fog computing-assisted energy-efficient resource...

Research ArticleFog Computing-Assisted Energy-Efficient Resource Allocationfor High-Mobility MIMO-OFDMA Networks

Lingyun Lu1 Tian Wang 1 Wei Ni2 Kai Li3 and Bo Gao1

1College of Computer Science Beijing Jiaotong University Beijing China2Cyber-Physical System Data61 CSIRO Australia3Real-Time and Embedded Computing Systems Research Centre (CISTER) 4249015 Porto Portugal

Correspondence should be addressed to Tian Wang 17120423bjtueducn

Received 3 May 2018 Accepted 27 June 2018 Published 11 July 2018

Academic Editor Fuhong Lin

Copyright copy 2018 Lingyun Lu 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

This paper presents a suboptimal approach for resource allocation of massive MIMO-OFDMA systems for high-speed train (HST)applications An optimization problem is formulated to alleviate the severe Doppler effect and maximize the energy efficiency (EE)of the systemWe propose to decouple the problem between the allocations of antennas subcarriers and transmit powers and solvethe problem by carrying out the allocations separately and iteratively in an alternatingmanner Fast convergence can be achieved forthe proposed approach within only several iterations Simulation results show that the proposed algorithm is superior to existingtechniques in terms of system EE and throughput in different system configurations of HST applications

1 Introduction

Recent development and deployment of high-speed trains(HSTs) have dramatically improved the efficiency and userexperience in interstate transportations However providinghigh data rates and good quality of service (QoS) to passen-gers in the presence of rapidly varying channel conditionsand scarce bandwidth availability is a challenging task [1]Critical challenges have arisen from real-time communica-tions between HSTs and fixed base stations (BS) Existingnarrow-band railway communication systems such as GSM-R are not suitable for HSTs due to typically low capacity5G technology is currently adopting a so-called networkdensification approach which involves the deployment of alarge number of base stations (BSs) to increase the networkcoverage and provide higher throughput to the users [2]Orthogonal-Frequency Division-Multiple-Access (OFDMA)has been extensively adopted for wideband communicationsbut severe Doppler shift exists in the communication processbecause of high mobility resulting in the difficulties inchannel estimation [3] and subsequently destructive inter-carrier interference (ICI) [4] On the other hand increasingthe number of antennas at both transmitters and receivers

also known asMultiple-InputMultiple-Output (MIMO) canimprove robustness against ICI Particularly MIMO witha large number of antennas has been increasingly studiedfor enhancing quality and reliability of wideband wirelesscommunications Unfortunately the benefits do not come forfree Energy consumption would grow substantially as thenumber of antennas increases An energy-efficient resourceallocation of MIMO-OFDMA is expected to balance spectralefficiency and energy efficiency (EE) [5]

There has been a lot of work on wireless resourceallocation in static and low-speed mobile system In [6] itwas revealed that network energy can be saved by assigningnonoverlapping frequency bands to different cells In [7] apower loading algorithm was proposed to maximize the EEofMIMO In [8] the authors investigated the energy-efficientbandwidth allocation in downlink flat fading OFDMA chan-nels and maximized the numbers of bits transmitted perjoule by using the Lagrangian and time-sharing techniquesIn [9] the authors proposed a hybrid structure of resourceallocation in OFDMA cellular systems which maximizedboth the EE and the downlink system capacityThe proposedstructure combined with resource allocation was shown toimprove the EE and the system capacity of OFDMA In [10]

HindawiWireless Communications and Mobile ComputingVolume 2018 Article ID 5296406 8 pageshttpsdoiorg10115520185296406

2 Wireless Communications and Mobile Computing

the resource allocation for energy-efficient OFDMA systemswas formulated as a mixed nonconvex and combinatorialoptimization problem and solved by exploiting fractionalprogramming In [11] the energy-efficient configuration ofspatial and frequency resources was studied to maximize theEE for downlink MIMO-OFDMA systems in the absence ofchannel state information (CSI) at the BS However none ofthe existing works have taken into account the destructiveICI For HSTs at a speed of over 500kmh the fast time-varying channel and the severe Doppler shift have yet to beaddressed and high-mobility communication shall be oneof the most important and extreme use scenarios in future5th generation (5G) mobile communication networks [12ndash16] The OFDMA resource allocation strategy was designedfor fast-changing mobile environments in [17] where asuboptimal allocation policy was developed at a significantcost of computational complexity

Fog computing also known as fogging is an architecturethat uses edge devices to carry out a substantial amountof local computation storage and communication [18ndash20]We use a fog server at the BS to concentrate data dataprocessing and applications The fog server can increaseoverall computing capability which helps in efficient resourceallocation and utilization

Fog computing emphasizes proximity to end-users andclient objectives dense geographical distribution and localresource pooling latency reduction and backbone band-width savings Therefore we use this technology to providepractical value for real-time implementation of HST commu-nications

This paper aims to design an efficient resource alloca-tion strategy to improve the communication performanceof HSTs After analyzing the multiuser MIMO-OFDMAdownlink system the influence of mobility on the system isquantified A mathematical model is put forth to maximizethe EE of the system To tackle the problem an iterativealgorithm with fast convergence is proposed Specifically wepropose to decouple the problem between the allocationsof antennas subcarriers and transmit powers and solvethe problem by carrying out the allocations separately anditeratively in an alternating manner Fast convergence canbe achieved for the proposed approach within only severaliterations Simulation results demonstrate the gain of theproposed approach in terms of EE and throughput ascompared with existing schemes

