Energy-Efficient Cooperative Beamforming in Clustered Wireless

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION 1

Energy-Efficient Cooperative Beamforming inClustered Wireless Networks

Gubong Lim, Student Member, IEEE, and Leonard J. Cimini, Jr., Fellow, IEEE

Abstract—Recently, due to the growing concern over the ever-increasing energy consumption, much attention has been givento the energy-efficient design of wireless communication systems.Various strategies for improving the energy efficiency, which isdefined as the transmitted bits per total energy consumed (inbits/Joule), have been proposed. In this paper, we analyze theenergy efficiency of clustered cooperative beamforming wheredistributed relay nodes construct a virtual Multiple-Input Single-Output beamforming system with a maximum transmit powerconstraint, and compare its performance with that of directcommunications. All the energy consumption overheads incurredare taken into account in the energy efficiency analysis assuminga constant circuit-power consumption model. We then study thenumber of relay nodes that maximizes the efficiency for a givenoutage constraint. In addition, we propose a mode switchingalgorithm which optimally chooses between using cooperativebeamforming or direct communications for transmission. Weshow that cooperative beamforming significantly outperformsdirect communications in energy efficiency, as well as in spectralefficiency, even though a much larger amount of circuit poweris consumed.

Index Terms—Energy efficiency, cooperative beamforming,virtual MISO, clustered wireless networks.

I. INTRODUCTION

IN wireless communications, most of the research has fo-cused on maximizing the capacity of the network. However,

with the rapid development of high-speed mobile devicesequipped with multi-core DSPs and the proliferation of smallbase stations (BS) and wireless routers (e.g., femtocells andpicocells as well as lightRadio [1]), there has been a growingconcern about the ever-increasing energy consumption ofthese systems [2]-[5]. From the viewpoint of the networkoperator, improving the energy efficiency for communicationscan increase the revenue through efficient management ofenergy usage of the network. From the mobile terminal’sperspective, energy efficiency is imperative for extending itsoperational life because it is powered by a limited-capacitybattery. However, the battery technology has not kept up withthe energy demand of mobile devices.

Most of the previous work on energy-efficient, physical-layer design has focused on minimizing the power consumedin transmission, for a given spectral efficiency constraint.

Manuscript received July 5, 2012; revised October 19, 2012; acceptedDecember 23, 2012. The associate editor coordinating the review of this paperand approving it for publication was H. Lin.

The authors are with the ECE Department, University of Delaware, Newark,DE, 19711 (e-mail: [email protected]; [email protected]).

This research has been supported by NSF under Grant No. 1017053.This paper was presented in part at the IEEE International Conference on

Communications (ICC), Ottawa, Canada, June 2012.Digital Object Identifier 10.1109/TWC.2013.012413.120975

Energy efficiency is considered in [6] from an information-theoretic perspective; however, the circuit power consumedby other parts of the device is neglected in the analysis.When the operating transmission range is relatively small,the power consumed in the baseband processor, and in theother components in the RF chain, might be much greaterthan the power consumed by the transmitter power amplifier.Thus, to properly optimize the performance, this circuit powerconsumption must be taken into account when designing thesystem.

Various resource allocation strategies have been developedto improve the energy efficiency, which is usually definedas the number of successfully received bits per unit energyconsumption. In [7]-[8], the authors proposed an energy-efficient adaptive modulation, using a constant circuit powermodel. They show that the energy efficiency is improved byusing higher modulation sizes for short distances where thecircuit power consumption is dominant. In a sensor network,the energy efficiency is of paramount importance since sensorsare typically powered by batteries, and it is usually difficult toreplace or recharge them due to the limited access to the regionin which they are deployed [9]. In [10], the authors analyzeoptimal energy-efficient strategies for centralized and de-centralized Multiple-Input Multiple-Output (MIMO) systems.The paper shows that, for large transmission distances, bothsystems can achieve higher energy efficiencies even thoughthey use extra circuitry, which consumes more energy. Thiswork has been extended in [11] for a distributed MIMO sensornetwork by including the power consumed by the training.

For an uplink cellular network, it has been shown [12]that switching from a MIMO to a Single-Input Multiple-Output (SIMO) system can save energy in the mobile terminalwhen the base station (BS) is underutilized. Similarly, forthe downlink, activating only a single antenna in the BS isoptimal when random beamforming is used [13]. In [14]-[15],the energy efficiency is analyzed, taking into considerationa system level power consumption model; the physical-layersystem parameters are also optimized to improve the energyefficiency. The authors in [16] study link adaptation thatmaximizes the energy efficiency when the complete CSI isonly given at the receiver and partial CSI is available at thetransmitter.

It has been shown that, when properly designed, cooperationnot only improves the spectral efficiency, but also increases theenergy efficiency [10]. In [17], the energy efficiency of cooper-ative communications, where there is a source, destination, andonly one relay, is analyzed for both amplify-and-forward (AF)and decode-and-forward (DF) relaying. Energy-efficient, best-

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2 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, ACCEPTED FOR PUBLICATION

select relaying, using a timer-based relay selection algorithm[18], is proposed in [19] using the Request-to-Send/Clear-to-Send (RTS/CTS) signal (such as used in the IEEE 802.11wireless LAN standard). In this paper, power allocation isused to optimize either the energy consumption per bit or thelifetime of the network; however, circuit power consumption isnot considered. In [20], best-select relaying is analyzed takingthe circuit power and energy overhead from relay selectioninto account; and, its performance is compared with M-groupall-select relaying. The results in [20] show that, in some cases,M-group outperforms best-select due to the overhead for relayselection.

Most previous work has assumed that the circuit powerconsumption is a constant. However, in [21], a simple linearcircuit power consumption model is proposed; specifically,the power consumed by the Digital Signal Processor (DSP)is modeled as a linear function of the transmission band-width. Using this model, energy-efficient, best-select relayingis analyzed and compared with direct communications. Withthe power consumption model proposed in [21], energy-efficient relay and radio mode selection has been proposedin a heterogeneous network where relay nodes are capable ofaccessing multiple radio access networks [22].

In [23], energy-efficient cooperative beamforming (CBF)with simple relay selection is studied where the selectedrelay nodes construct a Multiple-Input Single-Output (MISO)virtual beamforming system. In this work, the energy overheadto acquire the channel state information is included in theanalysis, and a minimum energy transmission strategy isproposed. However, the paper overlooks the impact of circuitpower consumption which, in general, leads to suboptimalsolutions.

