNDL (dB) SLL (dB) FNDL (dB) SLL (dB)minus3232 minus2945 minus8898 minus2653
Table 3 Recovery of one null
Comparison of NDL and SLL of one sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1047 minus3299 minus1115 minus2835 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure1 null recovered
120579 (deg)
Figure 4The original radiation pattern the1199087sensor damage and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF1 nulls recovered
120579 (deg)
Figure 5The original radiation pattern the1199087SSF and recovery of
one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure2 nulls recovered
120579 (deg)
Figure 6The original radiation pattern the1199087sensor damage and
recovery of two nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF2 nulls recovered
120579 (deg)
Figure 7The original radiation pattern the1199087SSF and recovery of
two nulls
The Scientific World Journal 7
Table 4 Recovery of two nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus953 minus2987 minus1151 minus3112 1st null recoveredminus9365 minus3075 minus1014 2707 2nd null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure3 nulls recovered
120579 (deg)
Figure 8The original radiation pattern the1199087sensor damage and
recovery of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF3 nulls recovered
120579 (deg)
Figure 9 The original radiation pattern the 1199087SSF and recovery
of three nulls
the corresponding nulls are given in Table 5 The NDL of allnulls in SSF is deeper than that of 7th sensor failure
Now the recovery of five nulls for 7th sensor failure andSSF originally at positions 1993∘ 3488∘ 4544∘6202∘ and6894∘ is carried out and shown in Figures 10 and 11 A
comparison of SLL and NDL for the recovery of five nullsis given in Table 6 In each case SSF produces deeper nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure5 nulls recovered
120579 (deg)
Figure 10The original radiation pattern the1199087sensor damage and
recovery of five nulls
compared to the 7th sensor failure From simulation it isobserved that we have received deeper depth of nulls in SSFscenarios as compared to 7th sensor failure discussed above
Case b In this case we discuss the failure of 1199084sensor If the
sensor1199084fails due to any reason the whole radiation pattern
became damage After optimization the SLL reduces andnulls are steered back to their original positions as shown inFigure 12Then to create symmetry we also force119908
minus4equal to
zero to achieve the requirednull depth levelThe advantage ofsymmetry sensor failure is to get deeper null depth level Thenumber of nulls achieved in 7th symmetry sensor failure issix and in case of 4th symmetry sensor failure the number ofnulls received are three From the simulation results it is clearthat the number of nulls reduces by one as the sensors getdamage near the centre sensor After optimization by CADEthe SLL reduces and nulls are steered back to their previouspositions at angles 120579
1= 3489
∘ 1205792= 5431
∘ and 1205793= 689
∘ asshown in Figure 13 The null depth level for single and SEF isgiven in Table 7
Case c In this section we discuss the possibility of gettingfailure near the centre sensor if the sensor 119908
1fails due to
unforeseen reason From Figure 14 it is clear that its SLLincreases and nulls are damaged and also lose null depth Tocreate the symmetry we also force its mirror sensor weight119908minus1
equal to zero The one advantage of symmetry sensorfailure is to get the deeper null depth level and on the otherhand due to 119908
1SSF its beamwidth also decreases In case of
8 The Scientific World Journal
Table 5 Recovery of three nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1116 minus3632 minus1185 minus3459 1st null recoveredminus9757 minus3492 minus1056 minus3268 2nd null recoveredminus9501 minus281 minus1033 minus2419 3rd null recovered
Table 6 Recovery of five nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1127 minus3734 minus120 minus378 1st null recoveredminus9816 minus3531 minus1084 minus3493 2nd null recoveredminus9533 minus249 minus1053 minus2291 3rd null recoveredminus946 minus3642 minus1025 minus3227 4th null recoveredminus9739 minus2269 minus9968 minus25832 5th null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF5 nulls recovered
120579 (deg)
Figure 11 The original radiation pattern the 1199087SSF and recovery
of five nulls
7th symmetry sensor failure the nulls are six and in 4th SSFthe achievable nulls are three but we received only one null incase of 119908
1SSF as shown in Figure 15 The null depth level for
single and SEF is given in Table 8
Case d The main beam can be steered at any desired angleIf the user changes their position than the main beam can besteered in the desired direction Figure 16 shows the correctedpattern with recovered nulls at main beam pointing at 120579
119904=
110∘ The main beam can be steered in the direction of the
desired user at any particular angleThe array factor for 2119872+
1 sensors in terms of main beam direction 120579119904is given by
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp 119895119899119896119889 (cos 120579
119894minus cos 120579
119904) (17)
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0N
orm
aliz
ed A
F (d
B)
Original4th element failure3 nulls recovered
120579 (deg)
Figure 12 The original radiation pattern the 1199084sensor failure and
recovery of three nulls
where 120579119904is themain beam direction to which it can be steered
to the desired angles
5 Conclusion and Future Work
