Energy-Efficient MIMO-OFDMA Systems based onSwitching Off RF Chains

Zhikun Xu, Chenyang Yang, Geoffrey Ye Li, Shunqing Zhang, Yan Chen, and Shugong Xu

School of Electronics and Information Engineering, Beihang University, Beijing 100191, P. R. ChinaSchool of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA

GREAT Research Team, Huawei Technologies Co. Ltd., Shanghai, P. R. ChinaEmail of corresponding author: xuzhikun@ee.buaa.edu.cn

AbstractIn this paper, both configuration of active radiofrequency (RF) chains and resource allocation are investigated forimproving energy efficiency of downlink multiple-input-multiple-output (MIMO) orthogonal frequency division multiple access(OFDMA) systems. We first formulate an optimization problemto minimize the total power consumed at the base station withthe maximum transmit power constraint and ergodic capacityconstraints from multiple users. Then a two-step suboptimalalgorithm is proposed. Specifically, the continuous variable op-timization problem is first solved, and then a discretizationalgorithm is presented to obtain the number of active RF chainsand the number of subcarriers allocated to each user. Simulationresults demonstrate that the proposed algorithm can providesignificant power-saving gain over the all-on RF chain schemeand the adaptive subcarrier allocation helps to save more power.

I. INTRODUCTIONWireless networks are expected to be designed in an energy-

efficient way since the explosive growth of wireless service issharply increasing their contribution to the carbon footprint[1]. Multiple-input-multiple-output (MIMO) transmission hasbeen widely applied in wireless networks nowadays owing toits high spectral efficiency. Although MIMO systems need lesstransmit power than single-input-single-output (SISO) systemsfor the same data rate, more circuit power is consumed sincemore active transmit or receive radio frequency (RF) chains areused, which has been shown comparable to the transmit powerin practical networks, such as wireless sensor networks [2] andcellular networks [3]. After the circuit power consumptionis taken into account, whether MIMO systems are energyefficient is not clear.

There have been some preliminary results on this topic.Energy efficiency (EE) of Alamouti diversity scheme has beendiscussed in [2]. It was shown that for short-range trans-mission, multiple-input-multiple-output (MISO) transmissiondecreases EE as compared with SISO transmission if adaptivemodulation is not used. However, if modulation order is This work was supported by the International S&T Cooperation Program

of China (ISCP) under Grant No. 2008DFA12100, Key project of NextGeneration Wideband Wireless Communication Network, Ministry of Industryand Information (MII): Coordinated Multiple-point Transmission for IMT-Advanced Systems under grant No. 2009ZX03003-003, and the Research Giftfrom Huawei Technologies Co., Ltd.

adaptively adjusted to balance the transmit and circuit powerconsumption, MISO systems will perform better. In [4], spatialmultiplexing, space-time coding, and single antenna transmis-sion have been adaptively selected based on the channel stateinformation, and the EE improvement is up to 30% comparedwith non-adaptive systems. In [5], adaptive switching betweenMIMO and single-input-multiple-output (SIMO) modes hasbeen addressed to save energy in uplink cellular networks. In[6], the number of active RF chains is optimized to maximizeEE given the minimum data rate. These works only considerpoint-to-point transmission. For downlink cellular networks,RF chains at the base station (BS) are shared by multiple usersand switching on or off RF chains will have different impacton the performance of different users. How to determine thenumber of active RF chains in this case is still unknown.

In this paper, we will study energy efficient configuration ofactive RF chains for downlink orthogonal frequency divisionmultiple access (OFDMA) networks. Different from existingworks, we will jointly optimize the number of active RFchains and resource allocation with capacity requirements formultiple users. A two-step algorithm is developed to find thesuboptimal solution, which can reduce power consumptionsignificantly.

The remainder of this paper is organized as follows. Thesystem model and problem formulation are presented in Sec-tion II and III, respectively. In Section IV, we propose atwo-step algorithm to find the suboptimal solution. Simulationresults are provided in Section V and the paper is concludedin Section VI.