In our paper, we derive and analyze the energy efficiency ofCBF assuming a constant circuit-power consumption modeland a constraint on the maximum transmit power. Also,different from [23], as a cooperative mechanism, we considerclustered cooperation where the cooperating relay nodes areclose to each other, and the performance is compared withdirect communications. In [24], the energy efficiency of clus-tered cooperative relaying is analyzed, but distributed STBC isused as the underlying cooperative mechanism. In general, theclustered cooperative scheme does not benefit from a reducedpath loss, but from using the multiple relay nodes to exploitthe potential diversity gains. As in [23], we explicitly quantifythe energy overhead incurred in implementing CBF includingthe circuit power consumption.

Based on the energy efficiency of CBF derived in thispaper, we directly use the energy efficiency for the evaluationand optimization problems, which is different from the powerminimization problems considered in [23]-[24]. Using theproposed framework, we investigate the energy and spectralefficiency tradeoff of CBF and direct communications, and theimpact of key physical layer parameters: constellation size,power adaptation, circuit power consumption, and trainingoverhead. From the analysis, we determine the number ofrelay nodes that maximizes the energy efficiency for a givenoutage probability constraint. In addition, a mode switchingalgorithm is proposed in which the transmission mode (eitherdirect communications or CBF) is chosen to maximize the

R

M potential relays

S D

Fig. 1. Beamforming with M potential cooperating nodes.

energy efficiency.The rest of the paper is organized as follows. In Section II,

we describe the energy consumption models used. We derivethe energy efficiency of a CBF system and of direct commu-nications in Sections III and IV, respectively. In Section V, theoptimal constellation size and a mode switching algorithm areproposed. In Section VI, the optimal number of relay nodesfor CBF is derived. Finally, simulation results are presentedin Section VII, and conclusions are given in Section VIII.

II. SYSTEM AND ENERGY CONSUMPTION MODEL

Consider a clustered cooperative beamforming schemewhere a source message is transmitted with the help of relaynodes by forming a virtual MISO beam to the destination, asshown in Fig. 1. We assume that M relay nodes are uniformlydistributed around the source node within a radius R; inthis case, the distance from the source to the relay has theprobability density function, f (d) = 2d/R2, 0 < d ≤ R. Wemodel the channel coefficient from the source to relay i, hi,as a complex Gaussian random variable with zero-mean andvariance, σ2

hi; similarly, denote the channel from relay i to

the destination, gi ∼ CN(0,σ2gi), and from the source to the

destination, g0 ∼CN(0,σ2g ). We assume a distance-based path-

loss component, included in the channel variance, given (indB) by

PL(d) = PLF(d0)+ 10β log10

(dd0

)(1)

where

PLF(d0) =−10log10

(λ

4πd0

)2

(2)

and where λ is the wavelength, d0 is a reference distance, andβ is the path-loss exponent.

Realizing CBF requires additional steps to forward thesource message to the destination. The beamforming processis as follows:

• The source and relay nodes estimate the channel.• The channel estimates are shared, and the beamforming

weight is calculated at each node.• The source broadcasts the message to the relays.• The relays beamform the message to the destination.

In the following subsections, we quantify the energy consumedin each step.


LIM and CIMINI: ENERGY-EFFICIENT COOPERATIVE BEAMFORMING IN CLUSTERED WIRELESS NETWORKS 3

A. Channel Estimation Phase

To implement cooperative beamforming, the estimatedchannel gain is required at each relay node to find the optimalbeamforming weight. Thus, in this phase of the process, thedestination broadcasts training symbols, and each of the Mrelays estimates the corresponding channel coefficient, gi.Here, we assume TDD is used; thus, the forward and reversechannel coefficients are assumed to be the same. The powerused for the training signals, PT R, is chosen such that theaverage Signal-to-Noise Ratio (SNR) at the receiver is γT R,that is, PT R = γT RPN/σ2

g . In the energy consumption analysis,we consider not only the power consumed in the transmitterpower amplifier, PPA, but also the power consumed in therest of the circuitry, PC. The amplifier power consumption ismodeled as PPA =Pt/ρ where Pt is the nominal transmit powerand ρ is the amplifier efficiency. We assume that PC is constantand the same in both the transmitter and receiver. We caneasily extend this analysis for cases where PC is different at thetransmitter and the receiver. If there are M relays estimatingtheir corresponding channel gains, the energy consumption bythis process is

ET R = (PT R/ρ +(1+M)PC)NT RTS (3)

where NT R is the number of training symbols, TS ≈ 1/B is thesymbol duration, and B is the transmission bandwidth.

B. Channel Information Sharing Phase

In order to find the beamforming weights, the channelcoefficient, gi, estimated during the previous phase, shouldbe shared with each relay. Then, the optimal beamformingweight for relay i can be calculated as gi/||g|| where g =[g1,g2, · · · ,gM]T . During this information-sharing phase, thesource node estimates the channel gain from the source toeach relay by overhearing the transmission of each relay. Mtransmission times are then required; so, for each transmission,the circuit power consumed is (1+M)PC. Thus, the energyconsumption during this phase is

ECS = M (PCS/ρ +(1+M)PC)bQ

bISTS (4)

where PCS is the transmit power in this phase, and is chosensuch that the outage at the maximum possible distance (2R,diameter of the relay set) satisfies the target outage threshold.bIS is the number of bits/symbol for sharing, and bQ is thenumber of bits used for quantization of the estimated channelgain.

C. Source Message Sharing Phase

After the beamforming weights are calculated, the sourcenode broadcasts its message to the relay nodes. We assumethe source node has an L-bit packet to send. In this message-sharing phase, the energy consumption for an L-bit packet is

ESR = (PSR/ρ +(1+M)PC)TSR (5)

where TSR = LbSRB is the required transmission time to share

the L bits and bSR is the number of bits/symbol used fortransmission. Here, we also consider adapting the transmit

power in response to the fading channel; then, the instanta-neous required transmit power is

PSR =γth(bSR)PN

Hmin(6)

where PN = N0B is the noise power, with N0 the noise powerspectral density. Hmin is the minimum channel power gainamong all the source-to-relay (SR) links. For the analysis,we assume that the relays are located at the same averagedistance, d̄ = E[d], and the corresponding channel varianceat d̄ is σ2

h . Then, using the order statistics of independentexponential random variables, we can show that Hmin is alsoexponentially distributed, but with mean σ2

sr = σ2h /M. γth(bSR)

in (6) is the SNR required to achieve the target M-QAM biterror probability, pth, and is given by

γth(bSR) =− 1c2

(2bSR −1

)ln

(pth

c1

)(7)

which is obtained by inverting the approximation [26]

pth(b) = c1exp

(− c2γ

2b −1

)(8)

where c1 = 0.2, c2 = 1.5, and γ = Pt |h|2PN

is the instantaneousreceived SNR.