We have proposed symmetric sensor failure (SSF) techniquealong cultural algorithm with differential evolution for thecorrection of faulty arrays The null depth of all nullsespecially the first one has been achieved with the help ofSSF technique Null steering at their original positions andsidelobe reduction has been achieved by a cultural algorithmwith differential evolution and using a proper fitness functiondemanding the sidelobe reduction and null constraints Dueto 7th SSF the number of nulls is six and in 4th SSF theachievable nulls are three but in case of 119908
1SSF we received
The Scientific World Journal 9
Table 7 Recovery of three nulls
Comparison of NDL and SLL of 4th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus8756 minus221 minus8624 minus2264 1st null recoveredminus1027 minus237 minus9797 minus1965 2nd null recoveredminus8881 minus2111 minus9401 minus2001 3rd null recovered
Table 8 Recovery of one nulls
Comparison of NDL and SLL of 1199081sensor failure and SSF
Correction of 1199081sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1133 minus2002 minus1151 minus211 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original4th SSF3 nulls recovered
120579 (deg)
Figure 13 The original radiation pattern the 1199084SSF and recovery
of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 element failure
Figure 14 The original radiation pattern the 1199081sensor failure and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 SSF
Figure 15 The original radiation pattern the 1199081SSF and recovery
of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSFRecovered nulls
120579 (deg)
Figure 16 The corrected pattern with main beam pointing at 110∘with recovered nulls
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World Journal 5
Generate the initial populationCalculate the initial populationInitialize the belief spaceDo
For each individual in the populationApply the variation operator influenced by a randomly knowledge componentCalculate the child generatedReplace the individual with child if the child is better
End forUpdate the belief space with the accepted individuals
Until the termination condition is achieved
Pseudocode 2 The pseudocode of the cultural algorithm
where
s (120579119894) =
[[[[[[[[[[[[[[
[
exp (minus119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
exp (minus119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp(119895 (119873 minus 3
2) 119896119889 cos 120579
119894)
exp (119895 (119873 minus 1
2) 119896119889 cos 120579
119894)
]]]]]]]]]]]]]]
]119873times1
(9)
and w119867 is119873 times 1 vector which is defined as
w = [119908minus119872 119908minus119872+1
1199080 119908
119872minus1 119908119872]119879 (10)
The null constraint is given as
w119867s (120579119894) = 0 119894 = 1 2 119872
0 (11)
We may define an119873 times1198720constraint matrix C as
C = [s (1205791) s (120579
2) s (120579
1198720
)] (12)
where 120579119894for 119894 = 1 2 119872
0is the direction of null Our
goal is to optimize the squared weighting error subject to thecondition that
w119867C = 0 (13)Our constraint is that the columns of C should be
orthogonal to theweight vectorw Accordinglywemaydefine119866119894 119894 = 1 2 and 119866 as follows
1198661=
119875
sum
119894=1
[1003816100381610038161003816AF119889(120579119894) minus AFCADE(120579119894)
1003816100381610038161003816]2 (14)
1198662=10038171003817100381710038171003817w119867C10038171003817100381710038171003817
2
(15)
119866 = 1198661+ 1198662 (16)
Hence 119866 is the fitness function for the problem givenabove which are to be minimized Best chromosome will givethe minimal value of 119866 The first term in (16) is used forSLL reduction where AF
119889(120579119894) represents the desired pattern
and AFCADE(120579119894) is the pattern obtained by using CADE Thesecond term in (16) is used for jammer suppression and place-ment of nulls at their original positions after sensor failure
4 Simulation Results
In the simulation a classical Dolph-Chebyshev linear arrayof 17 sensors with 1205822 intersensor spacing is used as the testantenna The array factor in this case represents a minus35 dBconstant SLL with the nulls at specific angles Analyticaltechniques are used to find out the nonuniform weights forclassical Dolph-Chebyshev array In case of sensor failurecultural algorithmwith differential evolution (CADE) is usedfor the reduction of sidelobes and placement of nulls in therequired positions
Case a At the first instant the 1199087sensor is assumed to fail
After sensor failure the radiation pattern is destroyed whichresults in an increase of the SLL and displacement of nullpositions In order to regain the symmetry its mirror sensorweight 119908
minus7is forced to zero We achieve the desired null
depth level (NDL) and deeper first null depth level (FNDL)as compared to that of nonsymmetric case The SLL rises tominus3232 dB due to the 119908
7sensor failure while due to SSF of
the 1199087sensor the SLL is minus2653 dB The advantage of SSF is
deeper nulls especially the first null The SLL and FNDL fora damage array of single sensor failure and SSF are shownin Table 2 It is clear from Figure 2 that SSF maintains betterFNDL as compared to that of single sensor failure
After optimization by a cultural algorithm with differen-tial evolution (CADE) the SLL of the 119908
7sensor failure are
reduced to minus3299 dB while due to SSF the SLL is reduced tominus2835 dB The recovery of one null due to 7th sensor failureand SSF to its original position 120579
1= 1993
∘ is shown inFigures 4 and 5The comparison of recovered patternwith 7thsensor and SSF for one null imposed is given in Table 3 Therecovered NDL of SSF is seven dB deeper than that of 7thsensor failure
