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Energy Efficiency Optimization for MIMO-OFDMMobile Multimedia Communication Systems with

QoS ConstraintsXiaohu Ge,Senior Member, IEEE,Xi Huang, Yuming Wang,Member, IEEE,Min

Chen,Senior Member, IEEE,Qiang Li, Member, IEEE,Tao Han,Member, IEEE,and Cheng-XiangWang,Senior Member, IEEE

Abstract—It is widely recognized that besides the qualityof service (QoS), the energy efficiency is also a key parameterin designing and evaluating mobile multimedia communicationsystems, which has catalyzed great interest in recent literature.In this paper, an energy efficiency model is first proposed formultiple-input multiple-output orthogonal-frequency-d ivision-multiplexing (MIMO-OFDM) mobile multimedia communica-tion systems with statistical QoS constraints. Employing thechannel matrix singular-value-decomposition (SVD) method,all subchannels are classified by their channel characteristics.Furthermore, the multi-channel joint optimization proble m inconventional MIMO-OFDM communication systems is trans-formed into a multi-target single channel optimization prob-lem by grouping all subchannels. Therefore, a closed-formsolution of the energy efficiency optimization is derived forMIMO-OFDM mobile mlutimedia communication systems. Asa consequence, an energy-efficiency optimized power allocation(EEOPA) algorithm is proposed to improve the energy effi-ciency of MIMO-OFDM mobile multimedia communicationsystems. Simulation comparisons validate that the proposedEEOPA algorithm can guarantee the required QoS withhigh energy efficiency in MIMO-OFDM mobile multimediacommunication systems.

I. I NTRODUCTION

A S the rapid development of the information and com-munication technology (ICT), the energy consumption

problem of ICT industry, which causes about 2% of world-wide CO2 emissions yearly and burdens the electrical bill

Copyright (c) 2013 IEEE. Personal use of this material is permitted. However,permission to use this material for any other purposes must be obtained from theIEEE by sending a request to pubs-permissions@ieee.org.

X. Ge, X. Huang, Yuming Wang(corresponding author), Qiang Li and Tao Hanare with the Department of Electronics and Information Engineering, HuazhongUniversity of Science and Technology, Wuhan 430074, Hubei,P. R. China (email:{xhge,ymwang,qlipatrick,hantao}@mail.hust.edu.cn, hbszhzm@163.com).

M. Chen is with the School of Computer Science and Technology,HuazhongUniversity of Science and Technology, Wuhan 430074, Hubei,P. R. China. (email:minchen2012@hust.edu.cn).

C.-X. Wang is with the Joint Research Institute for Signal and Image Processing,School of Engineering &Physical Sciences, Heriot-Watt University, Edinburgh, EH144AS, UK. (email: cheng-xiang.wang@hw.ac.uk).

The authors would like to acknowledge the support from the National NaturalScience Foundation of China (NSFC) under the grants 61103177 and 61271224,NFSC Major International Joint Research Project under the grant 61210002, National863 High Technology Program of China under the grant 2009AA01Z239 and theMinistry of Science and Technology (MOST) of China under thegrants 0903 and2014DFA11640, the Hubei Provincial Science and TechnologyDepartment under thegrant 2011BFA004, the Fundamental Research Funds for the Central Universitiesunder the grant 2011QN020 and the Opening Project of the Key Laboratory of Cog-nitive Radio and Information Processing (Guilin University of Electronic Technology),Ministry of Education (No. 2013KF01). This research is partially supported by EUFP7-PEOPLE-IRSES, project acronym S2EuNet (grant no. 247083), project acronymWiNDOW (grant no. 318992) and project acronym CROWN (grant no. 610524).

of network operators [1], has drawn universal attention. Mo-tivated by the demand for improving the energy efficiencyin mobile multimedia communication systems, various re-source allocation optimization schemes aiming at enhancingthe energy efficiency have become one of the mainstreamsin mobile multimedia communication systems, includingtransmission power allocation [2], [3], bandwidth alloca-tion [4]–[6], subchannel allocation [7], and etc. Multi-inputmulti-output (MIMO) technologies can create independentparallel channels to transmit data streams, which improvesspectrum efficiency and system capacity without increas-ing the bandwidth requirement [8]. Orthogonal-frequency-division-multiplexing (OFDM) technologies eliminate themultipath effect by transforming frequency selective chan-nels into flat channels. As a combination of MIMO andOFDM technologies, the MIMO-OFDM technologies arewidely used in mobile multimedia communication systems.However, how to improve energy efficiency with qualityof service (QoS)constraint is an indispensable problem inMIMO-OFDM mobile multimedia communication systems.

The energy efficiency has become one of the hot stud-ies in MIMO wireless communication systems in the lastdecade [9]–[14]. An energy efficiency model for Poisson-Voronoi tessellation (PVT) cellular networks consideringspatial distributions of traffic load and power consump-tion was proposed [9]. The energy-bandwidth efficiencytradeoff in MIMO multihop wireless networks was studiedand the effects of different numbers of antennas on theenergy-bandwidth efficiency tradeoff were investigated in[10]. An accurate closed-form approximation of the tradeoffbetween energy efficiency and spectrum efficiency over theMIMO Rayleigh fading channel was derived by consid-ering different types of power consumption model [11].A relay cooperation scheme was proposed to investigatethe spectral and energy efficiencies tradeoff in multicellMIMO cellular networks [12].The energy efficiency-spectralefficiency tradeoff of the uplink of a multi-user cellularV-MIMO system with decode-and-forward type protocolswas studied in [13]. The tradeoff between spectral andenergy efficiency was investigated in the relay-aided mul-ticell MIMO cellular network by comparing both the signalforwarding and interference forwarding relaying paradigms[14]. In our earlier work, we explored the tradeoff betweenthe operating power and the embodied power contained

2

in the manufacturing process of infrastructure equipmentsfrom a life-cycle perspective [1]. In this paper, we furtherinvestigate the energy efficiency optimization for MIMO-OFDM mobile multimedia communication systems.