The rest of the paper is organized as follows We presentthe system model in Section 2 and formulate and solve theproblem of interest in Section 3 In Section 4 the simulationresults are provided followed by conclusions in Section 5

2 System Model

The system of interest is a multiuserMIMO-OFDMA systemas illustrated in Figure 1 where there is a fixed BS equippedwith 119872 transmit antennas (119872 ≫ 1) and 119870 user terminalslocated in aHSTA fog server is employed at the BS to help theresource allocation computation Each of the user equipmenthas a single receive antenna The users share radio resourcesfor down services Each of the user equipment has a single

Figure 1 Networks architecture for multiuser MIMO system

receive antenna The users share radio resources for downservices Different users are assigned with different OFDMsubcarriers and different antennas given the large number oftransmit antennas Coherent beamforming is carried out atthe BS to produce physical beams towards the users

The speed of HST can lead to severe Doppler shifts Letℎ119896119899 denote the complex channel gain between the BS anduser119896 on subcarrier 119899 The total number of subcarriers is 119873 Theknowledge on ℎ119896119899 can be inaccurate at the BS because of thefast-changingHST environment and hence estimation errorsWe assume

ℎ119896119899 = ℎ119896119899 + Δℎ119896119899 (1)

where ℎ119896119899 is the estimate of ℎ119896119899 at the BS and Δℎ119896119899 is anindependent and identically distributed (iid) measurementerror Δℎ119896119899 yields a complex Gaussian distribution due to theuse of theMinimumMean Square Error (MMSE) estimatorsΔℎ119896119899 sim 119873(120583 1205902119890 ) and

1205902119890 = 11 + (Δ119891119891119889) (1199011198961198991198990) (2)

where Δ119891 is the subcarrier interval and 119891119889 is the maximumDoppler shift which can be written as 119891119889 = 119881 sdot 119891119888119888 119888 is thespeed of light 119891119888 is the carrier frequency 119901119896119899 is the transmitpower allocated to user 119896 on subcarrier 119899 1198990 is the noisepower spectral density [10]

We assume that each subcarrier has an equal bandwidthof 119861 Therefore the total bandwidth of the system is 119861119905119900119905 =119873119861 We also assume that each subcarrier is assigned an equaltransmit power ie 119901119896119899 = 119875119896119887119896 = 119901119896 where 119887119896 and 119875119896 arethe number of subcarriers and the transmit power of the BSallocated to user 119896 respectively

The Doppler shift can compromise the orthogonalitybetween OFDM subcarriers resulting in ICI [22] At a speedof 119881 the power of ICI on a subcarrier can be written as [23]

119868119862119868 (119881) = 119873sum119899=1

(119879119904119891119889)22119873sum119895=1119895 =119899

1(119895 minus 119899)2 (3)

where 119879119878 denotes the duration of an OFDM symbol

Wireless Communications and Mobile Computing 3

In the case that 119872 997888rarr infin the receive signal-to-noiseratio (SNR) can be approximated to [17]

120588119896119899 asymp 119901119896119899119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868 (119881) (4)

where 119872119896 is the number of antennas of the BS assigned touser 119896

The asymptotic rate of the MIMO can be achieved basedon the random matrix theory [17] Specifically the rateasymptotically converges to the average rate in mean squareThe asymptotic rate can be replaced with the average datarate The total data rate of user 119896 converges to

119903119896 = 119887119896119861 log2(1 + 119901119896119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868 (119881)) (5)

We also consider nonideal circuit power at the BSWe canadopt a linear model [24] at the BS to characterize the circuitpower consumption as given by

120601 = 119875119888max119896

119872119896 + 119870sum119896=1

119887119896119901119896 + 1198750 (6)

where 119875119888 is the power consumption per active antennaconsisting of the power consumption of filtering mixingpower amplification and digital-to-analog conversion 1198750 isthe constant part of the power consumption at the BS and isindependent of the number of active antennas

3 Optimization Problem Formulation

The goal of this paper is to maximize the EE of the BS whichcan be formulated as

max119872119861119875

119876 (119872119861119875) = 119877 (119872119861119875)120601 (119872119861119875) st 1198621 119870sum

119896=1

119875119896 le 1198751198791198622 119903119896 ge 119877min1198623 119870sum

119896

119887119896 le 1198731198624 119872119896 le 119872

(7)

where given (5) and (6) the EE of the BS can be written as

119876 = 119877120601= sum119870119896=1 119887119896119861 log2 (1 + 119901119896119897119896119872119896 (1 minus 1205902119890 ) (1198990119861 + 119901119896119868119862119868119899 (119881)))

119875119888max119896 119872119896 + sum119870119896=1 119887119896119901119896 + 1198750 (8)

the vector 119861 = [1198871 1198872 119887119870]T collects the subcarrierallocation of all119870 users119872 = [11987211198722 119872119870]T collects the

antenna allocations for the users and 119875 = [1198751 1198752 119875119870]Tcollects the power allocations of the users The constraint C1specifies the total transmit power constraint 119875119879 C2 specifiesthe minimum data rate per user C3 and C4 restrict the totalnumbers of subcarriers and antennas respectively

Clearly problem (7) is a combinatorialmixed integer pro-gramming problem The objective of (7) also has a fractionalform with variables in the denominator of the objectiveAll this makes (7) a NP-hard nonconvex problem withpoor tractability In order to solve the problem efficientlywe develop a suboptimal solution where the subcarriersallocation antennas and transmit powers are optimizedseparately and sequentially in an alternating manner