D. Cooperative Beamforming Phase

Assuming that each relay node receives the source packetwithout error, the M relay nodes cooperate to form a virtualMISO link to the destination. The energy consumed in formingthe beam and transmitting the source packet to the destinationis

ERD = (PRD/ρ +(1+M)PC)TRD (9)

where PRD = γth(bRD)PN||g||2 is the instantaneous required transmit

power to meet the target SNR threshold, γth(bRD). TRD = LbRDB

is the total transmission time to send L bits, and bRD is thenumber of bits/symbol for CBF.

E. Extra Energy Overhead in CBF

In this section, we analyze how much extra energy isrequired for CBF compared to direct communications. Toform CBF, additional energy is consumed during the channelestimation, channel information sharing, and source messagesharing phases. Then, the aggregate energy overhead for CBFrelative to the direct communications is

EOV = ET R(training)+ECS(channel information sharing)

+ESR(source message sharing) (10)

Combining all of the overheads, we get

EOV =1ρ

(PT RNT R +MPCS

bQ

bIS

)TS +

1ρ

PSRTSR

+PC

((1+M)NTR +M(1+M)

bQ

bIS

)TS

+(1+M)PCTSR (11)

We obtain the equivalent power overhead by dividing EOV in(11) by the total transmission time, TRD, giving



POV =

(PSR

ρ+(1+M)PC

)bRD

bSR+

(PTR

ρ+(1+M)PC

)bRDNT R

L(PCS

ρ+(1+M)PC

)MbQbRD

bISL(12)

For a slow fading channel, the coherence time, TC, is usuallylarge compared to the symbol duration, TS; thus, we assumethe total number of bits in a packet, L, is very large. Inthis case, the overhead from the channel information sharingphase is negligible. The proportion of training symbols inthe data packet is protocol- and system-dependent. Thus, weconsider the training overhead in the analysis and, later in thepaper, show its effect on performance. Then, the final energyoverhead is

POV ≈ (PSR/ρ +(1+M)PC)bRD

bSR+(PTR/ρ +(1+M)PC)

NT R

NRD

= PsrOV +Ptr

OV (13)

where PsrOV and Ptr

OV are the energy overheads from the sourcemessage sharing and channel estimation phases, respectively.NT R and NRD = L

bRDare the number of symbol durations for

the training and CBF phases, respectively.

III. ENERGY EFFICIENCY OF CBF

In this section, we evaluate the energy efficiency of CBFsubject to a constraint on the maximum transmit power,Pmax. Since the source and relays have all of the channelinformation, each can decide whether to transmit or not basedon the constraint. If, for a given channel gain, the requiredpower is greater than Pmax, then an outage is declared, andthe transmission will be suspended. We define the efficiencyin bits/Joule as

EECBF =Lpon

(PRD/ρ +(1+M)PC)TRD +EOV

=(bRDB)pon

PRD/ρ +(1+M)PC +POV(14)

where pon is the probability that an outage does not occurduring either the source message sharing phase or the CBFphase. Then, for large L, approximating POV as in (13), (14)becomes

EECBF ≈ (bRDB)pon1ρ (PRD +PSR

bRDbSR

)+ (1+ bRDbSR

)(1+M)PC +PtrOV

(15)

Since PRD and PSR are adapted over the fading, EE variesfor different channel realizations. In this case, we use theexpectation of (15) as the EE. Unfortunately, it is difficultto directly find the expectation. Thus, for the analysis, weapproximate the EE as the ratio of the expected values of thenumerator and the denominator,

EECBF ≈ (bRDB)pon1ρ (P̄RD +αP̄SR)+ (1+α)(1+M)PC+Ptr

OV

(16)

where α = bRDbSR

, and the average power for each link, with a

maximum power constraint, is defined as P̄RD � E[PRD|PRD ≤Pmax], and P̄SR � E[PSR|PSR ≤ Pmax], respectively.

In general, the approximation used in (16) holds for largevalues of PC. In its general form, EE is given as EE = Rt

Pt+PCwhere, in our case, the throughput Rt is a constant, and thenominal transmit power Pt is a random variable in a fadingchannel. Then, let Y = 1

Pt+PC. In this case, the random variable

Y ranges from 1Pmax+PC

to 1PC

, for a given maximum transmitpower constraint Pmax. For large PC, the variation of Y becomessmall and the approximation E[Y ] ≈ 1

E[Pt ]+PCbecomes very

accurate. In fact, we will show that the approximation isaccurate for most reasonable values of PC.

A. Average Power for CBF

Let G = ||g||2; G has a Gamma distribution with M degreesof freedom. Then, for M ≥ 2, the average power, under thepower constraint Pmax, is

P̄RD = PreqRD E

[1/G|G ≥ Preq

RD

Pmax

]

=Preq

RD

(M −1)σ2g

[1

1+ δ (ηrd,M)

](17)

where

δ (ηrd ,M) =

ηM−1rd

(M−1)!

∑M−2i=0

η irdi!

(18)

and ηrd =γth(bRD)PN

Pmaxσ 2g

=Preq

RDPrec

RD. Preq

RD is the required received power

to meet the target SNR, γth(bRD), and PrecRD is the average

received power when the maximum power is used. We assumethat the distance for the relay-to-destination (RD) link is muchlarger than that of the SR link; so, σ2

gi≈ σ2

g , for all the RDlinks. Thus, ηrd can be thought of as an inverse system power

margin. We can also show that PreqRD

(M−1)σ 2g

is equivalent to E[PRD],

the average transmit power without a power constraint. Then,we can write (17) as

P̄RD = E[PRD][1+ δ (ηrd,M)]−1 (19)

In (19), the second term comes from the power constraint,and, as the power margin increases, δ converges to zeroand P̄RD → E[PRD]. This is because, for a large margin, theoutage will be small in which case the adaptive CBF systemalmost always transmits. Thus, P̄RD = E[PRD]. Conversely, asthe margin decreases, the adaptive CBF system only transmitswhen the channel gain is above the threshold, which leads toP̄RD ≤ E[PRD]. However, even if the margin is not sufficientto make the outage very small, we can effectively increasethe margin by using more relays and increasing the diversityorder.