II. SYSTEM MODELConsider a downlink MIMO-OFDMA cellular network with

one BS and I users. It is assumed that M and N RF chains arerespectively configured at the BS and each user and M > N .Each RF chain is connected with an antenna to transmit orreceive signals. Overall K subcarriers are shared by differentusers with no overlap. The index set of subcarriers occupiedby user i is denoted as Si with size ki.

Since most power is consumed at the BS during downlinktransmission and a large portion of power is consumed bythe RF chains including both transmit and circuit power, we

978-1-4244-8327-3/11/$26.00 2011 IEEE

consider adaptive RF chain configuration for saving energy.Specifically, both the number of active RF chains and thetransmit power at the BS are adjusted to minimize the totalpower consumption with capacity constraints from multipleusers. Denoting m as the number of active RF chains, thenm M and N m MIMO channel is built from BS to eachuser. Closed-loop single-user MIMO (SU-MIMO) schemes areconsidered and capacity-achieving precoder is assumed in thispaper. Since the number of antennas is larger than that ofactive RF chains at the BS, transmit antenna selection can beapplied to enhance channel capacity [7]. However, to highlightthe impact of the number of active RF chains, the antennaselection will not be considered.

It is assumed that users undergo frequency-selective andspatial non-coherent block fading channels. Denote Hij asthe spatial channel matrix from BS to user i on subcarrier j.Elements in Hij are independent and identically distributed(i.i.d) random variables with zero mean and variance i, whichis the large-scale channel gain from the BS to user i. The noiseat the receiver of each user is assumed to be additive whiteGaussian with zero mean and variance 2.

III. PROBLEM FORMULATION

In this section, we will formulate the optimization problemto minimize the overall power consumed at the BS withconstraints on the upper bound of ergodic capacity for eachuser.

The overall power consumed at the BS, Ptot, includes thetransmit power and the circuit power. Denoting , Pt, and Prfas the efficiency of power amplifier, the radiated power, and thecircuit power consumed by each active RF chain, respectively,then the overall power consumption can be expressed as [5]

Ptot = Pt/ + mPrf . (1)As in Long Term Evolution (LTE) systems, we consider

that the transmit power is equally allocated over subcarriersand data streams. Then the transmit power on each subcarrierfor each data stream is

Pea =Pt

KD, (2)

where D min{m,N} is the number of data streams in anN m MIMO system.

The instantaneous capacity of user i on subcarrier j can beexpressed as

Tij = f log2(det(IN +12HijQxHHij )), (3)

where f is the subcarrier spacing, IN denotes an N Nidentity matrix, and Qx is the autocorrelation matrix oftransmit signal x.

When the capacity-achieving precoder and equal powerallocation are applied, (3) can be simplified as

Tij = fD

d=1

log2(1 +Pea

2ijd

2)

= fD

d=1

log2(1 +Pt

2ijd

KD2), (4)

where ijd denotes the dth singular value of Hij . The instan-taneous capacity of user i is then obtained as

Ci =jSi

Tij = fjSi

Dd=1

log2(1 +Pt

2ijd

KD2). (5)

Since RF chains cannot be switched between on and offstatuses frequently due to hardware constraints, we considerergodic capacity requirement of each user. Moreover, since theaccurate expression of ergodic capacity is rather complicatedand the channel distribution is hard to obtain in practicalsystems, we consider the constraints over the upper boundof ergodic capacity as follows,

fjSi

Dd=1

log2(1 +PtE[2ijd]KD2

) Ri, (6)

where the upper bound is obtained by using Jensens inequalityon (5), Ri is the requirement of user i on the upper bound ofergodic capacity , and E[] is the expectation operation.

The variance of singular value ijd is the same for differentj and d [8] and can be obtained from the derivation inAppendix A as

E[2ijd] = imN/D. (7)Substituting (7) into (6), the capacity constraints can be

finally expressed as

fkiDlog2(1 +imNPtKD22

) Ri. (8)It can be observed from (8) that the constraints only depend onthe large-scale channel gains, {i}Ii=1, which is easy to obtainin cellular networks. Note that the upper bound simplifies theanalysis of the problem and such constraint is effective whenthe ergodic capacity scales in the same way with the upperbound.