Figures 6 and 7 show the recovery of two nulls at anglesof 1205791= 1993
∘ and 1205792= 3488
∘ respectively for 7th sensorfailure and SSF The SLL and NDL for the correspondingnulls are given in Table 4 The NDL of the SSF is deeper ascompared to the 7th sensor failure
Now we check the recovery of three nulls at the requiredpositions Figures 8 and 9 show the recovery of three nullsoriginally at angles of 120579
1= 1993
∘ 1205792= 3488
∘ and 1205793=
4544∘ for 7th sensor failure and SSF The SLL and NDL for
6 The Scientific World Journal
Table 2 Comparison of FNDL and SLL of the damaged pattern
Comparison of FNDL and SLL of damage pattern of 7th sensor and SSF7th sensor failure SSF
FNDL (dB) SLL (dB) FNDL (dB) SLL (dB)minus3232 minus2945 minus8898 minus2653
Table 3 Recovery of one null
Comparison of NDL and SLL of one sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1047 minus3299 minus1115 minus2835 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure1 null recovered
120579 (deg)
Figure 4The original radiation pattern the1199087sensor damage and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF1 nulls recovered
120579 (deg)
Figure 5The original radiation pattern the1199087SSF and recovery of
one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure2 nulls recovered
120579 (deg)
Figure 6The original radiation pattern the1199087sensor damage and
recovery of two nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF2 nulls recovered
120579 (deg)
Figure 7The original radiation pattern the1199087SSF and recovery of
two nulls
The Scientific World Journal 7
Table 4 Recovery of two nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus953 minus2987 minus1151 minus3112 1st null recoveredminus9365 minus3075 minus1014 2707 2nd null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure3 nulls recovered
120579 (deg)
Figure 8The original radiation pattern the1199087sensor damage and
recovery of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF3 nulls recovered
120579 (deg)
Figure 9 The original radiation pattern the 1199087SSF and recovery
of three nulls
the corresponding nulls are given in Table 5 The NDL of allnulls in SSF is deeper than that of 7th sensor failure
Now the recovery of five nulls for 7th sensor failure andSSF originally at positions 1993∘ 3488∘ 4544∘6202∘ and6894∘ is carried out and shown in Figures 10 and 11 A
comparison of SLL and NDL for the recovery of five nullsis given in Table 6 In each case SSF produces deeper nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure5 nulls recovered
120579 (deg)
Figure 10The original radiation pattern the1199087sensor damage and
recovery of five nulls
compared to the 7th sensor failure From simulation it isobserved that we have received deeper depth of nulls in SSFscenarios as compared to 7th sensor failure discussed above
Case b In this case we discuss the failure of 1199084sensor If the
sensor1199084fails due to any reason the whole radiation pattern
became damage After optimization the SLL reduces andnulls are steered back to their original positions as shown inFigure 12Then to create symmetry we also force119908
minus4equal to
zero to achieve the requirednull depth levelThe advantage ofsymmetry sensor failure is to get deeper null depth level Thenumber of nulls achieved in 7th symmetry sensor failure issix and in case of 4th symmetry sensor failure the number ofnulls received are three From the simulation results it is clearthat the number of nulls reduces by one as the sensors getdamage near the centre sensor After optimization by CADEthe SLL reduces and nulls are steered back to their previouspositions at angles 120579
1= 3489
∘ 1205792= 5431
∘ and 1205793= 689
∘ asshown in Figure 13 The null depth level for single and SEF isgiven in Table 7
Case c In this section we discuss the possibility of gettingfailure near the centre sensor if the sensor 119908
1fails due to
unforeseen reason From Figure 14 it is clear that its SLLincreases and nulls are damaged and also lose null depth Tocreate the symmetry we also force its mirror sensor weight119908minus1
equal to zero The one advantage of symmetry sensorfailure is to get the deeper null depth level and on the otherhand due to 119908
1SSF its beamwidth also decreases In case of
8 The Scientific World Journal
Table 5 Recovery of three nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1116 minus3632 minus1185 minus3459 1st null recoveredminus9757 minus3492 minus1056 minus3268 2nd null recoveredminus9501 minus281 minus1033 minus2419 3rd null recovered
Table 6 Recovery of five nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1127 minus3734 minus120 minus378 1st null recoveredminus9816 minus3531 minus1084 minus3493 2nd null recoveredminus9533 minus249 minus1053 minus2291 3rd null recoveredminus946 minus3642 minus1025 minus3227 4th null recoveredminus9739 minus2269 minus9968 minus25832 5th null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF5 nulls recovered
120579 (deg)
Figure 11 The original radiation pattern the 1199087SSF and recovery
of five nulls
7th symmetry sensor failure the nulls are six and in 4th SSFthe achievable nulls are three but we received only one null incase of 119908
1SSF as shown in Figure 15 The null depth level for
single and SEF is given in Table 8
Case d The main beam can be steered at any desired angleIf the user changes their position than the main beam can besteered in the desired direction Figure 16 shows the correctedpattern with recovered nulls at main beam pointing at 120579
119904=
110∘ The main beam can be steered in the direction of the
desired user at any particular angleThe array factor for 2119872+