31 Subcarrier Allocation Given119872 and119875 we first propose toallocate subcarriers to maximize the EE while satisfying theminimum data rates of the users According to the objectiveof (8) the subcarrier allocation can be expressed as

119887119896 = argmax119861

119876 (119872119861119875) (9)

We propose to allocate subcarriers based on the criterion ofEE First we calculate the number of subcarriers allocated toeach user according to the minimum data rate of the userThen we choose the user with the highest EE and allocate asubcarrier to the user one user after another and this repeatsuntil all users are allocated or all subcarriers are assignedThe proposed allocation of subcarriers can be summarizedin Algorithm 1

32 Transmit Power and Antenna Allocation Given thesubcarrier allocation developed in Section 31 problem (7)can be reformulated to a fractional programing problemwithrespect to119872 and 119875 as given by [25]

119865 (119902) = max 119877 (119872119875) minus 119902120601 (119872119875)st C1C2C4 (10)

This is mixed integer programming We proceed to relax theinteger constraint C4 ie 119872119896 to 119896 isin [119872min119872] 119872min isthe minimum number of antennas to meet the requirementsof uninterrupted transmission for all users [10] As a result(10) can be further reformulated as

max 119877 (119872119875) minus 119902120601 (119872119875)st 1198621 119870sum

119896=1

119875119896 le 1198751198791198622 119903119896 ge 119877min1198624 119896 isin [119872min119872]

(11)

where 119902 is the optimal solution for problem (10)


1 Initialization Initialize transmit power allocation vector1198750 = [11987510 11987520 sdot sdot sdot 1198751198700]T and antenna allocation

vector1198720 = [1198721011987220 sdot sdot sdot 1198721198700]T Then wecalculate each userrsquos initial data rate1198770 = [11990310 11990320 sdot sdot sdot 1199031198700]T

2 for user 119896 = 0 to 119870 do3 Calculate 119887119896 = lceil119877min1199030119896rceil4 end5 while sum119870119896 119887119896 gt 119873 do6 larr997888 argmax119896isin[12sdotsdotsdot 119870]119887119896 119887119896 larr997888 07 end8 while sum119870119896 119887119896 gt 119873 do

9 119876119896 = (119887119896 + 1)119861 log2(1 + 119901119896119897119896119872119896(1 minus 1205902119890 )(1198990119861 + 119901119896119868119862119868119899(119881)))119875119888max119896119872119896 + (119887119896 + 1)119901119896 + 1198750 minus 119887119896119861 log2(1 + 119901119896119897119896119872119896(1 minus 1205902119890 )(1198990119861 + 119901119896119868119862119868119899(119881)))119875119888max119896119872119896 + 119887119896119901119896 + 119875010 119894 larr997888 max119896119876119896 119887119894 = 119887119894 + 111 end

Output Subcarrier allocation policy 119861lowast

Algorithm 1

We can prove that (11) is a concave function by evaluatingthe Hessian matrix of minus119865(119902) as given by

[[[[[[

11988621198871198751198962ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2 minus 11988611988721198990

ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2minus 11988611988721198990ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2

11988611988721198990119872119896 (21198871198881198990 + 1198861198871198990119872119896 + 21198882119875119896 + 2119886119888119875119896119872119896)ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2 (1198990119887 + 119888119875119896)2

]]]]]] (12)

where 119886 = 119897119896(1 minus 1205902119890 ) 119887 = 119861119887119896 and 119888 = 119868119862119868(119881) Both thedeterminant of the Hessianmatrix and its 119896th order principalmatrix are nonnegative Thus the Hessian matrix is positivesemidefinite Hence minus119865(119902) is strictly convex As a result theobjective function of problem (11) is jointly concave over(119872119875) while all the constraints are linear In addition (11)yields the Slater conditions [26] and therefore holds strongduality The dual problem of (11) and the primary problem(11) have zero duality gap

Given 119902 the Lagrangian function can be written as

119871 (119872119875 120582 120583)= 120583(119875119879 minus 119870sum

119896=1

119875119896)

+ 119870sum119896=1

(1 + 120582119896) 119887119896119861 log2(1 + 119901119896119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868119899 (119881))

minus 119870sum119896=1

120582119896119877min minus 119902[119875119888max119896

119872119896 + 119870sum119896=1

119887119896119901119896 + 1198750]

(13)

where 120582 collects the Lagrange multipliers associated withconstraint C2 and 120582119896 ge 0 120583 ge 0 is the Lagrange multiplier

associated with constraint C1 The dual problem of (11) isgiven by

min120582120583ge0

max119872119875

119871 (119872119875 120582 120583) (14)

Given (120582 120583) according to the KKT conditions the opti-mal power allocation denoted by119875lowast and antenna allocationdenoted by119872lowast can be obtained as

119875lowast119896 = 119887radic(11988621198990119889 + 41198862119888 + 41198861198882) 1198990119889 minus 119886 minus 21198882119886119888 + 21198861198882 (15)

119872lowast119896 = lceil119887119896119861 (1 + 120582119896)119902119875119888 ln (2) minus 1120572119872 (119881)rceil (16)

where 119886 = 119897119896119872119896(1 minus 1205902119890 ) 119887 = 1198990119861119887119896 119888 = 119868119862119868(119881) 119889 = (119902 +120583) ln 2(1 +120582119896) and 120572119872(119881) = 119875119896119897119896(1 minus1205902119890 )(1198990119861+119875119896119868119862119868(119881))The subgradientmethod can be employed to obtain (120582 120583)

in an interactive manner as given by

120583 (119905 + 1) = [120583 (119905) minus 1205751 (119905) 1198711015840 (120583 (119905))]+ 120582119896 (119905 + 1) = [120582119896 (119905) minus 1205752 (119905) 1198711015840 (120582119896 (119905))]+