B. Average Power for Source Message Sharing

The average power for source message sharing is

P̄SR = PreqSR E

[1/Hmin|Hmin ≥

PreqSR

Pmax

]

=−PreqSR

σ2sr

Ei(−ηsr)

e−ηsr(20)

where ηsr =γth(bSR)PN

Pmaxσ 2sr

=Preq

SRPrec

SR. Preq

SR is the required receivedpower to meet the target SNR and Prec

SR is the average receivedpower. Ei(·) is the exponential integral function.



C. Probability of Transmission, pon

The outage during the source message sharing phase isgiven by

pSRout = Pr

(Pmax

PNHmin < γth(bSR)

)= 1− e−ηsr (21)

Since G has a Gamma distribution with M degrees of freedom,the outage during the CBF phase is

pRDout = 1− e−ηrd

M−1

∑i=0

η ird

i!(22)

Then, the probability of transmission, pon, is (1− pSRout)(1−

pRDout).

IV. ENERGY EFFICIENCY OF DIRECT COMMUNICATIONS

In this section, we derive the energy efficiency of twodifferent direct communication systems: non-adaptive (DC)and adaptive (ADC). For non-adaptive direct communication,the source node always transmits at the maximum allowedpower, Pmax. In the adaptive system, the power is adjusted sothat the bit error probability meets the target, pth. Then theefficiency of DC and ADC is given as [25]

EEDC =(bSDB)psd

1ρ Pmax + 2PC

(23a)

and, using the same approximation as in Section III,

EEADC ≈ (bSDB)psd1ρ P̄SD + 2PC+Ptr

OV

(23b)

where bSD is the bits/symbol used for the source-to-destinationtransmission, psd = e−ηsd is the success probability for thedirect link, and Ptr

OV is the training overhead in the ADC

system. ηsd = γth(bSD)PNPmaxσ 2

g=

PreqSD

PrecSD

. PreqSD is the required received

power and PrecSD is the average received power. The average

power consumption, P̄SD, is given as

P̄SD =−PreqSD

σ2g

Ei(−ηsd)

e−ηsd(24)

V. ENERGY-EFFICIENT TRANSMISSION STRATEGY

In this section, we investigate the optimal constellation sizeand propose mode switching to improve the energy efficiency.Here, the adaptation is performed based on the mean channelgain, not on the instantaneous CSI. It is optimal to adapt theconstellation size and mode switching over the instantaneousfading; however, frequent adaptations will increase the systemcomplexity and also require additional signaling. Thus, theoptimal constellation size and mode switching techniques areproposed based on the mean channel gain which can improvethe energy efficiency, but with limited increase in overhead.

A. Optimal Constellation Size

Previously, we only considered a fixed constellation sizefor transmission. However, in this section, we derive theoptimal constellation size which improves the efficiency undera maximum power constraint. First, the optimal size for CBFcan be obtained by solving

(b∗SR,b∗RD) = max

bRD,bSR

EECBF(bRD,bSR) (25)

In (25), the maximum power constraint has been absorbed intothe objective function. Since it is difficult to find a closed-form solution for this problem, we find the optimal solutionby numerical search over bRD and bSR. Similarly, the optimalconstellation size for ADC can be obtained by maximizing

b∗SD = maxbSD

EEADC(bSD) (26)

A numerical search is also used in this case. In general,the range of constellation sizes for the numerical search isnot large. Also, the constellation size is adapted with themean channel gain, not with the instantaneous channel fading.Once the optimal sizes are obtained by numerical search, theycan be stored and used for transmission. In this respect, thecomputational complexity is not significant.

B. Optimal Mode Switching

In general, for short distances, ADC outperforms CBF sincethe circuit power consumption dominates the power consumedin transmitting the signal. However, as the distance increases,CBF provides a higher energy efficiency than ADC due toits lower outage probability. Then, the question arises how tobest utilize the benefits from both schemes; clearly, we shouldswitch between the two modes. In this section, we considermode switching between ADC and CBF, and determine theoptimal threshold for switching. For clarity, we will initiallyfocus on the case with only two relay nodes. We consider theratio between ADC and CBF, given by

EECBF

EEADC=

P̄SD +2ρPC

μ [P̄CBF +3ρ(1+α)PC](27)

where P̄CBF = P̄RD+αP̄SR and μ = psdpon

. The optimal switchingthreshold, μsw, is the one that makes the ratio in (27) equal to1; so, the optimal mode is

Optimal mode =

{ADC, for μ ≥ μsw

CBF, for μ < μsw(28)

If the circuit power consumption is dominant, that is, PC �Pmax/ρ , (27) reduces to

limPC→∞

EECBF

EEADC=

2μ3(1+α)

(29)

Thus, the optimal switching threshold, μsw = 23(1+α) . On the

other hand, if the circuit power consumption is negligible, theratio in (27) is always greater than 1 because the transmissionpower consumed for CBF is always less than that for ADC,P̄CBF < P̄SD. Thus, in this case, CBF is always preferred toADC.



VI. OPTIMAL NUMBER OF RELAYS FOR COOPERATIVE

BEAMFORMING

In the previous sections, we presented the analysis of theenergy efficiency for CBF with a fixed number of relay nodes,M; however, it is clear that there is an optimal number of relaynodes, M∗, for CBF. As M increases, the beamforming gainincreases which reduces the average required transmit power,as well as the outage probability. On the other hand, usingmore relay nodes increases the total circuit power consump-tion. Thus, there is a number of relay nodes which balances thetransmit power consumption, outage probability, and circuitpower consumption. Then, the optimization problem with anoutage and maximum power constraint can be formulated as

maxM

(bRDB)pon1ρ (P̄RD +αP̄SR)+ (1+α)(1+M)PC+Ptr

OV

(30)

subject to pon ≥ psuc

where psuc is the constraint on the probability of transmission.Then, the constraint in (30) can be transformed into Mmin ≤M ≤Mmax, where Mmin is the minimum number of relay nodesthat can satisfy the target psuc using Pmax; Mmin can be obtainedusing (21) and (22). We note that Mmin ≥ 2 since no diversitygain can be achieved with a single relay node. Mmax is themaximum number of available relay nodes. If psuc cannot bemet with Mmax, (30) does not have a feasible solution, and anoutage is declared. The optimal number of relay nodes, M∗,which maximizes the efficiency, can be obtained by numericalsearch.