1 sensors in terms of main beam direction 120579119904is given by
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp 119895119899119896119889 (cos 120579
119894minus cos 120579
119904) (17)
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0N
orm
aliz
ed A
F (d
B)
Original4th element failure3 nulls recovered
120579 (deg)
Figure 12 The original radiation pattern the 1199084sensor failure and
recovery of three nulls
where 120579119904is themain beam direction to which it can be steered
to the desired angles
5 Conclusion and Future Work
We have proposed symmetric sensor failure (SSF) techniquealong cultural algorithm with differential evolution for thecorrection of faulty arrays The null depth of all nullsespecially the first one has been achieved with the help ofSSF technique Null steering at their original positions andsidelobe reduction has been achieved by a cultural algorithmwith differential evolution and using a proper fitness functiondemanding the sidelobe reduction and null constraints Dueto 7th SSF the number of nulls is six and in 4th SSF theachievable nulls are three but in case of 119908
1SSF we received
The Scientific World Journal 9
Table 7 Recovery of three nulls
Comparison of NDL and SLL of 4th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus8756 minus221 minus8624 minus2264 1st null recoveredminus1027 minus237 minus9797 minus1965 2nd null recoveredminus8881 minus2111 minus9401 minus2001 3rd null recovered
Table 8 Recovery of one nulls
Comparison of NDL and SLL of 1199081sensor failure and SSF
Correction of 1199081sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1133 minus2002 minus1151 minus211 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original4th SSF3 nulls recovered
120579 (deg)
Figure 13 The original radiation pattern the 1199084SSF and recovery
of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 element failure
Figure 14 The original radiation pattern the 1199081sensor failure and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 SSF
Figure 15 The original radiation pattern the 1199081SSF and recovery
of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSFRecovered nulls
120579 (deg)
Figure 16 The corrected pattern with main beam pointing at 110∘with recovered nulls
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
6 The Scientific World Journal
Table 2 Comparison of FNDL and SLL of the damaged pattern
Comparison of FNDL and SLL of damage pattern of 7th sensor and SSF7th sensor failure SSF
FNDL (dB) SLL (dB) FNDL (dB) SLL (dB)minus3232 minus2945 minus8898 minus2653
Table 3 Recovery of one null
Comparison of NDL and SLL of one sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1047 minus3299 minus1115 minus2835 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure1 null recovered
120579 (deg)
Figure 4The original radiation pattern the1199087sensor damage and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF1 nulls recovered
120579 (deg)
Figure 5The original radiation pattern the1199087SSF and recovery of
one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure2 nulls recovered
120579 (deg)
Figure 6The original radiation pattern the1199087sensor damage and
recovery of two nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF2 nulls recovered
120579 (deg)
Figure 7The original radiation pattern the1199087SSF and recovery of
two nulls
The Scientific World Journal 7
Table 4 Recovery of two nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus953 minus2987 minus1151 minus3112 1st null recoveredminus9365 minus3075 minus1014 2707 2nd null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure3 nulls recovered
120579 (deg)
Figure 8The original radiation pattern the1199087sensor damage and
recovery of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF3 nulls recovered
120579 (deg)
Figure 9 The original radiation pattern the 1199087SSF and recovery
of three nulls
the corresponding nulls are given in Table 5 The NDL of allnulls in SSF is deeper than that of 7th sensor failure
Now the recovery of five nulls for 7th sensor failure andSSF originally at positions 1993∘ 3488∘ 4544∘6202∘ and6894∘ is carried out and shown in Figures 10 and 11 A
comparison of SLL and NDL for the recovery of five nullsis given in Table 6 In each case SSF produces deeper nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure5 nulls recovered
120579 (deg)
Figure 10The original radiation pattern the1199087sensor damage and
recovery of five nulls
compared to the 7th sensor failure From simulation it isobserved that we have received deeper depth of nulls in SSFscenarios as compared to 7th sensor failure discussed above
Case b In this case we discuss the failure of 1199084sensor If the
sensor1199084fails due to any reason the whole radiation pattern
became damage After optimization the SLL reduces andnulls are steered back to their original positions as shown inFigure 12Then to create symmetry we also force119908
minus4equal to
zero to achieve the requirednull depth levelThe advantage ofsymmetry sensor failure is to get deeper null depth level Thenumber of nulls achieved in 7th symmetry sensor failure issix and in case of 4th symmetry sensor failure the number ofnulls received are three From the simulation results it is clearthat the number of nulls reduces by one as the sensors getdamage near the centre sensor After optimization by CADEthe SLL reduces and nulls are steered back to their previouspositions at angles 120579
1= 3489
∘ 1205792= 5431
∘ and 1205793= 689
∘ asshown in Figure 13 The null depth level for single and SEF isgiven in Table 7
Case c In this section we discuss the possibility of gettingfailure near the centre sensor if the sensor 119908