We will optimize the number of active RF chains, m, thenumber of subcarriers for each user, ki, and the radiatedpower, Pt, to minimize the total power consumption with theconstraints on the upper bound of ergodic capacity for eachuser. The optimization problem is formulated as follows,

minm,{ki}Ii=1,Pt

Pt/ + mPrf (9)

s. t. fkiDlog2(1 +imNPtKD22

) Ri, (9a)I

i=1

ki = K, (9b)

0 < m M, (9c)0 < Pt Pmax, (9d)ki > 0, i = 1, 2, , I, (9e)

where (9b) is the total subcarrier constraint and (9d) is themaximum transmit power constraint.

IV. TWO-STEP SUBOPTIMAL ALGORITHM

In this section, we will develop an algorithm to find thesolution of problem (9). Since the number of active RF chains,m, and the number of subcarrier, {ki}Ii=1, are both integervariables and the transmit power, Pt, is a real variable, (9) isa combinational optimization problem. Exhaustive searching isrequired to find the solution but its complexity is prohibitive.In the following, a two-step searching algorithm is proposed,which first solves the problem by treating ki and m ascontinuous real variables and then discretizes them to find asuboptimal solution.

Since the number of data streams D is equal to the minimumof m and N , we divide the problem (9) into two casesdepending on whether m N or not, which yield differentsolutions. When m N , D = N and the constraint (9a) is

fkiN log2(1 +imPtKN2

) Ri. (10)When m < N , D = m and the constraint (9a) is

fkimlog2(1 +iNPtKm2

) Ri. (11)Replacing (9a) in the problem (9) by (10) and (11), twooptimization problems are formulated for the two cases andcalled problem (S1) and (S2), respectively. We will next solvethese two problems for continuous m and {ki}Ii=1.

A. Solving Continuous Variable Problems

It is easy to find that the global optimum of problem (S1) isachieved when the equality in constraint (10) holds since boththe objective function in (9) and the constraint in (10) increasemonotonically with m and Pt. By solving the equation, wehave

ki =Ri

fN log2(1 +imPtKN2 )

. (12)

Substituting (12) into constraint (9b), we obtainI

i=1

Ri

fN log2(1 +imPtKN2 )

= K. (13)

Since the left hand side of this equation is a decreasingfunction with respect to mPt, there exists a unique solutionfor mPt, which can be found numerically by the bisectionmethod. Denoting as the solution of mPt from (13), thenproblem (S1) can be rewritten as

minm,Pt

Pt/ + mPrf (14)s. t. mPt = (14a)

N m M (14b)0 < Pt Pmax. (14c)

We can derive that when > MPmax, there is nointersection among (14a) (14c). Hence, the problem (14) isinfeasible and outage occurs. When MPmax, accordingto the derivation in Appendix B, the solution of m to this

problem can be obtained as follows,

mo =

Prf, MPmax and Neq

Prf M

M, MPmax and

Prf

> M

Neq, MPmax and

Prf

< Neq,

where Neq = max{/Pmax, N}, and the optimal Pt can beobtained as

P ot =

mo.

When m < N , we need to solve the problem (S2). It isreadily shown that (11) is a convex constraint. In addition,the objective function and other constraints of the problem(S2) are linear. Therefore, the problem (S2) is convex, whichcan be solved by some efficient optimization methods, suchas the interior-point method [9].

After the two problems are solved, we compare the totalpower consumption in these two cases and select the one withsmaller power as the solution of m and Pt.

B. Variable DiscretizationThe solution of the continuous variable problem cannot be

applied directly since in practice m and {ki}Ii=1 have integervalues. In this subsection, we will discretize the optimizedvalues. It is reasonable to set the optimal discrete number ofactive RF chains to be the smallest number larger than mo,i.e., m = mo. The discrete number of ki can be foundby the following algorithm, whose basic idea is as follows.First, assign user i with the integer part of continuous koiobtained from solving the continuous variable problem in lastsubsection. Then allocate the remaining subcarriers one by oneto the user who has the largest capacity gap from the expectedergodic capacity. The detailed algorithm is summarized inTable I.