A. Suboptimal Approach

Since the optimal approach is computationally demanding,especially as the number of relay nodes increases, we proposea suboptimal, but efficient, approach. In practical communica-tion systems, in order for the transmission link to be useful, theoutage must be kept low. Thus, in the suboptimal scheme, weassume a low outage probability (pon ≈ 1). Then, maximizing(30) is equivalent to minimizing the denominator for a givenbRD and B, that is,

minM

1ρ(P̄RD +αP̄SR)+ (1+α)(1+M)PC+Ptr

OV (31)

subject to Mmin ≤ M ≤ Mmax

For pon ≈ 1, we can approximate P̄RD ≈ E[PRD] because thesecond term in (19) converges to 1. Also, for most reason-able circuit power consumption PC ≥ Pmax, we can assumethat αP̄SR/ρ Ptot = E[PRD]/ρ + (1 + α)(1 + M)PC + Ptr

OV .A typical maximum transmit power constraint for WLANand cellular systems ranges between 15 dBm and 25 dBm.From [10], the sum of the power consumption in the RFchain is approximately 100 mW, and if we also consider thepower consumed at the baseband circuit, we can assume thatPC ≥ Pmax. For the fixed bSR, P̄SR is fixed and its maximumpossible value is Pmax. Usually, in the clustered cooperationscenario, P̄SR Pmax since the distance from the source tothe relay is small (the radius R is small), and, thus, P̄SR PC

when PC ≥ Pmax. As the distance increases, to meet the outageconstraint, E[PRD] approaches Pmax. In addition, the number

TABLE ISIMULATION PARAMETERS

Radius of relay set, R 20 mReference distance, d0 1 mBandwidth, B 10 MHzAmplifier efficiency, ρ 38 %Path-loss exponent, β 3.0Noise power spectral density, N0 -174 dBm/HzMaximum transmit power, Pmax 20 dBmCircuit power, PC 100 mWTarget bit error probability, pth 10−4

Carrier frequency, fc 2.5 GHz

of relay nodes, M, increases and Ptot increases by a factor of(1+α)PC. Thus, in this case, Ptot mostly dominates P̄SR, andit can be neglected in the objective function. Then, we havethe simplified objective

minM

PreqRD

ρ(M−1)σ2g+(1+α)(1+M)PC+Ptr

OV (32)

subject to Mmin ≤ M ≤ Mmax

We can see that (32) is a one-dimensional integer optimizationproblem. If we relax the integer constraint on M, then theproblem becomes convex, and a closed-form solution can beobtained by taking the derivative of (32) with respect to M,giving

M∗ = round

(√Preq

RD

ρσ2g (1+α + NT R

NRD)PC

)+1 (33)

where “round(·)” represents rounding to the nearest integer.From (33), we see that the optimal number of relay nodesthat maximizes (32) increases if Preq

RD increases or if the meanchannel gain, σ2

g decreases. This is because, for these cases,more relay nodes are needed to reduce the required trans-mission power given the maximum power constraint. We alsosee that as the circuit power consumption, PC, decreases, M∗increases since the benefit from the increased diversity gainsoutweighs the penalty for consuming more circuit power. Inthe extreme case where PC → 0, we notice that M∗ approachesinfinity and, due to the constraint, we always use the maximumavailable number of relay nodes. This is because when PC

is not considered in the optimization problem, it is alwaysoptimal to use all available relay nodes for beamforming toreduce the required transmit power.

VII. RESULTS

In the simulation, we assume that M relay nodes areuniformly distributed around the source node within a radiusR. We set NT = 100NTR, in which case 1% of the packet isused for training. Since we have assumed a clustered systemwhere the distance from the source to the relays is small,a higher level of modulation can be used; here we use 6bits/symbol (64-QAM) for bSR. In the simulation, we assumethat the circuit power consumption is 100 mW. Typically,the sum of the power consumed in the components in thetransmit/receive chain is approximately 100 mW [10]; ifthe baseband power consumption is considered, then PC willbe higher. The parameters used in the simulation are listedin Table I. We denote CBF(M) as the CBF scheme withM relay nodes. We plot the analytical EEs evaluated with



(16) for CBF with the average power for CBF (19) andsource message sharing (20). For direct communications, theanalytical EEs are plotted using (23a), (23b) and (24). Theanalytical EEs are denoted as ”Analysis” in the figure. Inorder to obtain the curves in the simulation for CBF, PRD

and PSR are obtained for a single channel realization and usedto evaluate the EE with (14). Then, the instantaneous EEs forseveral channel realizations are averaged. Similarly, we canobtain the simulated curves for direct communications.

In Fig. 2(a), we present the energy efficiency (EE) of CBFand ADC/DC as a function of the distance to the destinationwith bSD = bRD = 2 bits/symbol (4-QAM). As we can see,the EEs obtained from the analysis agree well with thoseobtained from the simulation, for a given Pmax. Note thatthe approximation becomes inaccurate for low values of PC.However, the approximation error for the typical range of PC

(≥ 100 mW) is small. For short distances, ADC providesa higher EE than CBF. This is due to the fact that, forshort distances, the circuit power consumption is much largerthan the power consumed in the transmit amplifier. Thus, inthis case, the increase in circuit power consumption fromusing more relay nodes is greater than the reduction in thetransmission power required from the increased beamforminggains. However, as the distance increases, the EE of ADCdecreases due to the increased outage probability and requiredtransmission power. CBF with more relay nodes providesbetter performance for larger distances due to the increasedbeamforming gain, which decreases the outage probability andthe required transmit power.