1fails due to
unforeseen reason From Figure 14 it is clear that its SLLincreases and nulls are damaged and also lose null depth Tocreate the symmetry we also force its mirror sensor weight119908minus1
equal to zero The one advantage of symmetry sensorfailure is to get the deeper null depth level and on the otherhand due to 119908
1SSF its beamwidth also decreases In case of
8 The Scientific World Journal
Table 5 Recovery of three nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1116 minus3632 minus1185 minus3459 1st null recoveredminus9757 minus3492 minus1056 minus3268 2nd null recoveredminus9501 minus281 minus1033 minus2419 3rd null recovered
Table 6 Recovery of five nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1127 minus3734 minus120 minus378 1st null recoveredminus9816 minus3531 minus1084 minus3493 2nd null recoveredminus9533 minus249 minus1053 minus2291 3rd null recoveredminus946 minus3642 minus1025 minus3227 4th null recoveredminus9739 minus2269 minus9968 minus25832 5th null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF5 nulls recovered
120579 (deg)
Figure 11 The original radiation pattern the 1199087SSF and recovery
of five nulls
7th symmetry sensor failure the nulls are six and in 4th SSFthe achievable nulls are three but we received only one null incase of 119908
1SSF as shown in Figure 15 The null depth level for
single and SEF is given in Table 8
Case d The main beam can be steered at any desired angleIf the user changes their position than the main beam can besteered in the desired direction Figure 16 shows the correctedpattern with recovered nulls at main beam pointing at 120579
119904=
110∘ The main beam can be steered in the direction of the
desired user at any particular angleThe array factor for 2119872+
1 sensors in terms of main beam direction 120579119904is given by
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp 119895119899119896119889 (cos 120579
119894minus cos 120579
119904) (17)
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0N
orm
aliz
ed A
F (d
B)
Original4th element failure3 nulls recovered
120579 (deg)
Figure 12 The original radiation pattern the 1199084sensor failure and
recovery of three nulls
where 120579119904is themain beam direction to which it can be steered
to the desired angles
5 Conclusion and Future Work
We have proposed symmetric sensor failure (SSF) techniquealong cultural algorithm with differential evolution for thecorrection of faulty arrays The null depth of all nullsespecially the first one has been achieved with the help ofSSF technique Null steering at their original positions andsidelobe reduction has been achieved by a cultural algorithmwith differential evolution and using a proper fitness functiondemanding the sidelobe reduction and null constraints Dueto 7th SSF the number of nulls is six and in 4th SSF theachievable nulls are three but in case of 119908
1SSF we received
The Scientific World Journal 9
Table 7 Recovery of three nulls
Comparison of NDL and SLL of 4th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus8756 minus221 minus8624 minus2264 1st null recoveredminus1027 minus237 minus9797 minus1965 2nd null recoveredminus8881 minus2111 minus9401 minus2001 3rd null recovered
Table 8 Recovery of one nulls
Comparison of NDL and SLL of 1199081sensor failure and SSF
Correction of 1199081sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1133 minus2002 minus1151 minus211 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original4th SSF3 nulls recovered
120579 (deg)
Figure 13 The original radiation pattern the 1199084SSF and recovery
of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 element failure
Figure 14 The original radiation pattern the 1199081sensor failure and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 SSF
Figure 15 The original radiation pattern the 1199081SSF and recovery
of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSFRecovered nulls
120579 (deg)
Figure 16 The corrected pattern with main beam pointing at 110∘with recovered nulls
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World Journal 7
Table 4 Recovery of two nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus953 minus2987 minus1151 minus3112 1st null recoveredminus9365 minus3075 minus1014 2707 2nd null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure3 nulls recovered
120579 (deg)
Figure 8The original radiation pattern the1199087sensor damage and
recovery of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF3 nulls recovered
120579 (deg)
Figure 9 The original radiation pattern the 1199087SSF and recovery
of three nulls
the corresponding nulls are given in Table 5 The NDL of allnulls in SSF is deeper than that of 7th sensor failure
Now the recovery of five nulls for 7th sensor failure andSSF originally at positions 1993∘ 3488∘ 4544∘6202∘ and6894∘ is carried out and shown in Figures 10 and 11 A
comparison of SLL and NDL for the recovery of five nullsis given in Table 6 In each case SSF produces deeper nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th element failure5 nulls recovered
120579 (deg)
Figure 10The original radiation pattern the1199087sensor damage and
recovery of five nulls
compared to the 7th sensor failure From simulation it isobserved that we have received deeper depth of nulls in SSFscenarios as compared to 7th sensor failure discussed above
Case b In this case we discuss the failure of 1199084sensor If the
sensor1199084fails due to any reason the whole radiation pattern
became damage After optimization the SLL reduces andnulls are steered back to their original positions as shown inFigure 12Then to create symmetry we also force119908