(17)


1 Initialization Set 120582 = 0 120583 = 02 repeat3 Initialize 119875lowast = 1198750119872lowast =11987204 repeat5 Update 119875lowast119872lowast according to (15) and (16) by

using antennas and power distribution strategies6 until 119871(119872119875120582 120583) converges7 Update 120582 and 120583 according to (17)8 until (14) converges

Output 119875lowast and119872lowast

Algorithm 2

1 Initialization Initialize 119902 = 0 and the maximumtolerance 120576 = 001

2 Solve (14) according to CA algorithm and obtainresource allocation policies 11987510158401198721015840

3 if 119877(11987210158401198751015840) minus 119902120601(11987210158401198751015840) lt 120576 then4 return (119872lowast119875lowast) = (11987210158401198751015840) the current

combination is the optimal combination5 else6 Set 119902 = 119877(11987210158401198751015840)120601(11987210158401198751015840)7 end

Output Resource allocation policies 119875lowast119872lowast andenergy efficiency 119902lowast

Algorithm 3

where [119909]+ = max 0 119909 119905 ge 0 is the index for the iterations1205751(119905) gt 0 and 1205752(119905) gt 0 are the step sizes to adjust 120583(119905)and 120582119896(119905) respectively and 1198711015840(120583(119905)) and 1198711015840(120582119896(119905)) are thesubgradients of the Lagrangian function at 120583(119905) and 120582119896(119905)respectively

The resource allocation policy can be developed basedon (15)ndash(17) Since (120582 120583) and (119872 119875) can be decoupled in(15) (16) and (17) we can use an improved coordinate ascent(CA) method where during each iteration we first optimize(119872 119875) given (120582 120583) and 119902 and then optimize (120582 120583) given(119872 119875) in an alternating fashion until convergence Given 119902the proposed allocation of transmit antennas and subcarriersis summarized in Algorithm 2

Finally we can use the Dinkelbachmethod [25] to update119902 The solution for problem (11) can be summarized inAlgorithm 3

4 Simulation Results

In this section we simulate the proposed algorithm to verifyits effectiveness where block Rayleigh fading channels areconsidered Other simulation parameters are listed in Table 1We note that the proposed algorithm can be applied underany channel conditions such as Rician fading channels

For comparison purpose the following two resourceallocation schemes are also stimulated

(1) Band allocation based on SNR (BABS) algorithm [27]it is used for subcarrier allocation The transmit powers and

Table 1 Simulation parameters

Parameter Notation ValueSpeed of electromagnetic wave 119888 3 times 108msNoise power spectral density 1198990 2 times 10minus7WHzMinimum data rate 30 times 107 bitsCenter carrier frequency 119891119888 26GHzSubcarriers number119873 64Total Bandwidth Btot 5MHzPower consumption per antenna 119875119888 30dBm [21]Static power consumption 1198750 40dBm [21]Minimum antenna119872min 24 [8]Maximum antenna119872max 100

0 1 2 3 4 5 6 7 8 9Iteration Numbers

0

02

04

06

08

1

12

14

16

18

2

EE (b

itJo

ule)

Pt=42dBmPt=24dBmPt=12dBm

Max EE Pt=42dBmMax EE Pt=24dBmMax EE Pt=12dBm

times106

Figure 2 System EE versus iteration numbers for different transmitpower with 119870 = 20119873 = 64 119881 = 500kmh

antennas are allocated in the same way as in the proposedalgorithm

(2) EMMPA algorithm [28] this algorithm first allocatessubcarriers evenly and then allocates the rest of subcarriersto the users with the best channel condition The schemedeveloped in [26] is used for the transmit power and antennaallocation

Figure 2 shows the convergence of the proposed algo-rithm with different transmit powers where119870 = 20119873 = 64and 119881 = 500kmh It is seen that the EE of the proposedalgorithm increases and quickly stabilizes with the growthof iterations The maximum of the EE can be attained afteraround only six iterations

Figure 3 plots the system EE versus the maximum trans-mit power where 119870 = 20 and 119881 = 500kmh We cansee that the system EE increases with maximum transmitpower When the transmit power is large enough the systemEE stabilizes This is because the BS does not need toactivate extra antennas or consume extra power when the


Max Transport Power (dBm)

05

1

15

2

EE (b

itJo

ule)

EMMPAProposed AlgorithmBABS

times106

0 10 20 30 40 50 60

Figure 3 System EE versus maximum transmit power with119870 = 20119881 = 500kmh

system maximum EE is reached The figure also shows thatour proposed algorithm performs between the BABS andEMMPA algorithms The system EE of EMMPA is higherthan our proposed algorithm since EMMPA does not havethe constraint of 119875119879 and thus has a fixed EE value Addi-tionally EMMPA is an unconstrained problem to maximizethe system EE The system EE of our proposed algorithm ishigher than that of the BABS algorithm because our approachis based on the maximization of EE while the BABS is basedon the minimization of SNR

Figure 4 presents the system throughput versus the mov-ing speed119881 where119875119879 = 40dBm and119870 = 20 We can see thatas119881 increases the system throughput significantly decreasesThis is because ICI power and channel estimation error areincreasingly severe and thus increasingly detrimental to com-munication quality The system throughput is about 207higher under our proposed algorithm than under BABSalgorithm EMMPA provides the lowest throughput becauseof its nature of an unconstrained optimization of maximizingEE without constraints BABS is to minimize the transmitpower while allocating subcarriers The conclusion drawnis that our proposed algorithm can significantly improvethroughput