Based on the Wishart matrix theory [15]–[18], numerouschannel models have been proposed in the literature forMIMO communication systems [19]–[26]. A closed-formjoint probability density function (PDF) of eigenvalues ofWishart matrix was derived for evaluating the performanceof MIMO communication systems [19]. Moreover, a closed-form expression for the marginal PDF of the ordered eigen-values of complex noncentral Wishart matrices was derivedto analyze the performance of singular value decomposition(SVD) in MIMO communication systems with Ricean fad-ing channels [20]. Based on the distribution of eigenvaluesof Wishart matrix, the performance of high spectrum effi-ciency MIMO communication systems withM -PSK (Mul-tiple Phase Shift Keying) signals in a flat Rayleigh-fadingenvironment was investigated in terms of symbol error prob-abilities [21]. Furthermore, the cumulative density functions(CDF) of the largest and the smallest eigenvalue of a centralcorrelated Wishart matrix were investigated to evaluate theerror probability of a MIMO maximal ratio combing (MRC)communication system with perfect channel state informa-tion at both transmitter and receiver [22]. Based on PDFand CDF of the maximum eigenvalue of double-correlatedcomplex Wishart matrices, the exact expressions for the PDFof the output signal-to-noise ratio (SNR) were derived forMIMO-MRC communication systems with Rayleigh fadingchannels [23]. The closed-form expressions for the outageprobability of MIMO-MRC communication systems withRician-fading channels were derived under the conditionof the largest eigenvalue distribution of central complexWishart matrices in the noncentral case [24]. Furthermore,The closed-form expressions for the outage probabilityof MIMO-MRC communication systems with and withoutco-channel interference were derived by using CDFs ofWishart matrix [25]. Meanwhile, the PDF of the smallesteigenvalue of Wishart matrix was applied to select antennasto improve the capacity of MIMO communication systems[26]. However, most existing studies mainly worked on thejoint PDF of eigenvalues of Wishart matrix to measure thechannel performance for MIMO communication systems.In our study, subchannels’ gains derived from the marginalprobability distribution of Wishart matrix is investigated toimplement energy efficiency optimization in MIMO-OFDMmobile multimedia communication systems.

In conventional mobile multimedia communication sys-tems, many studies have been carried out [27]–[33]. In termsof the corresponding QoS demand of different throughputlevels in MIMO communication systems, an effective an-tenna assignment scheme and an access control scheme wereproposed in [27]. A downlink QoS evaluation scheme wasproposed from the viewpoint of mobile users in orthogo-nal frequency-division multiple-access (OFDMA) wirelesscellular networks [28]. To guarantee the QoS in wirelessnetworks, a statistical QoS constraint model was built to ana-lyze the queue characteristics of data transmissions [29].The

energy efficiency in fading channels under QoS constraintswas analyzed in [30], where the effective capacity wasconsidered as a measure of the maximum throughput undercertain statistical QoS constraints. Based on the effectivecapacity of the block fading channel model, a QoS drivenpower and rate adaptation scheme over wireless links wasproposed for mobile wireless networks [31]. Furthermore, byintegrating information theory with the effective capacity,some QoS-driven power and rate adaptation schemes wasproposed for diversity and multiplexing systems [32]. Sim-ulation results showed that multi-channel communicationsystems can achieve both high throughput and stringentQoS at the same time. Aiming at optimizing the energyconsumption, the key tradeoffs between energy efficiencyand link-level QoS metrics were analyzed in different wire-less communication scenarios [33]. However, there has beenfew research work addressing the problem of optimizing theenergy efficiency under different QoS constraints in MIMO-OFDM mobile multimedia communication systems.

Motivated by aforementioned gaps, this paper is devotedto the energy efficiency optimization with statistical QoSconstraints in MIMO-OFDM mobile multimedia communi-cation systems with statistical QoS constraints which usesastatistical exponent to measure the queue characteristicsofdata transmission in wireless systems.”. All subchannels inMIMO-OFDM communication systems are first grouped bytheir channel gains. On this basis, a novel subchannel group-ing scheme is developed to allocate the corresponding trans-mission power to each of subchannels in different groups,which simplifies the multi-channel optimization problem toamulti-target single channel optimization problem. The maincontributions of this paper are summarized as follows.

1) An energy efficiency model with statistical QoS con-straints is proposed for MIMO-OFDM mobile multi-media communication systems.

2) A subchannel grouping scheme is designed by usingthe channel matrix single-value-decomposition (SVD)method, which simplifies the multi-channel optimiza-tion problem to a multi-target single channel optimiza-tion problem. Based on marginal probability densityfunctions (MPDFs) of subchannels in different groups,a closed-form solution of energy efficiency optimiza-tion is derived for MIMO-OFDM mobile multimediacommunication systems.

3) A novel algorithm is developed to optimize the energyefficiency in MIMO-OFDM mobile multimedia com-munication systems. Numerical results validate thatthe proposed algorithm improves the energy efficiencyof MIMO-OFDM mobile multimedia communicationsystems with statistical QoS constraints.

The remainder of this paper is organized as follows. Thesystem model is introduced in Section II. In Section III, theenergy efficiency model of MIMO-OFDM mobile multime-dia communication systems with statistical QoS constraintsis proposed. Based on the subchannel grouping scheme, aclosed-form solution of energy efficiency optimization isderived for MIMO-OFDM mobile multimedia communica-tion systems in Section IV. Moreover, a novel transmission

3

QoS constraint CSI feedback

Power control

policy

Channel

decomposition

through SVD

Subchannel 1

Subchannel M N

OFDM symbols

Transmitter Receiver

rM

tM

Subchannel 2

Fig. 1. MIMO-OFDM system model.

power allocation algorithm is presented. Numerical resultsare illustrated in Section V. Finally, Section VI concludesthe paper.

II. SYSTEM MODEL

The MIMO-OFDM mobile multimedia communicationsystem is illustrated in Fig. 1. It has aMr × Mt antennamatrix, N subcarriers andS OFDM symbols, whereMt isthe number of transmit antennas andMr is the number ofreceive antennas. We denoteB as the system bandwidthand Tf as the frame duration. The OFDM signals areassumed to be transmitted within a frame duration. Thenthe received signal of MIMO-OFDM communication systemcan be expressed as follows:

yk[i] = Hkxk[i] + n, (1)

where yk[i] and xk[i] are the received signal vector andtransmitted signal vector at thekth (k = 1, 2, ..., N) subcar-rier of the ith (i = 1, 2, ..., S) OFDM symbol, respectively.Hk is the frequency-domain channel matrix at thekthsubcarrier andn is the additive noise vector. LetC denotethe complex space, then we haveyk ∈ CMr , xk ∈ CMt ,Hk ∈ C

Mr×Mt , andn ∈ CMr . Without loss of generality,

we assumeE{nnH} = IMr×Mr , whereE{·} denotes theexpectation operator.