minus4equal to
zero to achieve the requirednull depth levelThe advantage ofsymmetry sensor failure is to get deeper null depth level Thenumber of nulls achieved in 7th symmetry sensor failure issix and in case of 4th symmetry sensor failure the number ofnulls received are three From the simulation results it is clearthat the number of nulls reduces by one as the sensors getdamage near the centre sensor After optimization by CADEthe SLL reduces and nulls are steered back to their previouspositions at angles 120579
1= 3489
∘ 1205792= 5431
∘ and 1205793= 689
∘ asshown in Figure 13 The null depth level for single and SEF isgiven in Table 7
Case c In this section we discuss the possibility of gettingfailure near the centre sensor if the sensor 119908
1fails due to
unforeseen reason From Figure 14 it is clear that its SLLincreases and nulls are damaged and also lose null depth Tocreate the symmetry we also force its mirror sensor weight119908minus1
equal to zero The one advantage of symmetry sensorfailure is to get the deeper null depth level and on the otherhand due to 119908
1SSF its beamwidth also decreases In case of
8 The Scientific World Journal
Table 5 Recovery of three nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1116 minus3632 minus1185 minus3459 1st null recoveredminus9757 minus3492 minus1056 minus3268 2nd null recoveredminus9501 minus281 minus1033 minus2419 3rd null recovered
Table 6 Recovery of five nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1127 minus3734 minus120 minus378 1st null recoveredminus9816 minus3531 minus1084 minus3493 2nd null recoveredminus9533 minus249 minus1053 minus2291 3rd null recoveredminus946 minus3642 minus1025 minus3227 4th null recoveredminus9739 minus2269 minus9968 minus25832 5th null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF5 nulls recovered
120579 (deg)
Figure 11 The original radiation pattern the 1199087SSF and recovery
of five nulls
7th symmetry sensor failure the nulls are six and in 4th SSFthe achievable nulls are three but we received only one null incase of 119908
1SSF as shown in Figure 15 The null depth level for
single and SEF is given in Table 8
Case d The main beam can be steered at any desired angleIf the user changes their position than the main beam can besteered in the desired direction Figure 16 shows the correctedpattern with recovered nulls at main beam pointing at 120579
119904=
110∘ The main beam can be steered in the direction of the
desired user at any particular angleThe array factor for 2119872+
1 sensors in terms of main beam direction 120579119904is given by
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp 119895119899119896119889 (cos 120579
119894minus cos 120579
119904) (17)
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0N
orm
aliz
ed A
F (d
B)
Original4th element failure3 nulls recovered
120579 (deg)
Figure 12 The original radiation pattern the 1199084sensor failure and
recovery of three nulls
where 120579119904is themain beam direction to which it can be steered
to the desired angles
5 Conclusion and Future Work
We have proposed symmetric sensor failure (SSF) techniquealong cultural algorithm with differential evolution for thecorrection of faulty arrays The null depth of all nullsespecially the first one has been achieved with the help ofSSF technique Null steering at their original positions andsidelobe reduction has been achieved by a cultural algorithmwith differential evolution and using a proper fitness functiondemanding the sidelobe reduction and null constraints Dueto 7th SSF the number of nulls is six and in 4th SSF theachievable nulls are three but in case of 119908
1SSF we received
The Scientific World Journal 9
Table 7 Recovery of three nulls
Comparison of NDL and SLL of 4th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus8756 minus221 minus8624 minus2264 1st null recoveredminus1027 minus237 minus9797 minus1965 2nd null recoveredminus8881 minus2111 minus9401 minus2001 3rd null recovered
Table 8 Recovery of one nulls
Comparison of NDL and SLL of 1199081sensor failure and SSF
Correction of 1199081sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1133 minus2002 minus1151 minus211 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original4th SSF3 nulls recovered
120579 (deg)
Figure 13 The original radiation pattern the 1199084SSF and recovery
of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 element failure
Figure 14 The original radiation pattern the 1199081sensor failure and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 SSF
Figure 15 The original radiation pattern the 1199081SSF and recovery
of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSFRecovered nulls
120579 (deg)
Figure 16 The corrected pattern with main beam pointing at 110∘with recovered nulls
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
8 The Scientific World Journal
Table 5 Recovery of three nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1116 minus3632 minus1185 minus3459 1st null recoveredminus9757 minus3492 minus1056 minus3268 2nd null recoveredminus9501 minus281 minus1033 minus2419 3rd null recovered
Table 6 Recovery of five nulls
Comparison of NDL and SLL of 7th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1127 minus3734 minus120 minus378 1st null recoveredminus9816 minus3531 minus1084 minus3493 2nd null recoveredminus9533 minus249 minus1053 minus2291 3rd null recoveredminus946 minus3642 minus1025 minus3227 4th null recoveredminus9739 minus2269 minus9968 minus25832 5th null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSF5 nulls recovered
120579 (deg)