Figure 5 shows the system EE versus the number of users119870 where 119875119879 = 40dBm and 119881 = 500kmh It can be seenthat the system EE decreases with the number of users Thisis because when the number of subcarriers is fixed each usercan be allocatedwith a less number of subcarriers resulting inan increase of the transmit powers to satisfy the users data raterequirement EMMPA has no demand for the data rate butthe subcarriers assigned to the users who have better channelconditions decrease and thus system EE also decreases

Moving Speed (kmh)

4

6

8

10

12

14

16

18

Thro

ughp

ut (M

bits

)

Proposed AlgorithmBABSEMMPA

300 350 400 450 500

Figure 4 System throughput versus the moving speed with 119875119879 =40dBm 119870 = 20

Number of Users

0

05

1

15

2

25

EE (b

itJo

ule)


times106

10 20 30 40 50 60 70 80 90 100

Figure 5 System EE versus number of users with 119875119879 = 40dBm119881 = 500kmh

5 Conclusion

This paper models the resource allocation strategy for mul-tiuser MIMO-OFDMA downlink system for HSTs wheresubcarriers transmit power and antennas are jointly opti-mized Specifically we propose an iterative suboptimal algo-rithm to optimize the system EE with fast convergence Interms of the system performance simulation results show


that both EE and throughput are improved Furthermore theproposed approach is able to fast stabilize within only severaliterations and therefore provides practical value for real-timeimplementation of HST communications

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request Noadditional data are available

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

This project is supported by the National Natural ScienceFoundation of China (Grant no 61771002)

References

[1] A O Laiyemo P Luoto P Pirinen and M Latva-Aho ldquoFeasi-bility studies on the use of higher frequency bands and beam-forming selection scheme for high speed train communicationrdquoWireless Communications andMobile Computing vol 2017 2017

[2] DThembelihle M Rossi and DMunaretto ldquoSoftwarization ofMobile Network Functions towards Agile and Energy Efficient5G Architectures A Surveyrdquo Wireless Communications andMobile Computing vol 2017 2017

[3] C Zhang P Fan Y Dong and K Xiong ldquoService-based high-speed railway base station arrangementrdquoWireless Communica-tions and Mobile Computing vol 15 no 13 pp 1681ndash1694 2015

[4] D Gesbert S Hanly H Huang S Shamai Shitz O SimeoneandW Yu ldquoMulti-cellMIMO cooperative networks a new lookat interferencerdquo IEEE Journal on Selected Areas in Communica-tions vol 28 no 9 pp 1380ndash1408 2010

[5] I Chih-Lin C Rowell S Han Z Xu G Li and Z Pan ldquoTowardgreen and soft a 5G perspectiverdquo IEEE Communications Maga-zine vol 52 no 2 pp 66ndash73 2014

[6] OHolland V Friderikos andAH Aghvami ldquoGreen spectrummanagement for mobile operatorsrdquo in Proceedings of the 2010Ieee Globecom Workshops pp 1458ndash1463 Miami FL USADecember 2010

[7] R S Prabhu and B Daneshrad ldquoEnergy-efficient power loadingfor a MIMO-SVD system and its performance in flat fadingrdquoin Proceedings of the 53rd IEEE Global Communications Con-ference GLOBECOM 2010 IEEE Miami FL USA December2010

[8] A Akbari R Hoshyar and R Tafazolli ldquoEnergy-efficientresource allocation inwireless OFDMA systemsrdquo in Proceedingsof the IEEE 21st International Symposium on Personal Indoorand Mobile Radio Communications (PIMRC rsquo10) pp 1731ndash1735IEEE Instanbul Turkey September 2010

[9] X Xiao X Tao Y Jia and J Lu ldquoAn energy-efficient hybridstructure with resource allocation in OFDMA networksrdquo inProceedings of the 2011 IEEE Wireless Communications andNetworking Conference WCNC 2011 pp 1466ndash1470 MexicoMarch 2011

[10] DW K Ng E S Lo and R Schober ldquoEnergy-efficient resourceallocation in OFDMA systems with large numbers of base sta-tion antennasrdquo IEEE Transactions onWireless Communicationsvol 11 no 9 pp 3292ndash3304 2012

[11] G Y Li Z Xu C Xiong et al ldquoEnergy-efficient wireless com-munications tutorial survey and open issuesrdquo IEEE WirelessCommunications Magazine vol 18 no 6 pp 28ndash34 2011

[12] K Xiong P Fan Y Zhang and K Ben Letaief ldquoTowards5G High Mobility A Fairness-Adjustable Time-Domain PowerAllocation Approachrdquo IEEE Access vol 5 pp 11817ndash11831 2017

[13] Y Lu K Xiong P Fan and Z Zhong ldquoOptimal MulticellCoordinated Beamforming for Downlink High-Speed RailwayCommunicationsrdquo IEEE Transactions on Vehicular Technologyvol 66 no 10 pp 9603ndash9608 2017

[14] K Xiong Y Zhang P Fan H-C Yang and X Zhou ldquoMobileService Amount Based Link Scheduling for High-MobilityCooperative Vehicular Networksrdquo IEEE Transactions on Vehic-ular Technology vol 66 no 10 pp 9521ndash9533 2017

[15] T Li K Xiong P Fan and K B Letaief ldquoService-OrientedPower Allocation for High-Speed Railway Wireless Communi-cationsrdquo IEEE Access vol 5 pp 8343ndash8356 2017