Discrete-time channels are assumed to experience a block-fading, in which the frame duration is shorter than the

channel coherence time. Based on this assumption, thechannel gain is invariant within a frame durationTf , butvaries independently from one frame to another. In eachframe duration, the channel at each subcarrier is dividedinto M (M = min(Mt,Mr)) parallel SISO channels by theSVD method. As a consequence, a total number ofM ×Nparallel space-frequency subchannels can be generated ineach OFDM symbol. Transmitters are assumed to obtain thechannel state information (CSI) from receivers without delayvia feedback channels. Furthermore, an average transmissionpower constraintP is configured for each subchannel in theMIMO-OFDM communication system. With this averagetransmission power constraint, transmitters are able to per-form power control adaptively according to the feedback CSIand system QoS constraints, so that the energy efficiencyin the MIMO-OFDM mobile multimedia communicationsystem can be optimized. To facilitate reading, the notationsand symbols used in this paper are listed in TABLE I.

III. E NERGY EFFICIENCY MODELING OF MIMO-OFDMMOBILE MULTIMEDIA COMMUNICATION SYSTEMS

Applying the SVD method to the channel matrixHk ateach subcarrier, whereHk ∈ CMr×Mt (k = 1, 2, ..., N), wehave

Hk = Uk

√∆̃kV

Hk , (2)

4

TABLE INOTATIONS AND SYMBOLS USED IN THE PAPER

Symbol Definition/explanationMt The number of transmit antennasMr The number of receive antennasM M = min(Mt,Mr)N The number of subcarriersS The number of OFDM symbolsB The system bandwidthTf The frame durationyk The received signal vector at thekth subcarrier of theith OFDM symbolxk The transmitted signal vector at thekth subcarrier of theith OFDM symbolHk The frequency-domain channel matrix at thekth subcarriern The additive noise vectorM The number of parallel SISO channels at each subcarrierP The average transmission power constraint for a subchannelλ The subchannel gainλm,k The channel gain of themth subchannel at thekth subcarrierΛ The transmission power allocation threshold over a subchannelΛm,k The transmission power allocation threshold of themth subchannel at thekth subcarrierΛn The transmission power allocation threshold of thenth grouped subchannelsη The energy efficiency of MIMO-OFDM mobile multimedia communication systemsηopt The optimized energy efficiencyθ The QoS statistical exponentβ The normalized QoS exponentCtotal(θ) The total effective capacityCe(θ)m,k The effective capacity of themth subchannel over thekth subcarrierCe(θ) The effective capacity for a subchannel with QoS constraintCe(θ)opt n The optimized effective capacity of thenth grouped subchannelsE {Ptotal} The expectation of the total transmission powerR The instantaneous bit rate within a frame durationµ(θ, λ) The transmission power allocated over a subchannelµm,k(θ, λ) The transmission power allocated over themth subchannel at thekth orthogonal subcarrierµopt(θ, λ) The optimized transmission power allocated over a channelµopt n(θ, λ) The optimized transmission power allocated for subchannels in thenth grouppΓm,k

(λ) The channel gain MPDF of themth subchannel at thekth orthogonal subcarrierpΓn

(λ) The channel gain MPDF of the subchannels over thenth grouped subchannelsp(λ1, λ2, ..., λM ) The joint PDF of ordered eigenvalues of a Wishart matrixKM,Q The normalizing factor

where Uk ∈ CMr×Mr and Vk ∈ CMt×Mt are uni-tary matrices. WhenMr > Mt, we have block ma-trix ∆̃k = [∆k,0Mr,Mt−Mr

]; otherwise whenMr <

Mt we have ∆̃k = [∆k,0Mt,Mr−Mt]T , where ∆k =

diag(λ1,k, ..., λM,k) and λm,k > 0, ∀m = 1, ...,M, k =1, ..., N . {λm,k}

Mm=1 denotes the subchannel gain set at the

kth subcarrier.. In this way, the MIMO channel at eachsubcarrier is decomposed intoM parallel SISO subchannelsby SVD method. Therefore,M×N parallel space-frequencysubchannels are obtained atN orthogonal subcarriers foreach OFDM symbol.

In traditional energy efficiency optimization researches,Shannon capacity is usually used as the index which mea-sures the system output. However, in any practical wirelesscommunication systems, the system capacity is obviouslyless than Shannon capacity, especially in the scenario withstrict QoS constraint. In this paper, the effective capacityof each subchannel is taken as the practical data rate withcertain QoS constraint.The total effective capacity ofM×Nsubchannels is configured as the system output and thetotal transmission power allocated toM×N subchannels isconfigured as the system input. As a consequence, the energyefficiency of MIMO-OFDM mobile multimedia communi-

cation systems is defined as follows

η =Ctotal(θ)

E {Ptotal}=

M∑m=1

N∑k=1

Ce(θ)m,k

E {Ptotal}, (3)

whereCe(θ)m,k(m = 1, 2, ...,M, k = 1, 2, ..., N) is theeffective capacity of themth subchannel over thekthsubcarrier, andE {Ptotal} is the expectation of the totaltransmission power allocated to allM×N subchannels.θ isthe QoS statistical exponent, which indicates the exponentialdecay rate of QoS violation probabilities [31]. A smallerθcorresponds to a slower decay rate, which implies that themultimedia communication system provides a looser QoSguarantee; while a largerθ leads to a faster decay rate, whichmeans that a higher QoS requirement should be supported.

Practical MIMO-OFDM mobile multimedia communica-tion systems involve multiple services, such as speech andvideo services, which are sensitive to the delay parame-ter. Different services in MIMO-OFDM mobile multimediacommunication systems have different QoS constraints. Inview of this, the effective capacity of each subchanneldepends on the corresponding QoS constraint. A statis-tical QoS constraint is adopted to evaluate the effectivecapacity of each subchannel which is calculated as thesystem practical output in MIMO-OFDM mobile multimediacommunication systems. Assuming the fading process over

5

wireless channels is independent among frames and keepsinvariant within a frame duration, the effective capacityCe(θ) for a subchannel with QoS statistical exponentθ inMIMO-OFDM mobile multimedia communication systemsis expressed as follows [31]

Ce(θ) = −1

θlog(E{e−θR

}), (4a)

R = TfBlog2(1 + µ(θ, λ)λ), (4b)

whereR denotes the instantaneous bit rate within a frameduration,λ denotes the subchannel gain, andµ(θ, λ) denotesthe transmission power allocated to a subchannel.

After SVD of channel matrices atN orthogonal sub-carriers,M × N parallel subchannels are obtained. Thechannel gain over each of theseM×N parallel subchannelsfollows a marginal probability distribution (MPDF). Assum-ing pΓm,k

(λ) as the MPDF of channel gain over themth(m = 1, 2, ...,M) subchannel at thekth (k = 1, 2, ..., N)orthogonal subcarrier, then the corresponding effective ca-pacityCe(θ)m,k over themth subchannel at thekth orthog-onal subcarrier is derived as (5). whereµm,k(θ, λ) is thetransmission power allocated to themth subchannel at thekth orthogonal subcarrier.