Figure 11 The original radiation pattern the 1199087SSF and recovery
of five nulls
7th symmetry sensor failure the nulls are six and in 4th SSFthe achievable nulls are three but we received only one null incase of 119908
1SSF as shown in Figure 15 The null depth level for
single and SEF is given in Table 8
Case d The main beam can be steered at any desired angleIf the user changes their position than the main beam can besteered in the desired direction Figure 16 shows the correctedpattern with recovered nulls at main beam pointing at 120579
119904=
110∘ The main beam can be steered in the direction of the
desired user at any particular angleThe array factor for 2119872+
1 sensors in terms of main beam direction 120579119904is given by
AF (120579119894) =
119872
sum
119899=minus119872
119908119899exp 119895119899119896119889 (cos 120579
119894minus cos 120579
119904) (17)
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0N
orm
aliz
ed A
F (d
B)
Original4th element failure3 nulls recovered
120579 (deg)
Figure 12 The original radiation pattern the 1199084sensor failure and
recovery of three nulls
where 120579119904is themain beam direction to which it can be steered
to the desired angles
5 Conclusion and Future Work
We have proposed symmetric sensor failure (SSF) techniquealong cultural algorithm with differential evolution for thecorrection of faulty arrays The null depth of all nullsespecially the first one has been achieved with the help ofSSF technique Null steering at their original positions andsidelobe reduction has been achieved by a cultural algorithmwith differential evolution and using a proper fitness functiondemanding the sidelobe reduction and null constraints Dueto 7th SSF the number of nulls is six and in 4th SSF theachievable nulls are three but in case of 119908
1SSF we received
The Scientific World Journal 9
Table 7 Recovery of three nulls
Comparison of NDL and SLL of 4th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus8756 minus221 minus8624 minus2264 1st null recoveredminus1027 minus237 minus9797 minus1965 2nd null recoveredminus8881 minus2111 minus9401 minus2001 3rd null recovered
Table 8 Recovery of one nulls
Comparison of NDL and SLL of 1199081sensor failure and SSF
Correction of 1199081sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1133 minus2002 minus1151 minus211 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original4th SSF3 nulls recovered
120579 (deg)
Figure 13 The original radiation pattern the 1199084SSF and recovery
of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 element failure
Figure 14 The original radiation pattern the 1199081sensor failure and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 SSF
Figure 15 The original radiation pattern the 1199081SSF and recovery
of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSFRecovered nulls
120579 (deg)
Figure 16 The corrected pattern with main beam pointing at 110∘with recovered nulls
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
The Scientific World Journal 9
Table 7 Recovery of three nulls
Comparison of NDL and SLL of 4th sensor failure and SSFCorrection of 7th sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus8756 minus221 minus8624 minus2264 1st null recoveredminus1027 minus237 minus9797 minus1965 2nd null recoveredminus8881 minus2111 minus9401 minus2001 3rd null recovered
Table 8 Recovery of one nulls
Comparison of NDL and SLL of 1199081sensor failure and SSF
Correction of 1199081sensor failure Correction of SSF Recovery of nulls
NDL (dB) SLL (dB) NDL (dB) SLL (dB)minus1133 minus2002 minus1151 minus211 1st null recovered
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original4th SSF3 nulls recovered
120579 (deg)
Figure 13 The original radiation pattern the 1199084SSF and recovery
of three nulls
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 element failure
Figure 14 The original radiation pattern the 1199081sensor failure and
recovery of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original
1 null recovered
120579 (deg)
w1 SSF
Figure 15 The original radiation pattern the 1199081SSF and recovery
of one null
0 20 40 60 80 100 120 140 160 180minus120
minus100
minus80
minus60
minus40
minus20
0
Nor
mal
ized
AF
(dB)
Original7th SSFRecovered nulls
120579 (deg)
Figure 16 The corrected pattern with main beam pointing at 110∘with recovered nulls
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
10 The Scientific World Journal
only one null with reduced beamwidthThe simulation resultshows that as the faulty sensor gets near the central sensorthe number of nulls reduces by oneThe reduction in the cor-rected sidelobe level comes at the cost of broader main beamThe corrected pattern has beamwidth broader than that of theoriginal one Using the approach of symmetric sensor failurewith the reduction of the SLL we can steer single doubleand multiple nulls in the direction of known interferencesThis method can be extended to planar arrays
Conflict of Interests
The authors declare that there is no conflict of interestsregarding the publication of this paper
References
[1] S Applebaum ldquoAdaptive arraysrdquo IEEE Transactions on Anten-nas and Propagation vol 24 no 5 pp 585ndash598 1976
[2] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[3] F Zaman I M Qureshi J A Khan and Z U Khan ldquoAnapplication of artificial intelligence for the joint estimation ofamplitude and two-dimensional direction of arrival of far fieldsources using 2-L-shape arrayrdquo International Journal of Anten-nas and Propagation vol 2013 Article ID 593247 10 pages 2013