[16] K Xiong B Wang C Jiang and K J R Liu ldquoA BroadBeamforming Approach for High-Mobility CommunicationsrdquoIEEE Transactions on Vehicular Technology vol 66 no 11 pp10546ndash10550 2017

[17] R Couillet and M Debbah Random Matrix Methods for Wire-less Communications Cambridge University Press CambridgeUK 2011

[18] X Lyu H Tian W Ni Y Zhang P Zhang and R PLiu ldquoEnergy-Efficient Admission of Delay-Sensitive Tasks forMobile Edge Computingrdquo IEEE Transactions on Communica-tions vol 66 no 6 pp 2603ndash2616 2018

[19] X Lyu W Ni H Tian et al ldquoOptimal schedule of mobile edgecomputing for internet of things using partial informationrdquoIEEE Journal on Selected Areas in Communications vol 35 no11 pp 2606ndash2615 2017

[20] X Lyu C Ren W Ni H Tian and R P Liu ldquoDistributedOptimization of Collaborative Regions in Large-Scale Inhomo-geneous Fog Computingrdquo IEEE Journal on Selected Areas inCommunications vol 36 no 3 pp 574ndash586 2018

[21] T M Nguyen V N Ha and L Bao Le ldquoResource allocationoptimization in multi-user multi-cell massive MIMO networksconsidering pilot contaminationrdquo IEEE Access vol 3 pp 1272ndash1287 2015

[22] Y Zhao X Li Y Li and H Ji ldquoResource allocation for high-speed railway downlinkMIMO-OFDMsystemusing quantum-behaved particle swarmoptimizationrdquo inProceedings of the 2013IEEE International Conference on Communications ICC 2013pp 2343ndash2347 Hungary June 2013

[23] TWang J G Proakis E Masry and J R Zeidler ldquoPerformancedegradation of OFDM systems due to doppler spreadingrdquo IEEETransactions on Wireless Communications vol 5 no 6 pp1422ndash1432 2006

[24] T M Nguyen and L B Le ldquoJoint pilot assignment and resourceallocation in multicell massive MIMO network Throughputand energy efficiency maximizationrdquo in Proceedings of the 2015IEEE Wireless Communications and Networking ConferenceWCNC 2015 pp 393ndash398 IEEE NewOrleans LA USAMarch2015

[25] W Dinkelbach ldquoOn nonlinear fractional programmingrdquoMan-agement Science vol 13 no 7 pp 492ndash498 1967


[26] S Boyd andLVandenbergheConvexOptimization CambridgeUniversity Press 2004

[27] D Kivanc G Li and H Liu ldquoComputationally efficientbandwidth allocation and power control for OFDMArdquo IEEETransactions onWireless Communications vol 2 no 6 pp 1150ndash1158 2003

[28] G Miao ldquoEnergy-efficient uplink multi-user MIMOrdquo IEEETransactions on Wireless Communications vol 12 no 5 pp2302ndash2313 2013

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the resource allocation for energy-efficient OFDMA systemswas formulated as a mixed nonconvex and combinatorialoptimization problem and solved by exploiting fractionalprogramming In [11] the energy-efficient configuration ofspatial and frequency resources was studied to maximize theEE for downlink MIMO-OFDMA systems in the absence ofchannel state information (CSI) at the BS However none ofthe existing works have taken into account the destructiveICI For HSTs at a speed of over 500kmh the fast time-varying channel and the severe Doppler shift have yet to beaddressed and high-mobility communication shall be oneof the most important and extreme use scenarios in future5th generation (5G) mobile communication networks [12ndash16] The OFDMA resource allocation strategy was designedfor fast-changing mobile environments in [17] where asuboptimal allocation policy was developed at a significantcost of computational complexity

Fog computing also known as fogging is an architecturethat uses edge devices to carry out a substantial amountof local computation storage and communication [18ndash20]We use a fog server at the BS to concentrate data dataprocessing and applications The fog server can increaseoverall computing capability which helps in efficient resourceallocation and utilization

Fog computing emphasizes proximity to end-users andclient objectives dense geographical distribution and localresource pooling latency reduction and backbone band-width savings Therefore we use this technology to providepractical value for real-time implementation of HST commu-nications

This paper aims to design an efficient resource alloca-tion strategy to improve the communication performanceof HSTs After analyzing the multiuser MIMO-OFDMAdownlink system the influence of mobility on the system isquantified A mathematical model is put forth to maximizethe EE of the system To tackle the problem an iterativealgorithm with fast convergence is proposed Specifically wepropose to decouple the problem between the allocationsof antennas subcarriers and transmit powers and solvethe problem by carrying out the allocations separately anditeratively in an alternating manner Fast convergence canbe achieved for the proposed approach within only severaliterations Simulation results demonstrate the gain of theproposed approach in terms of EE and throughput ascompared with existing schemes

The rest of the paper is organized as follows We presentthe system model in Section 2 and formulate and solve theproblem of interest in Section 3 In Section 4 the simulationresults are provided followed by conclusions in Section 5

2 System Model

The system of interest is a multiuserMIMO-OFDMA systemas illustrated in Figure 1 where there is a fixed BS equippedwith 119872 transmit antennas (119872 ≫ 1) and 119870 user terminalslocated in aHSTA fog server is employed at the BS to help theresource allocation computation Each of the user equipmenthas a single receive antenna The users share radio resourcesfor down services Each of the user equipment has a single