Considering the practical power consumption limitationat transmitters, an average transmission power constraintPover each subchannel is derived as (6). With the averagetransmission power constraint, the expectation of transmis-sion powerE {Ptotal} is given by

E {Ptotal} = P ×M ×N. (7)

Substituting expression (6) and (7) into (3), we derive theenergy efficiency model as (8).

From (8), the energy efficiency of MIMO-OFDM mobilemultimedia communication systems depends on the MPDFpΓm,k

(λ) (m = 1, 2, ...,M, k = 1, 2, ..., N) over M × Nsubchannels. Since there is a relationship between the MPDFpΓm,k

(λ) and statistical characteristics of the subchannel, themarginal distribution characteristics of each subchannelgainis investigated to optimize the energy efficiency in MIMO-OFDM mobile multimedia communication systems.

IV. ENERGY EFFICIENCY OPTIMIZATION OF MOBILE

MULTIMEDIA COMMUNICATION SYSTEMS

In MIMO wireless communication systems, statisticalcharacteristics of channel gain depend on the eigenvalues’distribution of Hermitian channel matrixHHH , whereHis the channel matrix [34]–[36]. When the elements ofH

are complex valued with real and imaginary parts eachgoverned by a normal distributionN(0, 1/2) with meanvalue 0 and variance value 1/2, the Hermitian channel matrixW = HHH is called a central Wishart channel matrix [15]–[17], [19]. In this case,E {H} = 0 and wireless channelshave the Rayleigh fading characteristic. IfE {H} 6= 0,W = HHH is a noncentral Wishart channel matrix andwireless channels have the Rician fading characteristic [20].

Based on SVD results of wireless channel matrix, sub-channels at each orthogonal subcarrier are sorted in a de-scending order of channel gains. Starting from the joint PDF

of eigenvalues of Wishart channel matrix, the channel gainMPDF of subchannels ordered at themth position in the de-scending order of channel gains is derived. Furthermore, allsubchannels atN subcarriers are grouped according to theirMPDFs. In terms of subchannel grouping results, a closed-form solution is derived to optimize the energy efficiency ofMIMO-OFDM mobile multimedia communication systemsin this section.

A. Optimization Solution of Energy Efficiency

To maximize the energy efficiency of MIMO-OFDMmobile multimedia communication systems with statisticalQoS constraints, the optimization problem can be formulatedas (9).

whereηopt is the optimized energy efficiency.From the problem formulation in (9) and (10), it is

remarkable that the energy efficiency of MIMO-OFDM mo-bile multimedia communication systems depends on trans-mission power allocation resultsµm,k(θ, λ) over M × Nsubchannels. In this case, the optimization problem in (9)and (10) is a multi-channel optimization problem, which isintractable to obtain a closed-form solution in mathematics.

In most studies on MIMO wireless communication sys-tems, the energy efficiency optimization problem is solvedby a single channel optimization model [32]. How to changethe multi-channel energy efficiency optimization probleminto the single channel energy efficiency optimization prob-lem and derive a closed-form solution are great challengesin this paper. Without loss of generality, the optimized trans-mission power allocation of single subchannelµopt(θ, λ) isexpressed as follows [32]

µopt(θ, λ) =

{1

Λ1

β+1 λβ

β+1

− 1λ, λ > Λ

0, λ < Λ, (11a)

β = θTfB/ log 2, (11b)

whereΛ is the transmission power allocation threshold overa subchannel andβ is the normalized QoS exponent.

It is critical to determine the transmission power al-location thresholdΛ for the implemention of optimizedtransmission power allocation in (11a). An average transmis-sion power constraintP is configured for each subchannel,thus the transmission power allocation threshold of eachsubchannel should satisfy the following constraint

∫ ∞

Λm,k

1

Λ1

β+1

m,k λβ

β+1

−1

λ

pΓm,k

(λ)dλ ≤ P , (12)

whereΛm,k (m = 1, 2, ...,M, k = 1, 2, ..., N) is the trans-mission power allocation threshold of themth subchannelat thekth subcarrier.

Assuming that the channel matrixHk (k = 1, 2, ..., N)at each subcarrier is a complex matrix and its elementsare complex valued with real and imaginary parts eachgoverned by a normal distributionN(0, 1/2) with meanvalue 0 and variance value 1/2, then elements ofHk followan independent and identically distributed (i.i.d.) circularsymmetric complex Gaussian distribution with zero-mean

6

Ce(θ)m,k = −1

θlog

(∫ ∞

0

e−θTfBlog2(1+µm,k(θ,λ)λ)pΓm,k(λ)dλ

), (5)

P =

∫ ∞

0

µm,k(θ, λ)pΓm,k(λ)dλ (∀m = 1, 2, ...,M, k = 1, 2, ..., N). (6)

η =

M∑m=1

N∑k=1

− 1θlog(∫∞

0e−θTfBlog2(1+µm,k(θ,λ)λ)pΓm,k

(λ)dλ)

P ×M ×N. (8)

ηopt = max

M∑m=1

N∑k=1

− 1θlog(∫∞

0e−θTfBlog2(1+µm,k(θ,λ)λ)pΓm,k

(λ)dλ)

P ×M ×N

=

max

{M∑

m=1

N∑k=1

− 1θlog(∫∞

0 e−θTfBlog2(1+µm,k(θ,λ)λ)pΓm,k(λ)dλ

)}

P ×M ×N,

s.t. :

(9)

∫ ∞

0

µm,k(θ, λ)pΓm,k(λ)dλ ≤ P , ∀m = 1, 2, ...,M, k = 1, 2, ..., N. (10)

and unit-variance. In this case, wireless channels betweentransmit and receive antennas are Reyleign fading channelswith unit energy.