[4] F Zaman ldquoAmplitude and directional of arrival estimationcomparison between different techniquesrdquo Progress in Electro-magnetics Research B vol 39 pp 319ndash335 2012
[5] J A Hejres A Peng and J Hijres ldquoFast method for sidelobenulling in a partially adaptive linear array using the elementspositionsrdquo IEEE Antennas andWireless Propagation Letters vol6 pp 332ndash335 2007
[6] J A Hejres ldquoNull steering in phased arrays by controlling thepositions of selected elementsrdquo IEEE Transactions on Antennasand Propagation vol 52 no 11 pp 2891ndash2895 2004
[7] T J Peters ldquoA conjugate gradient-based algorithm to minimizethe sidelobe level of planar arrays with element failuresrdquo IEEETransactions on Antennas and Propagation vol 39 no 10 pp1497ndash1504 1991
[8] R J Mailloux ldquoArray failure correction with a digitally beam-formed arrayrdquo IEEE Transactions on Antennas and Propagationvol 44 no 12 pp 1543ndash1550 1996
[9] K Guney and S Basbug ldquoInterference suppression of linearantenna arrays by amplitude-only control using a bacterialforaging algorithmrdquo Progress in Electromagnetics Research vol79 pp 475ndash497 2008
[10] K Guney and M Onay ldquoAmplitude-only pattern nulling oflinear antenna arrays with the use of bees algorithmrdquo Progress inElectromagnetics Research vol 70 pp 21ndash36 2007
[11] H Li and B Himed ldquoTransmit subaperturing forMIMO radarswith co-located antennasrdquo IEEE Journal on Selected Topics inSignal Processing vol 4 no 1 pp 55ndash65 2010
[12] Y W Zhong L J Wang C Y Wang and H Zhang ldquoMulti-agent simulated annealing algorithm on differential evolutionalgorithmrdquo International Journal of Bio-Inspired Computationvol 4 no 4 pp 217ndash228 2012
[13] T J Choi C W Ahn and J An ldquoAn adaptive Cauchy differ-ential evolution algorithm for global numerical optimizationrdquo
The Scientific World Journal vol 2013 Article ID 969734 12pages 2013
[14] Y Wang Z Cai and Q Zhang ldquoDifferential evolution withcomposite trial vector generation strategies and control param-etersrdquo IEEE Transactions on Evolutionary Computation vol 15no 1 pp 55ndash66 2011
[15] O P Acharya A Patnaik and S N Sinha ldquoNull steering infailed antenna arraysrdquo Applied Computational Intelligence andSoft Computing vol 2011 Article ID 692197 9 pages 2011
[16] S U Khan I M Qureshi F Zaman and A Naveed ldquoNullplacement and sidelobe suppression in failed array usingsymmetrical element failure technique and hybrid heuristiccomputationrdquo Progress in Electromagnetics Research B vol 52pp 165ndash184 2013
[17] S U Khan I M Qureshi F Zaman A Basit and W KhanldquoApplication of firefly algorithm to fault finding in linear arraysantennardquoWorld Applied Sciences Journal vol 26 no 2 pp 232ndash238 2013
[18] R G Reynolds ldquoAn introduction to cultural algorithmsrdquo inEvolutionary Programming Proceedings of the Third AnnualConference A V Sebald and L J Fogel Eds pp 131ndash139 WorldScientific Publishing River Edge NJ USA 1994
[19] R G Reynolds and C Chung ldquoThe use of cultural algorithmsto evolve multi agent cooperationrdquo in Proceedings of the Micro-RobotWorld Cup Soccer Tournament pp 53ndash56 Taejon Repub-lic of Korea 1996
[20] X Jin and R G Reynolds ldquoUsing knowledge-based evolu-tionary computation to solve nonlinear constraint optimizationproblems a cultural algorithm approachrdquo in Proceedings ofthe Congress on Evolutionary Computation pp 1672ndash1678Washington DC USA 1999
[21] I Wolf ldquoDetermination of the radiating system which willproduce a specified directional characteristicrdquoProceedings of theInstitute of Radio Engineers vol 25 pp 630ndash643 1937
[22] R Storn and K Price ldquoDifferential evolution a simple and effi-cient adaptive scheme for global optimization over continuousspacesrdquo Tech Rep TR-95-012 International Computer ScienceInstitute Berkeley Calif USA 1995
[23] R L Becerra and C A C Coello ldquoCultured differentialevolution for constrained optimizationrdquo Computer Methods inApplied Mechanics and Engineering vol 195 no 33ndash36 pp4303ndash4322 2006
[24] H Steyskal R A Shore and R L Haupt ldquoMethods for nullcontrol and their effects on the radiation patternrdquo IEEETransac-tions on Antennas and Propagation vol 34 no 3 pp 404ndash4091986
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Submit your manuscripts athttpwwwhindawicom
Computer Games Technology
International Journal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Distributed Sensor Networks
International Journal of
Advances in
FuzzySystems
Hindawi Publishing Corporationhttpwwwhindawicom
Volume 2014
International Journal of
ReconfigurableComputing
Hindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Applied Computational Intelligence and Soft Computing
thinspAdvancesthinspinthinsp
Artificial Intelligence
HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014
Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Electrical and Computer Engineering
Journal of
Journal of
Computer Networks and Communications
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporation
httpwwwhindawicom Volume 2014
Advances in
Multimedia
International Journal of
Biomedical Imaging
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
ArtificialNeural Systems
Advances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
RoboticsJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Computational Intelligence and Neuroscience
Industrial EngineeringJournal of
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014
The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
Human-ComputerInteraction
Advances in
Computer EngineeringAdvances in
Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014
top related