Figure 1 Networks architecture for multiuser MIMO system

receive antenna The users share radio resources for downservices Different users are assigned with different OFDMsubcarriers and different antennas given the large number oftransmit antennas Coherent beamforming is carried out atthe BS to produce physical beams towards the users

The speed of HST can lead to severe Doppler shifts Letℎ119896119899 denote the complex channel gain between the BS anduser119896 on subcarrier 119899 The total number of subcarriers is 119873 Theknowledge on ℎ119896119899 can be inaccurate at the BS because of thefast-changingHST environment and hence estimation errorsWe assume

ℎ119896119899 = ℎ119896119899 + Δℎ119896119899 (1)

where ℎ119896119899 is the estimate of ℎ119896119899 at the BS and Δℎ119896119899 is anindependent and identically distributed (iid) measurementerror Δℎ119896119899 yields a complex Gaussian distribution due to theuse of theMinimumMean Square Error (MMSE) estimatorsΔℎ119896119899 sim 119873(120583 1205902119890 ) and

1205902119890 = 11 + (Δ119891119891119889) (1199011198961198991198990) (2)

where Δ119891 is the subcarrier interval and 119891119889 is the maximumDoppler shift which can be written as 119891119889 = 119881 sdot 119891119888119888 119888 is thespeed of light 119891119888 is the carrier frequency 119901119896119899 is the transmitpower allocated to user 119896 on subcarrier 119899 1198990 is the noisepower spectral density [10]

We assume that each subcarrier has an equal bandwidthof 119861 Therefore the total bandwidth of the system is 119861119905119900119905 =119873119861 We also assume that each subcarrier is assigned an equaltransmit power ie 119901119896119899 = 119875119896119887119896 = 119901119896 where 119887119896 and 119875119896 arethe number of subcarriers and the transmit power of the BSallocated to user 119896 respectively

The Doppler shift can compromise the orthogonalitybetween OFDM subcarriers resulting in ICI [22] At a speedof 119881 the power of ICI on a subcarrier can be written as [23]

119868119862119868 (119881) = 119873sum119899=1

(119879119904119891119889)22119873sum119895=1119895 =119899

1(119895 minus 119899)2 (3)

where 119879119878 denotes the duration of an OFDM symbol



120588119896119899 asymp 119901119896119899119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868 (119881) (4)



119903119896 = 119887119896119861 log2(1 + 119901119896119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868 (119881)) (5)


120601 = 119875119888max119896

119872119896 + 119870sum119896=1

119887119896119901119896 + 1198750 (6)




max119872119861119875

119876 (119872119861119875) = 119877 (119872119861119875)120601 (119872119861119875) st 1198621 119870sum

119896=1

119875119896 le 1198751198791198622 119903119896 ge 119877min1198623 119870sum

119896

119887119896 le 1198731198624 119872119896 le 119872

(7)


119876 = 119877120601= sum119870119896=1 119887119896119861 log2 (1 + 119901119896119897119896119872119896 (1 minus 1205902119890 ) (1198990119861 + 119901119896119868119862119868119899 (119881)))

119875119888max119896 119872119896 + sum119870119896=1 119887119896119901119896 + 1198750 (8)





119887119896 = argmax119861

119876 (119872119861119875) (9)



119865 (119902) = max 119877 (119872119875) minus 119902120601 (119872119875)st C1C2C4 (10)


max 119877 (119872119875) minus 119902120601 (119872119875)st 1198621 119870sum

119896=1

119875119896 le 1198751198791198622 119903119896 ge 119877min1198624 119896 isin [119872min119872]

(11)








Algorithm 1


[[[[[[

11988621198871198751198962ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2 minus 11988611988721198990

ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2minus 11988611988721198990ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2

11988611988721198990119872119896 (21198871198881198990 + 1198861198871198990119872119896 + 21198882119875119896 + 2119886119888119875119896119872119896)ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2 (1198990119887 + 119888119875119896)2

]]]]]] (12)



119871 (119872119875 120582 120583)= 120583(119875119879 minus 119870sum

119896=1

119875119896)

+ 119870sum119896=1

(1 + 120582119896) 119887119896119861 log2(1 + 119901119896119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868119899 (119881))

minus 119870sum119896=1

120582119896119877min minus 119902[119875119888max119896

119872119896 + 119870sum119896=1

119887119896119901119896 + 1198750]

(13)



min120582120583ge0

max119872119875

119871 (119872119875 120582 120583) (14)






120583 (119905 + 1) = [120583 (119905) minus 1205751 (119905) 1198711015840 (120583 (119905))]+ 120582119896 (119905 + 1) = [120582119896 (119905) minus 1205752 (119905) 1198711015840 (120582119896 (119905))]+

(17)





Algorithm 2






Algorithm 3











0

02

04

06

08

1

12

14

16

18

2

EE (b

itJo

ule)



times106








05

1

15

2

EE (b

itJo

ule)


times106

0 10 20 30 40 50 60





Moving Speed (kmh)

4

6

8

10

12

14

16

18

Thro

ughp

ut (M

bits

)


300 350 400 450 500


Number of Users

0

05

1

15

2

25

EE (b

itJo

ule)


times106

10 20 30 40 50 60 70 80 90 100


5 Conclusion




Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




120588119896119899 asymp 119901119896119899119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868 (119881) (4)



119903119896 = 119887119896119861 log2(1 + 119901119896119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868 (119881)) (5)


120601 = 119875119888max119896

119872119896 + 119870sum119896=1

119887119896119901119896 + 1198750 (6)




max119872119861119875

119876 (119872119861119875) = 119877 (119872119861119875)120601 (119872119861119875) st 1198621 119870sum