DenoteQ = max(Mt,Mr), and setW̃ as aM × MHermitian matrix:

W̃ =

{HkH

Hk

HHk Hk

Mr < Mt

Mr > Mt, (13)

then W̃ is a central Wishart matrix. The joint PDF ofordered eigenvalues of̃W follows Wishart distributions[37] as (14). whereλ1, λ2, ..., λM

(λ1 > λ2 > ... > λM) are

ordered eigenvalues of̃W, KM,Q is a normalizing factorwhich is denoted as follows:

KM,Q =

M∏

i=1

(Q− i)!(M − i)!. (15)

Based on SVD results of channel matrixHk, orderedeigenvalues of matrixHH

k Hk are denoted by elementsλ1,k, λ2,k..., λM,k of diagonal matrix∆k. That means sub-channel gainsλ1,k, ..., λM,k at the kth subcarrier can bedenoted by eigenvalues of the Wishart matrix̃W. Whensubchannel gains at each subcarrier are sorted in a descend-ing order, i.e.,∀1 6 i 6 j 6 M, 1 6 k 6 N, λi,k > λj,k,the ordered subchannel gains can be denoted by the orderedeigenvaluesλ1, λ2, ..., λM

(λ1 > λ2 > ... > λM) of Wishart

matrix W̃, which follow the joint PDFp(λ1, λ2, ..., λM ) ofthe ordered eigenvalues of Wishart matrix̃W. After sub-channel gains at each subcarrier are sorted in a descendingorder, the MPDF of themth (1 6 n 6 M ) subchannelgain at thekth subcarrierpΓm,k

(λ) is derived as (16). After

subchannels at each subcarrier are sorted by subchannelgains, subchannels with the same order position at differentorthogonal subcarriers have the identical MPDF based on(16). According to this property, a subchannel groupingscheme is proposed for subchannels at different orthogonalsubcarriers:

1) Sort subchannels at each orthogonal subcarriers by adescending order of subchannel gains:λ1,k > λ2,k >

... > λM,k > 0, k = 1, 2, ..., N .2) For n = 1 : M , select the subchannels with the

same order position at different orthogonal subcarriers(λn,1, λn,2, ..., λn,N ) into different channel groups.

3) Repeat steps 1) and 2) for all OFDM symbols.4) M groups with the same order position subchannels

are obtained.Since subchannels in the same group have an identical

MPDF, the MPDF of subchannels in thenth grouppΓn,k(λ)

(1 6 n 6 M, 1 6 k 6 N ) is simply denoted aspΓn(λ)

(1 6 n 6 M ).Based on the proposed subchannel grouping scheme,

we can optimize the effective capacity of each groupedsubchannels according to their MPDFs in (16), in which allsubchannels in the same group have an identical MPDF. Inthis process, the multi-channel joint optimization problem istransformed into a multi-target single channel optimizationproblem, which significantly reduces the complexity ofenergy efficiency optimization. Substituting (16) into (12),the average power constraint is derived as (17). whereΛn

(1 6 n 6 M ) is the transmission power allocation thresholdof thenth grouped subchannels. Based on the transmissionpower allocation threshold for each grouped subchannels in

7

p(λ1, λ2, ..., λM ) = K−1M,Qe

−M∑

i=1

λiM∏

i=1

λQ−Mi

∏

16i6j6M

(λi − λj)2, (14)

pΓm,k(λ) =

∫...

︸︷︷︸M−1

∫p(λ1, λ2, ..., λM )dλidλi+1...dλj (1 6 i < j 6 M andi 6= n, j 6= n). (16)

∫ ∞

Λn

(1

Λ1

β+1

n λβ

β+1

−1

λ

)

∫...

︸︷︷︸M−1

∫p(λ1, λ2, ..., λM )dλidλi+1...dλj

dλ ≤

−

P ,

(1 6 i < j 6 M andi 6= n, j 6= n)

(17)

ηopt =

M∑n=1

−Nθlog(∫∞

0 e−θTfBlog2(1+µopt n(θ,λ)λ)pΓn(λ)dλ

)

P ×M ×N(19)

= −1

θ × P ×M

M∑

n=1

log

(∫ ∞

0

e−θTfBlog2(1+µopt n(θ,λ)λ)pΓn(λ)dλ

). (20)

(17), the optimized transmission power allocation for thenth grouped subchannels is formulated as follows

µopt n(θ, λ) =

{1

Λ1

β+1n λ

ββ+1

− 1λ, λ > Λn

0, λ < Λn

, (18)

where µopt n(θ, λ) is the optimized transmission powerallocated for subchannels in thenth group. Therefore,the optimized energy efficiency of MIMO-OFDM mobilemultimedia communication systems with statistical QoSconstraints is derived as (19) and (20).

B. Algorithm Design

The core idea of energy efficiency optimization algorithm(EEOPA) with statistical QoS constraints for MIMO-OFDMmobile multimedia communication systems is described asfollows. Firstly, the SVD method is applied for the channelmatrix Hk, k = 1, 2, ..., N , at each orthogonal subcarrierto obtain M × N parallel space-frequency subchannels.Secondly, subchannels at each subcarrier are pushed intoa subchannel gain set, where subchannels are sorted bythe subchannel gain in a descending order. And then sub-channles with the same order position in the subchannelgain set are selected into the same group. Since subchan-nels within the same group have the identical MPDF, thetransmission power allocation threshold for subchannelswithin the same group is identical. Therefore, the optimizedtransmission power allocation for the grouped subchannelsis implemented to improve the energy efficiency of MIMO-OFDM mobile multimedia communication systems. Thedetailed EEOPA algorithm is illustrated in Algorithm 1.

V. SIMULATION RESULTS AND PERFORMANCE

ANALYSIS

In the proposed algorithm, the transmission power allo-cation thresholdΛn is the core parameter to optimize theenergy efficiency of MIMO-OFDM mobile multimedia com-munication systems. The configuration of the transmissionpower allocation thresholdΛn depends on the MPDF ofeach grouped subchannels. Without loss of generation, thenumber of transmitter and receiver antennas is configured asMt = 4 andMr = 4, respectively. Based on the extensionof (16), MPDFs of each grouped subchannels are extendedas (27)-(30).

Substituting (27), (28), (29) and (30) into (12), the trans-mission power allocation thresholdΛn can be calculated.To analyze the performance of the transmission powerallocation threshold, some default parameters are configuredas: Tf = 1ms and B = 1MHz. The numerical resultsare illustrated in Fig. 2 and Fig. 3. Fig. 2 shows numer-ical results of the transmission power allocation thresholdΛn with respect to each grouped subchannels consideringdifferent QoS statistical exponentsθ. For each groupedsubchannels, the transmission power allocation thresholdΛn

decreases with the increase of the QoS exponentθ. Con-sidering subchannels are sorted by the descending order ofsubchannel gains, the subchannel gain of subchannel groupsdecreases with the increase of group indexes. Therefore,the transmission power allocation thresholdΛn increaseswith the increase of subchannel gains in subchannel groupswhen the QoS exponentθ 6 10−3. When the QoS exponentθ > 10−3, the transmission power allocation thresholdΛn

start to decrease with the increase of subchannel gains insubchannel groups.

8

Algorithm 1 EEOPA.