In Fig. 2(b), we show the corresponding spectral efficiency(SE) of CBF and direct communications. The SE of DC isgiven as LDC

BTSDpsd where LDC is the number of bits in a packet

for direct communications. We assume that the packet durationis equal to the coherence time, TC. Then, LDC = bSDNT , where,as before, NT is the number of symbol durations within onecoherence time, NT = TC

TS�. For ADC, the effective number of

transmission times considering the overhead from the trainingphase is NADC = NT −NT R. Then, LADC = bSDNADC; so theSE of ADC is LADC

BTSDpsd . In the same manner, for CBF, NCT =

NT −NOV where NOV represents the total number of overheadsymbols in the training and channel gain sharing phases. Usingthe fact that the total number of bits in a packet for the CBFsystem, LCT , is the same for the source message sharing andCBF phases, LCT =

⌊NCT

bRD+bSR

⌋bSRbRD . Thus, the SE can be

calculated as LCTBTCT

pon. The total transmission time to send LCT

bits is the sum of the transmission times during the sourcemessage sharing and CBF phases which is given by TCT =TSR +TRD. The results show that the SE of ADC is close to 2bits/sec/Hz, and higher than that of CBF for short distances.However, as the distance increases, the SE of CBF is betterthan that of ADC due to the higher diversity gains. Note thatCBF suffers a 0.5 bits/sec/Hz loss in spectral efficiency dueto the transmission overhead.

The EE of CBF and direct communications is presentedin Fig. 3 using a 16-QAM constellation (i.e. 4 bits/symbolfor bSD = bRD). With the increased constellation size, the EEof all the schemes improves at short distances. However, theefficiency rapidly decreases with distance due to the increased

90

100

80

90

oule

) Analysis:Simulation: DC

60

70

MBi

ts/J ADC

CBF(2)

50

60

ency

(M CBF(3)CBF(4)

30

40

Effic

ie

20

30

Ener

gy

0

10

E

100 150 200 250 300 350 400 450 5000Distance (meter)

(a) Energy Efficiency

3 5

4

3

3.5

ec/H

z)

ADC

2.5

3

Bits

/SeCBF(2)CBF(3)

2

ency

(B CBF(4)

1.5

l Effi

cie

1

pect

ra

0

0.5Sp

100 150 200 250 300 350 400 450 5000Distance (meter)

(b) Spectral Efficiency

Fig. 2. Energy and spectral efficiency of CBF and direct communicationswith 4-QAM for Pmax = 20 dBm.

transmit power consumption and the higher outage probability.Up to now, we have fixed the number of training symbols

relative to the total number of symbol durations, specificallyNT = 100NTR. However, it is worth noting that differentamounts of energy overhead from training will lead to differentoptimal transmission schemes. So, we investigate the effect ofthe energy overhead from training on the EE. In Fig. 4, wepresent the EE as a function of the fraction of the packets usedfor training, NT R/NT ; we evaluate the performance for a fixeddistance, 200 m. In the simulations, we assume that the error inthe channel estimate is small. In practice, the required traininglength to obtain an accurate estimate depends on the specificalgorithm employed. Here, we do not consider any particularalgorithm, but rather simply assume that there is negligibleerror. We observe that the EE of CBF and ADC degrades asthe training overhead increases, and even becomes worse thanDC when more than 25% of the packet is required for training.

In Fig. 5, we show the influence of the circuit powerconsumption on the EE for a fixed distance (200 m); the resultsare plotted as a function of the normalized power consumption,



90

100

80

90ou

le) Analysis:

Simulation: DC

60

70

MBi

ts/J ADC

CBF(2)

50

60

ency

(M CBF(3)CBF(4)

30

40

Effic

ie

20

30

Ener

gy

0

10

E

100 150 200 250 300 350 400 450 5000Distance (meter)

Fig. 3. Energy efficiency of CBF and direct communications with 16-QAM.

50

Analysis:

40Joul

e)

Analysis:Simulation: DC

ADC40

MBi

ts/J CBF(2)

CBF(3)

30

ency

(M CBF(4)

y Ef

ficie

20

Ener

gy

10

E

0 0.1 0.2 0.3 0.4 0.510NTR/NT

Fig. 4. Energy efficiency versus training overhead for 4-QAM.

ρPC/Pmax. As the normalized power consumption increases,the performance of all the schemes degrades because of theincreased energy used. However, the EE of CBF decreasesmore rapidly than for ADC/DC due to the larger amount ofcircuit power consumed and, for relatively high circuit powerconsumption, DC even outperforms CBF(2).

Since the EE obtained from the analysis matches well withthe simulation results, we will use the analytical EE to obtainthe curves for ADC and CBF. In Fig. 6(a), the EE of CBFand ADC is presented, using the optimal constellation size.With an optimal constellation size, we can see that the EE ofboth ADC and CBF improves. This is due to the fact thatboth schemes adopt the higher constellation size for shortdistances to speed up the data transmission, and less circuitpower will be consumed by turning off the RF circuitry. Forlarge distances, a smaller constellation size is used to reducethe outage probability. We also observe from the results in Fig.6(a) that CBF with more relay nodes performs better as thedistance increases due to the trade-off between circuit powerconsumption and beamforming gain. The corresponding SEis given in Fig. 6(b). It shows that CBF provides a higher

50

40

oule

) Analysis:Simulation: DC

30MBi

ts/J

o

ADCCBF(2)

30

ency

(M CBF(3)CBF(4)

20

Effic

ie

10

Ener

gy

E

0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 220Normalized Power Consumption

Fig. 5. Energy efficiency as a function of the normalized power consumption,circuit power normalized by the maximum power consumed, for 4-QAM.

SE than ADC even for short distances due to better outageperformance. Also, we observe that CBF is optimized with ahigher order modulation compared with ADC. As the distanceincreases, the optimal constellation size decreases to maintainan acceptable outage probability.

From the previous results, we see that the improvementof CBF over direct communications depends on the systemparameters. In general, as the path loss and the transmissionbandwidth increases, the required transmit power and outageprobability also increase, in which case the performance ben-efit from CBF increases compared to direct communications.On the other hand, with increased circuit power consumptionand training duration, the relative benefit over ADC decreasesdue to the increased energy consumption overhead. Thus, tomost accurately evaluate the EE of a particular system, preciseestimates of the system parameters are necessary.