119896=1

119875119896 le 1198751198791198622 119903119896 ge 119877min1198623 119870sum

119896

119887119896 le 1198731198624 119872119896 le 119872

(7)


119876 = 119877120601= sum119870119896=1 119887119896119861 log2 (1 + 119901119896119897119896119872119896 (1 minus 1205902119890 ) (1198990119861 + 119901119896119868119862119868119899 (119881)))

119875119888max119896 119872119896 + sum119870119896=1 119887119896119901119896 + 1198750 (8)





119887119896 = argmax119861

119876 (119872119861119875) (9)



119865 (119902) = max 119877 (119872119875) minus 119902120601 (119872119875)st C1C2C4 (10)


max 119877 (119872119875) minus 119902120601 (119872119875)st 1198621 119870sum

119896=1

119875119896 le 1198751198791198622 119903119896 ge 119877min1198624 119896 isin [119872min119872]

(11)








Algorithm 1


[[[[[[

11988621198871198751198962ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2 minus 11988611988721198990

ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2minus 11988611988721198990ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2

11988611988721198990119872119896 (21198871198881198990 + 1198861198871198990119872119896 + 21198882119875119896 + 2119886119888119875119896119872119896)ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2 (1198990119887 + 119888119875119896)2

]]]]]] (12)



119871 (119872119875 120582 120583)= 120583(119875119879 minus 119870sum

119896=1

119875119896)

+ 119870sum119896=1

(1 + 120582119896) 119887119896119861 log2(1 + 119901119896119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868119899 (119881))

minus 119870sum119896=1

120582119896119877min minus 119902[119875119888max119896

119872119896 + 119870sum119896=1

119887119896119901119896 + 1198750]

(13)



min120582120583ge0

max119872119875

119871 (119872119875 120582 120583) (14)






120583 (119905 + 1) = [120583 (119905) minus 1205751 (119905) 1198711015840 (120583 (119905))]+ 120582119896 (119905 + 1) = [120582119896 (119905) minus 1205752 (119905) 1198711015840 (120582119896 (119905))]+

(17)





Algorithm 2






Algorithm 3











0

02

04

06

08

1

12

14

16

18

2

EE (b

itJo

ule)



times106








05

1

15

2

EE (b

itJo

ule)


times106

0 10 20 30 40 50 60





Moving Speed (kmh)

4

6

8

10

12

14

16

18

Thro

ughp

ut (M

bits

)


300 350 400 450 500


Number of Users

0

05

1

15

2

25

EE (b

itJo

ule)


times106

10 20 30 40 50 60 70 80 90 100


5 Conclusion




Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








Algorithm 1


[[[[[[

11988621198871198751198962ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2 minus 11988611988721198990

ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2minus 11988611988721198990ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2

11988611988721198990119872119896 (21198871198881198990 + 1198861198871198990119872119896 + 21198882119875119896 + 2119886119888119875119896119872119896)ln 2 (1198990119887 + 119888119875119896 + 119886119875119896119872119896)2 (1198990119887 + 119888119875119896)2

]]]]]] (12)



119871 (119872119875 120582 120583)= 120583(119875119879 minus 119870sum

119896=1

119875119896)

+ 119870sum119896=1

(1 + 120582119896) 119887119896119861 log2(1 + 119901119896119897119896119872119896 (1 minus 1205902119890 )1198990119861 + 119901119896119868119862119868119899 (119881))

minus 119870sum119896=1

120582119896119877min minus 119902[119875119888max119896

119872119896 + 119870sum119896=1

119887119896119901119896 + 1198750]

(13)



min120582120583ge0

max119872119875

119871 (119872119875 120582 120583) (14)






120583 (119905 + 1) = [120583 (119905) minus 1205751 (119905) 1198711015840 (120583 (119905))]+ 120582119896 (119905 + 1) = [120582119896 (119905) minus 1205752 (119905) 1198711015840 (120582119896 (119905))]+

(17)





Algorithm 2






Algorithm 3











0

02

04

06

08

1

12

14

16

18

2

EE (b

itJo

ule)



times106








05

1

15

2

EE (b

itJo

ule)


times106

0 10 20 30 40 50 60





Moving Speed (kmh)

4

6

8

10

12

14

16

18

Thro

ughp

ut (M

bits

)


300 350 400 450 500


Number of Users

0

05

1

15

2

25

EE (b

itJo

ule)


times106

10 20 30 40 50 60 70 80 90 100


5 Conclusion




Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia






Algorithm 2






Algorithm 3











0

02

04

06

08

1

12

14

16

18

2

EE (b

itJo

ule)



times106








05

1

15

2

EE (b

itJo

ule)


times106

0 10 20 30 40 50 60





Moving Speed (kmh)

4

6

8

10

12

14

16

18

Thro

ughp

ut (M

bits

)


300 350 400 450 500


Number of Users

0

05

1

15

2

25

EE (b

itJo

ule)


times106

10 20 30 40 50 60 70 80 90 100


5 Conclusion




Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




05

1

15

2

EE (b

itJo

ule)


times106

0 10 20 30 40 50 60





Moving Speed (kmh)

4

6

8

10

12

14

16

18

Thro

ughp

ut (M

bits

)


300 350 400 450 500


Number of Users

0

05

1

15

2

25

EE (b

itJo

ule)


times106

10 20 30 40 50 60 70 80 90 100


5 Conclusion




Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




Data Availability




Acknowledgments


References
































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia








RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


fog computing-assisted energy-efficient resource...

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