Input: Mt, Mr, N , Hk, P ,B,Tf ,θ;Initialization: Decompose the MIMO-OFDM channel matrixHk(k = 1, 2, ..., N) into M × N space-frequencysubchannels through the SVD method.Begin:

1) Sort subchannel gains of each subcarrier in a decreasing order:

λ1,k > λ2,k > ... > λM,k(k = 1, 2, ..., N). (21)

2) Assignλn,1, λn,2, ..., λn,N from all N subcarriers into thenth grouped subchannel set:

Group n = {λn,1, λn,2, ..., λn,N}(n = 1, 2, ...,M). (22)

3) for n = 1 : M doCalculate the optimized transmission power allocation thresholdΛn for Group naccording to the average power constraint as follows:

∫ ∞

Λn

(1

Λ1

β+1

n λβ

β+1

−1

λ)pΓn(λ)dλ ≤ P. (23)

Execute the optimized transmission power allocation policy for Group n:

µopt n(θ, λ) =

{1

Λ1

β+1n λ

ββ+1

− 1λ, λ > Λn

0, λ < Λn

. (24)

Calculate the optimized effective-capacity for Groupn:

Ce(θ)opt n = −N

θlog

(∫ ∞

0

e−θTfBlog2(1+µopt n(θ,λ)λ)pΓn(λ)dλ

). (25)

end for4) Calculate the optimized energy-efficiency of the MIMO-OFDM mobile multimedia communication system:

ηopt = −1

θ ×−

P×M

M∑

n=1

log

(∫ ∞

0

e−θTfBlog2(1+µopt n(θ,λ)λ)pΓn(λ)dλ

). (26)

end BeginOutput: Λn, ηopt.

pΓ1(λ) =− 4e−4λ − (1/36)e−λ(144− 432λ+ 648λ2 − 408λ3 + 126λ4

− 18λ5 + λ6) + (1/12)e−3λ(144− 144λ + 72λ2 + 56λ3 + 46λ4

+ 10λ5 + λ6)− (1/72)e−2λ(864− 1728λ + 1728λ2 − 192λ3

+ 96λ4 − 96λ5 + 32λ6 − 4λ7 + λ8),

(27)

pΓ2(λ) =12e−4λ − (1/6)e−3λ(144− 144λ+ 72λ2 + 56λ3 + 46λ4

+ 10λ5 + λ6) + (1/72)e−2λ(864− 1728λ+ 1728λ2 − 192λ3

+ 96λ4 − 96λ5 + 32λ6 − 4λ7 + λ8),

(28)

pΓ3(λ) =− 12e−4λ + (1/12)e−3λ(144− 144λ+ 72λ2 + 56λ3 + 46λ4

+ 10λ5 + λ6),(29)

pΓ4(λ) = 4e−4λ. (30)

Fig. 3 illustrates the transmission power allocation thresh-old Λn with respect to each grouped subchannels consider-

ing different average power constraintsP . For each groupedsubchannels, the transmission power allocation thresholdΛn

9

10-4

10-3

10-2

10-1

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

QoS statistical exponents

Tra

nsm

issio

n p

ow

er

allo

cati

on

th

resh

old

Group 1

Group 2

Group 3

Group 4

Fig. 2. Transmission power allocation thresholdΛn with respectto each grouped subchannels considering different QoS statisticalexponentsθ.

10-1

100

101

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Average power constriant [W]

Tra

nsm

issio

n p

ow

er

allo

cati

on

th

resh

old

Group 1

Group 2

Group 3

Group 4

Fig. 3. Transmission power allocation thresholdΛn with respectto each grouped subchannels considering different averagepowerconstraintsP .

decreases with the increase of the average power constraintP . When P 6 0.13, the transmission power allocationthresholdΛn increases with the increase of subchannel gainsin subchannel groups. WhenP > 0.13, the transmissionpower allocation thresholdΛn start to decrease with theincrease of subchannel gains in subchannel groups.

To evaluate the energy efficiency and the effective ca-pacity of MIMO-OFDM mobile multimedia communica-tion systems, three typical scenarios with different antennanumbers are configured in Fig. 4 and Fig. 5: (1)Mt = 2,Mr = 2; (2) Mt = 3, Mr = 2; (3) Mt = 4, Mr = 4. Fig. 4shows the impact of QoS statistical exponentsθ on theeffective capacity of MIMO-OFDM mobile multimediacommunication systems in three different scenarios. Fromcurves in Fig. 4, the effective capacity decreases with the

10-7

10-6

10-5

10-4

10-3

10-2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

4

QoS statistical exponent

Eff

ecti

ve c

ap

acit

y [

bit

s/H

z]

Mt=2,Mr=2

Mt=3,Mr=2

Mt=4,Mr=4

Fig. 4. Effective capacityCtotal(θ) with respect to the QoSstatistical exponentθ considering different scenarios.

increase of the QoS statistical exponentθ. The reason of thisresult is that the larger values ofθ correspond to the higherQoS requirements, which result in a smaller number of sub-channels are selected to satisfy the higher QoS requirements.When the QoS statistical exponentθ is fixed, the effectivecapacity increases with the number of antennas in MIMO-OFDM mobile multimedia communication systems. Thisresult indicates the channel spatial multiplexing can improvethe effective capacity of MIMO-OFDM mobile multimediacommunication systems.

Fig. 5 illustrates the impact of QoS statistical exponentsθ on the energy efficiency of MIMO-OFDM mobile multi-media communication systems in three different scenarios.From curves in Fig. 5, the energy efficiency decreases withthe increase of the QoS statistical exponentθ. The reasonof this result is that the larger values ofθ correspond tothe higher QoS requirements, which result in a smallernumber of subchannels are selected to satisfy the higherQoS requirements. This result conduces to the effectivecapacity is decreased. If the total transmission power isconstant, the decreased effective capacity will lead to thedecrease of the energy efficiency in communication systems.When the QoS statistical exponentθ is fixed, the energyefficiency increases with the number of antennas in MIMO-OFDM mobile multimedia communication systems. Thisresult indicates the channel spatial multiplexing can improvethe energy efficiency of MIMO-OFDM mobile multimediacommunication systems.

When the QoS statistical exponent is fixed asθ = 10−3,the impact of the average power constraint on the en-ergy efficiency and the effective capacity of MIMO-OFDMmobile multimedia communication systems is investigatedin Fig. 6. From Fig. 6, the energy efficiency decreaseswith the increase of the average power constraint and theaffective capacity increases with the increase of the averagepower constraint. This result implies there is an optimizationtradeoff between the energy efficiency and effective capacity

10

10-7

10-6

10-5

10-4

10-3

10-2

2000

2500

3000

3500

4000

4500

5000

QoS statistical exponent

En

erg

y e

ffic

ien

cy [b

its/H

z/J

ou

le]

Mt=2,Mr=2

Mt=3,Mr=2

Mt=4,Mr=4

Fig. 5. Energy efficiencyη with respect to the QoS statisticalexponentθ considering different scenarios.