In Fig. 7(a), we present the EE of CBF for an optimalnumber of relay nodes with maximum power and minimumsuccess probability constraints. For the simulation, 16-QAMand a minimum success probability, psuc = 0.8, are used. Wedenote the optimal scheme as CBF-opt and suboptimal asCBF-sub. As shown in the figure, the EE of ADC rapidlydecreases with distance, and becomes zero. This is becauseADC, for large distances, suspends transmission since thetarget success probability constraint cannot be satisfied. How-ever, CBF can meet the target constraints for any distance byoptimally increasing the number of relay nodes. We also noticethat the suboptimal scheme provides performance that is veryclose to the optimum even with a moderate outage probabilityconstraint (psuc = 0.8); in this case, BS-sub provides the sameperformance as BS-opt. Thus, CBF-sub is preferred since itrequires less computations. The corresponding number of relaynodes for each scheme is presented in Fig. 7(b). For shortdistances, M=2 relay nodes are optimal for all schemes; andthe optimal M increases with distance. Note that the numberof relay nodes chosen by CBF-sub is exactly the same as thatfor the optimal scheme. For a given set of parameters, thesource node calculates the optimal number of relay nodes,M∗, using (33). Assuming that a unique ID is given for each



90

100

80

90ou

le)

ADC

70

Bits

/Jo

CBF(2)CBF(3)

50

60

ncy

(MB

CBF(4)

40

Effic

ien

20

30

nerg

y E

10

20

En

100 150 200 250 300 350 400 450 5000Distance (meter)


3

4

3

3.5

ec/H

z)

ADC

2.5

3

Bits

/Se

CBF(2)CBF(3)

2

ency

(B CBF(4)

1.5

l Effi

cie

1

pect

ra

0.5S

100 150 200 250 300 350 400 450 5000Distance (meter)

(b) Spectral Efficiency

Fig. 6. Energy and spectral efficiency of CBF and direct communicationswith an optimal constellation size.

relay in the relay cluster, the source node can choose the M∗relay nodes by broadcasting the IDs of the selected relay nodesby the source. However, we note that the M∗ obtained fromCBF-sub deviates from that obtained from CBF-Opt as psuc

decreases.

From the previous discussion, we see that ADC outperformsCBF for short distances; this is because the circuit powerconsumption dominates the total power consumption. Basedon these results, we propose to switch between ADC andCBF. In Fig. 8, we present the optimal mode switchingthreshold, μsw, versus the normalized power consumption forα = bRD/bSR = 1/3 (bRD = 2 bits/symbol) and 2/3 (bRD = 4bits/symbol). In the figure, the solid line represents the resultsfrom using (27), and numerical simulation is used for thedashed line. Due to the assumption used to obtain the approx-imated EE for ADC and CBF, the optimal switching thresholdobtained from (27) deviates from numerical simulation forlow PC. However, the threshold gap becomes smaller as PC

increases; the gap is small if PC ≥ 50 mW. As discussed above,for PC ≈ 0, μsw = 1, and it decreases with PC, converging to

100 150 200 250 300 350 400 450 5000

10

20

30

40

50

60

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100

Distance (meter)

Ener

gy E

ffici

ency

(MBi

ts/J

oule

)

ADC CBF-Opt CBF-Sub


100 150 200 250 300 350 400 450 5000

2

4

6

8

10

12

14

Distance (meter)

Opt

imal

Num

ber o

f Rel

ay N

odes

CBF-Opt CBF-Sub

(b) Optimal Number of Relay Nodes

Fig. 7. Energy efficiency of CBF with optimal number of relays for 4-QAMfor psuc = 0.8.

23(1+α)

. For a given μsw, if μ = psdpon

> μsw, ADC is consideredto be optimal. Thus, the lower μsw for the increased PC

means that the chance that ADC is selected for transmissionis increased. Note that the pair (psd , pon) for μsw is uniquesince both are strictly decreasing functions of the transmissiondistance. For example, for fixed PC, constellation size, andPmax, finding μsw is equivalent to finding the critical distanceat which the EEs of both schemes are equal. Since, for eachdistance, the success probability pair (psd , pon) is unique,using μsw is, thus, equivalent to using the corresponding psd .Once the psd corresponding to a specific μsw is calculated, wecan store it in a look-up table to use for choosing the optimalmode. For example, if ρPC/Pmax = 0.3 for α = 1/3, then thecorresponding threshold μsw = psd ≈ 0.65. In this case, if thesuccess probability of ADC is below 65%, then it is best toswitch to CBF.

VIII. CONCLUSION

In this paper, we presented an analysis of the energyefficiency of the clustered cooperative beamforming where



0.9

11

A l i0.8

0.9ho

ldAnalysis:

Simulation:

0 6

0.7

Thre

s

0.5

0.6

tchi

ng

1/3

0 3

0.4

mal

Sw

i = 1/3

= 2/3

0.2

0.3

Opt

im

0

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 110Normalized Power Consumption

Fig. 8. Optimal switching threshold for cooperative beamforming as afunction of the normalized power consumption, circuit power normalized bythe maximum power consumed, for Pmax = 20 dBm.

the transmit power is adapted over the fading, subject to amaximum power constraint. In the analysis, we considered theenergy overhead incurred in cooperating to form a beam. Weassumed a constant level of circuit power consumption. Weshowed that, even with the extra energy overhead, cooperativebeamforming can provide not only higher energy efficiency,but also larger spectral efficiency, using either fixed or adaptivemodulation, compared to a system using direct communica-tions. We also investigated the optimal and suboptimal strategywhich finds the number of relay nodes to maximize the energyefficiency. Finally, we proposed mode switching techniquewhich optimally selects the transmission mode among adaptivedirect communications and cooperative beamforming.

REFERENCES

[1] [Online]. Available: http://www.alcatel-lucent.com/features/light radio[2] Y. Chen, S. Zhang, S. Xu, and Y. (G.) Li, ”Fundamental trade-offs on

green wireless networks,” IEEE Commun. Mag., vol. 49, no. 6, pp. 30-37, June 2011.

[3] G. Miao, N. Himayat, Y. (G.) Li, and A. Swami, ”Cross-layer optimiza-tion for energy-efficient wireless communications: a survey,” Wiley J.Wireless Commun. Mobile Comput., vol. 9, no. 4, pp. 529-542, Apr.2009.

[4] Y. (G.) Li, Z. Xu, C. Xiong, C. Yang, S. Zhang, Y. Chen, and S. Xu,”Energy-efficient wireless communications: Tutorial, survey, and openissues,” IEEE Commun. Mag., vol. 18, no. 6, pp. 28-35, Dec. 2011.

[5] D. Feng, C. Jiang, G. Lim, L. J. Cimini, Jr., G. Feng, and Y. (G.) Li,”A survey of energy-efficient wireless communications,” to appear inIEEE Commun. Surveys Tuts., (10.1109/SURV.2012.020212.00049).

[6] S. Verdu, ”Spectral efficiency in the wideband regime,” IEEE Trans. Inf.Theory, vol. 48, no. 6, pp. 1319-1343, June 2002.

[7] S. Cui, A. J. Goldsmith, and A. Bahai, ”Energy-constrained modulationoptimization,” IEEE Trans. Wireless Commun., vol. 4, no. 5, pp. 2349-2360, Sept. 2005.

[8] Q. Chen and M. C. Gursoy, ”Energy-efficient modulation design forreliable communication in wireless networks,” in Proc. IEEE CISS, Mar.2009.

[9] V. Raghunathan, C. Schurgers, S. Park, and M. B. Srivastava, ”Energy-aware wireless microsensor networks,” IEEE Signal Proc. Mag., vo. 19,no. 2, pp. 40-50, Mar. 2002.

[10] S. Cui, A. J. Goldsmith, and A. Bahai, ”Energy-efficiency of MIMOand cooperative MIMO techniques in sensor networks,” IEEE J. Sel.Area Commun., vol. 22, no. 6, pp. 1089-1098, Aug. 2004.

[11] S. K. Jayaweera, ”Virtual MIMO-based cooperative communication forenergy-constrained wireless sensor networks,” IEEE Trans. WirelessCommun., vol. 5, no. 5, pp. 984-989, May 2006.

[12] H. S. Kim, C.-B. Chae, G. D. Veciana, and R. W. Heath, ”A cross-layerapproach to energy efficiency for adaptive MIMO systems exploitingspare capacity,” IEEE Trans. Wireless Commun., vol. 8, no. 8, pp. 4624-4725, Aug. 2009.

[13] Z. Chong, and E. A. Jorswieck, ”Energy efficiency in random oppor-tunistic beamforming,” in Proc. IEEE VTC, May 2011.

[14] Y. Li, B. Bakkaloglu, and C. Chakrabarti, ”A system level energymodel and energy-quality evaluation for integrated transceiver front-ends,” IEEE Trans. Very Large Scale Integration Syst., vol. 15, no. 1,pp. 90-103, Jan. 2007.

[15] W. Gabran and B. Daneshrad, ”Hardware and physical layer adaptationfor a power constrained MIMO OFDM system,” in Proc. IEEE ICC,Apr. 2011.

[16] C. Isheden and G. Fettweis, ”Energy-efficient link adaptation on aRayleigh fading channel with receiver CSI,” in Proc. IEEE ICC, Apr.2011.

[17] Q. Chen and M. C. Gursoy, ”Energy efficiency analysis in amplify-and-forward and decode-and-forward cooperative networks,” in Proc. IEEEWCNC, Apr. 2010.

[18] A. Bletsas, A. Khisti, D. P. Reed, and A. Lippman, ”A simple cooper-ative diversity method based on network path selection,” IEEE J. Sel.Areas Commun., vol. 24, no. 3, pp. 659-672, Mar. 2006.

[19] Z. Zhou, S. Zhou, J.-H. Cui, and S. Cui, ”Energy-efficient cooperativecommunication based on power control and selective single-relay inwireless sensor networks,” IEEE Trans. Wireless Commun., vol. 7, no.8, pp. 3066-3078, Aug. 2008.

[20] Y. Xiao, and L. J. Cimini, Jr., ”Energy efficiency of distributed cooper-ative relaying,” in Proc. IEEE Milcom, May 2011.

[21] G. Lim and L. J. Cimini, Jr., ”Energy-efficient best-select relaying inwireless cooperative networks,” in Proc. IEEE CISS, Mar. 2012.

[22] G. Lim and L. J. Cimini, Jr., ”Energy-efficient cooperative relaying inheterogeneous radio access networks,” IEEE Wireless Commun. Lett.,vol. 1, no. 5, pp. 476-479, Oct. 2012.

[23] R. Madan, N. B. Mehta, A. F. Molisch, and J. Zhang, ”Energy-efficientcooperative relaying over fading channels with simple relay selection,”IEEE Trans. Wireless Commun., vol. 7, no. 8, pp. 3013-3025, Aug. 2008.

[24] Z. Zhou, S. Zhou, S. Cui, and J.-H. Cui, ”Energy-efficient cooperativecommunication in a clustered wireless sensor network,” IEEE Trans.Veh. Technol., vol. 57, no. 6, pp. 3618-3628, Nov. 2008.

[25] G. Lim and L. J. Cimini, Jr., ”Energy efficiency of cooperative beam-forming in wireless ad-hoc networks,” in Proc. IEEE ICC, June 2012.

[26] A. J. Goldsmith, Wireless Communications. Cambridge, UK: CambridgeUniversity Press, 2005.

Gubong Lim (S’09) received the B.S. in Electri-cal Engineering in 2003 from Gangneung NationalUniversity, Gangneung, Korea, and the M.S. degreefrom the University of Delaware, Newark, DE, in2005. From 2005 to 2009, he worked as an engineerat Samsung Electronics. From 2009, he is currentlyworking toward the Ph.D degree in the Universityof Delaware. His research includes wireless OFDM,cooperative communications, and energy-efficientwireless communication system design.

Leonard J. Cimini, Jr. (S’77-M’82-SM’89-F’00)received the Ph.D. from the University of Pennsyl-vania in 1982. He worked at AT&T, first in Bell Labsand then AT&T Labs, for 20 years. He has been aProfessor at the University of Delaware, Newark,since 2002.

Dr. Cimini began his ComSoc activities twenty-five years ago in the Communication Theory Tech-nical Committee. He is currently VP - TechnicalActivities, and, among other publications-related po-sitions, is the founding Editor-in-Chief of the IEEE

J-SAC: WIRELESS COMMUNICATIONS SERIES. He was elected an IEEEFellow in 2000 for contributions to the theory and practice of high-speedwireless communications. For this pioneering work, he was given the 2007James R. Evans Avant Garde Award from the IEEE Vehicular TechnologySociety and the 2010 Innovators Award from the NJ Inventors Hall of Fame.In 2010, he received several ComSoc awards, including the Stephen O.Rice Prize, the Donald W. McLellan Meritorious Service Award, and theRecognition Award from the Wireless Communications Technical Committee.


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Energy-Efficient Cooperative Beamforming in Clustered Wireless