0.1 0.12 0.14 0.16 0.18 0.23.5

3.6

3.7

3.8

3.9

4

4.1

4.2

4.3

4.4

4.5

En

erg

y e

ffic

ien

cy [

kb

its/H

z/J

ou

le]

0.1 0.12 0.14 0.16 0.18 0.210

12

14

16

18

20

22

24

26

28

30

Average power constraint [W]

Eff

ecti

ve c

ap

acit

y [

kb

its/H

z]

The energy efficiency

The effective capacity

Fig. 6. Impact of the average power constraint on the energyefficiencyη and the effective capacityCtotal(θ).

in MIMO-OFDM mobile multimedia communication sys-tems:as the transmission power increases which leads tolarger effective capacity, the energy consumption of thesystem also rises; therefor, the larger power input resultsin the decline of energy efficiency.

To analyze performance of the EEOPA algorithm, thetraditional average power allocation (APA) algorithm [38],i.e., every subchannel with the equal transmission poweralgorithm is compared with the EEOPA algorithm by Fig. 7–Fig. 10. Three typical scenarios with different antennanumbers are configured in Fig. 7–Fig. 10: (1)Mt = 2,Mr = 2; (2) Mt = 3, Mr = 2; (3) Mt = 4, Mr = 4.In Fig. 7, the effect of the QoS statistical exponentθ onthe energy efficiency of EEOPA and APA algorithms isinvestigated with constant average power constraintP = 0.1Watt. Considering changes of the QoS statistical exponent,the energy efficiency of EEOPA algorithm is always higherthan the energy efficiency of APA algorithm in three sce-

10-7

10-6

10-5

10-4

10-3

10-2

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

QoS statistical exponent

En

erg

y e

ffic

ien

cy [

bit

s/H

z/J

ou

le]

EEOPA for Mt=2,Mr=2

APA for Mt=2,Mr=2

EEOPA for Mt=3,Mr=2

APA for Mt=3,Mr=2

EEOPA for Mt=4,Mr=4

APA for Mt=4,Mr=4

Fig. 7. Energy efficiencyη of EEOPA and APA algorithms asvariation of QoS statistical exponentθ under different scenarios.

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.51500

2000

2500

3000

3500

4000

4500

Average power constraint [W]

En

erg

y e

ffic

ien

cy [

bit

s/H

z/J

ou

le] EEOPA for Mt=2,Mr=2

APA for Mt=2,Mr=2

EEOPA for Mt=3,Mr=2

APA for Mt=3,Mr=2

EEOPA for Mt=4,Mr=4

APA for Mt=4,Mr=4

Fig. 8. Energy efficiencyη of EEOPA and APA algorithms asvariation of average power constraintP under different scenarios.

narios. In Fig. 8, the impact of the average power constrainton the energy efficiency of EEOPA and APA algorithms isevaluated with the fixed QoS statistical exponentθ = 10−3.Considering changes of the average power constraint, theenergy efficiency of EEOPA algorithm is always higher thanthe energy efficiency of APA algorithm in three scenarios.In Fig. 9, the effect of the QoS statistical exponentθ onthe effective capacity of EEOPA and APA algorithms iscompared with constant average power constraintP = 0.1Watt. Considering changes of the QoS statistical exponent,the effective capacity of EEOPA algorithm is always higherthan the effective capacity of APA algorithm in three scenar-ios. In Fig. 10, the impact of the average power constrainton the effective capacity of EEOPA and APA algorithms isevaluated with the fixed QoS statistical exponentθ = 10−3.Considering changes of the average power constraint, theeffective capacity of EEOPA algorithm is always higher thanthe effective capacity of APA algorithm in three scenarios.

11

10-7

10-6

10-5

10-4

10-3

10-2

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2x 10

4

QoS statistical exponent

Eff

ecti

ve c

ap

acit

y [

bit

s/H

z]

EEOPA for Mt=2,Mr=2

APA for Mt=2,Mr=2

EEOPA for Mt=3,Mr=2

APA for Mt=3,Mr=2

EEOPA for Mt=4,Mr=4

APA for Mt=4,Mr=4

Fig. 9. Effective capacityCtotal(θ) of EEOPA and APA algorithmsas variation of QoS statistical exponentθ under different scenarios.

0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50

1

2

3

4

5

6x 10

4

Average power constraint [W]

Eff

ecti

ve c

ap

acit

y [

bit

s/H

z]

EEOPA for Mt=2,Mr=2

APA for Mt=2,Mr=2

EEOPA for Mt=3,Mr=2

APA for Mt=3,Mr=2

EEOPA for Mt=4,Mr=4

APA for Mt=4,Mr=4

Fig. 10. Effective capacityCtotal(θ) of EEOPA and APA algo-rithm as variation of average power constraintP under differentscenarios.

Based on above comparison results, our proposed EEOPAalgorithm can improve the energy efficiency and effectivecapacity of MIMO-OFDM mobile multimedia communica-tion systems.

VI. CONCLUSIONS

In this paper, an energy efficiency model is proposedfor MIMO-OFDM mobile multimedia communication sys-tems with statistical QoS constraints. An energy efficiencyoptimization scheme is presented based on the subchannelgrouping method, in which the complex multi-channel jointoptimization problem is simplified into a multi-target singlechannel optimization problem. A closed-form solution ofthe energy efficiency optimization is derived for MIMO-

OFDM mobile multimedia communication systems. More-over, a novel algorithm, i.e., EEOPA, is designed to improvethe energy efficiency of MIMO-OFDM mobile multimediacommunication systems. Compared with the traditional APAalgorithm, simulation results demonstrate that our proposedalgorithm has advantages on improving the energy efficiencyand effective capacity of MIMO-OFDM mobile multimediacommunication systems with QoS constraints.

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Xiaohu Ge (M’09-SM’11) is currently a Pro-fessor with the Department of Electronics andInformation Engineering at Huazhong Universityof Science and Technology (HUST), China. Hereceived his PhD degree in Communication andInformation Engineering from HUST in 2003. Hehas worked at HUST since Nov. 2005. Prior tothat, he worked as a researcher at Ajou Uni-versity (Korea) and Politecnico Di Torino (Italy)from Jan. 2004 to Oct. 2005. He was a visitingresearcher at Heriot-Watt University, Edinburgh,

UK from June to August 2010. His research interests are in theareaof mobile communications, traffic modeling in wireless networks, greencommunications, and interference modeling in wireless communications.He has published about 60 papers in refereed journals and conferenceproceedings and has been granted about 15 patents in China. He receivedthe Best Paper Awards from IEEE Globecom 2010. He is leading severalprojects funded by NSFC, China MOST, and industries. He is taking partin several international joint projects, such as the RCUK funded UK-ChinaScience Bridges: R&D on (B)4G Wireless Mobile Communications and theEU FP7 funded project: Security, Services, Networking and Performanceof Next Generation IP-based Multimedia Wireless Networks.

Dr. Ge is currently serving as an Associate Editor forInternationalJournal of Communication Systems (John Wiley & Sons), IET WirelessSensor Systems, KSII Transactions on Internet and Information SystemsandJournal of Internet Technology. Since 2005, he has been actively involvedin the organisation of more than 10 international conferences, such asExecutive Chair of IEEE GreenCom 2013 and Co-Chair of workshop ofGreen Communication of Cellular Networks at IEEE GreenCom 2010. Heis a Senior Member of the IEEE, a Senior member of the Chinese Instituteof Electronics, a Senior member of the China Institute of Communications,and a member of the NSFC and China MOST Peer Review College.

Xi Huang received her Bachelor’s degree intelecommunication engineering from HuazhongUniversity of Science and Technology (HUST)in June 2011. She is currently working towardher Master’s degree in communication and in-formation systems at HUST. Her research in-terests include energy efficiency modeling andperformance analysis in wireless communicationsystems.

Yuming Wang received his Ph.D. degree in Com-munication and Information Engineering fromHuazhong University of Science and Technology,China in 2005. He is currently an associate pro-fessor with the Department of Electronics andInformation Engineering, Huazhong Universityof Science and Technology, China. His researchinterests include wired/wireless communications,vehicular networks, mobile applications, databaseand data processing. Since 1999, he had beenworking in the design of high speed network

router and switch products for nearly 10 years. In the recentyears, he hasbeen researching on energy efficiency modeling in wireless communica-tions, mobile IP networks, vehicular ad hoc networks, software applicationsystem, statistical analysis and data mining. He has published over 10papers in refered journals and conference proceedings and has been grantedseveral patents in China. He is leading projects funded by NSFC and MOEof China.

13

Min Chen is a professor in School of ComputerScience and Technology at Huazhong Universityof Science and Technology (HUST). He was anassistant professor in School of Computer Scienceand Engineering at Seoul National University(SNU) from Sep. 2009 to Feb. 2012. He wasR&D director at Confederal Network Inc. from2008 to 2009. He worked as a Post-DoctoralFellow in Department of Electrical and ComputerEngineering at University of British Columbia(UBC) for three years. Before joining UBC, he

was a Post-Doctoral Fellow at SNU for one and half years. He receivedBest Paper Award from IEEE ICC 2012, and Best Paper Runner-upAwardfrom QShine 2008. He has more than 180 paper publications, including85 SCI papers. He is a Guest Editor for IEEE Network, IEEE WirelessCommunications Magazine, etc. He is Co-Chair of IEEE ICC 2012-Communications Theory Symposium, and Co-Chair of IEEE ICC 2013-Wireless Networks Symposium. He is General Co-Chair for the12th IEEEInternational Conference on Computer and Information Technology (IEEECIT-2012). He is Keynote Speaker for CyberC 2012 and Mobiquitous 2012.His research focuses on Internet of Things, Machine to Machine Com-munications, Body Area Networks, Body Sensor Networks, E-healthcare,Mobile Cloud Computing, Cloud-Assisted Mobile Computing,UbiquitousNetwork and Services, Mobile Agent, and Multimedia Transmission overWireless Network, etc.

Qiang Li received his B.Eng degree in commu-nication engineering from the School of Commu-nication and Information Engineering, Universityof Electronic Science and Technology of China,in 2007, and the Ph.D. degree in electrical andelectronic engineering from Nanyang Technolog-ical University, in 2011. From 2011-2013, hewas with Nanyang Technological University as aResearch Fellow. From 2013, he is an AssociateProfessor at Huazhong University of Science andTechnology. His current research interests include

cooperative communications, cognitive wireless networks, and wirelessnetwork coding .

Tao Han received the Ph.D. degree in com-munication and information engineering fromHuazhong University of Science and Technology(HUST), Wuhan, China in December, 2001. Heis currently an Associate Professor with the De-partment of Electronics and Information Engi-neering, HUST. From August, 2010 to August,2011, he was a Visiting Scholar with Universityof Florida, Gainesville, FL, USA, as a CourtesyAssociate Professor. His research interests includewireless communications, multimedia communi-

cations, and computer networks. Dr. Han is currently serving as an AreaEditor for the EAI Endorsed Transactions on Cognitive Communications.He is a Reviewer for the IEEE Transactions on Vehicular Technology andother journals.

Cheng-Xiang Wang (S’01-M’05-SM’08) re-ceived the BSc and MEng degrees in Commu-nication and Information Systems from ShandongUniversity, China, in 1997 and 2000, respectively,and the PhD degree in Wireless Communicationsfrom Aalborg University, Denmark, in 2004.

He has been with Heriot-Watt University, Ed-inburgh, UK, since 2005, first as a Lecturer,then as a Reader in 2009, and was promotedto a Professor in 2011. He is also an HonoraryFellow of the University of Edinburgh, UK, and

a Chair/Guest Professor of Shandong University and Southeast University,China. He was a Research Fellow at the University of Agder, Grimstad,Norway, from 2001–2005, a Visiting Researcher at Siemens AG-MobilePhones, Munich, Germany, in 2004, and a Research Assistant at TechnicalUniversity of Hamburg-Harburg, Hamburg, Germany, from 2000–2001. Hiscurrent research interests include wireless channel modeling and simulation,green communications, cognitive radio networks, vehicular communicationnetworks, massive MIMO, millimetre wave communications, and 5Gwireless communication networks. He has edited 1 book and published1 book chapter and over 190 papers in refereed journals and conferenceproceedings.

Prof. Wang served or is currently serving as an editor for 8 internationaljournals, includingIEEE Transactions on Vehicular Technology(2011–)and IEEE Transactions on Wireless Communications(2007–2009). He wasthe leading Guest Editor forIEEE Journal on Selected Areas in Commu-nications, Special Issue on Vehicular Communications and Networks. Heserved or is serving as a TPC member, TPC Chair, and General Chair forover 70 international conferences. He received the Best Paper Awards fromIEEE Globecom 2010, IEEE ICCT 2011, ISIT 2012, and IEEE VTC 2013-Fall. He is a Fellow of the IET, a Fellow of the HEA, and a memberofEPSRC Peer Review College.