TABLE IALGORITHM FOR DISCRETIZING THE NUMBER OF SUBCARRIERS

Input: koi , m, and P ot .Output: the number of subcarriers for user i, ki ,.

1. Initialize ki = koi , and K = K I

i=1

koi .2. while K > 03. Calculate the capacity gaps from the expected

ergodic capacity as follows,

i Ri fkiDlog2(1 +mNiP

ot

KD22), (15)

where D = min{m, N}.4. imx = argmax{1, , K} and kimx = kimx +1.5. K = K 16. end7. return ki = ki

After discretizing the number of active RF chains at the BSand the number of subcarriers for each user, the transmit power

TABLE IILIST OF SIMULATION PARAMETERS

Subcarrier spacing, f 15 kHzNumber of subcarrier, K 1024Number of users, I 10Number of RF chains at BS, M 8Number of RF chains at each user, N 2Radius of a cell, R 500 m

Uniformly distributedUser distribution in the cellPower spectral density of noise -174 dBm/HzNoise amplifier gain 7 dBiMinimum distance from BS to users 35 mPath loss (dB) 35+38log10 dStandard variance of Shadowing 8 dBEfficiency of power amplifier, 38%Maximum transmit power, Pmax 40 WCircuit Power of a RF chain, Pc 5-20 W

2 4 6 8 10 12 14 161

2

3

4

5

6

7

8

Rmax

(Mbps)

m*

Prf=5W

Prf=10W

Prf=20W

Fig. 1. Number of active RF chains at BS vs.capacity requirement

P ot may not satisfy the capacity requirement any more. We willfind the suboptimal transmit power from (9a) as follows,

P t = max{Pt,1, , Pt,I},

where Pt,i = KD22(2

Rifk

iD 1)

imN.

V. SIMULATION RESULTS

In this section, we will demonstrate the performance ofthe proposed energy-efficient algorithm and study the impactof the capacity requirement, circuit power consumption andsubcarrier allocation. System parameters are listed in TableII. The maximum transmit power, the efficiency of poweramplifier, and the range of circuit power are configured asin [3]. In the simulation, the capacity requirements from allusers, {Ri}Ii=1, are set to the same value and denoted as Rmaxin the figures.

Figure 1 shows the number of active RF chains found bythe proposed algorithm versus the capacity requirement withdifferent circuit powers. It can be observed that the numberof active RF chains increases with the capacity requirement.With the increase of the circuit power, the number of active

2 4 6 8 10 12 14 160

5

10

15

20

25

30

35

40

Rmax

(Mbps)

P t (W

)

Prf=5W

Prf=10W

Prf=20W

Fig. 2. Overall transmit power vs. capacity requirement

2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Rmax

(Mbps)

Prf=5W

Prf=10W

Prf=20W

Fig. 3. Power saving gain vs. capacity requirement, where = PallPt

Palland Pall is the power consumption when all RF chains are open.

RF chains decreases.Figure 2 shows the overall transmit power versus the ca-

pacity requirement with different circuit powers. It is shownthat the overall transmit power increases with the capacityrequirement as well as the circuit power. The opposite trendwith the circuit power implies that a tradeoff exists betweenthe optimal number of active RF chains and the optimal overalltransmit power.

To show the power saved by switching off RF chains, wecompare the performance of the proposed scheme with that ofall RF chains open at the BS. Fig. 3 shows the power savinggain versus the capacity requirement with different circuitpower consumption. We can see that the power saving gainreduces with the capacity requirement and increases with thecircuit power. For example, when Rmax = 4 Mbps, the powersaving gain is up to 60% when Prf = 20 W.

Adaptively allocating the number of subcarriers to eachuser based on channel gains and capacity requirements helpsto save more power. To show this, we compare the outageprobability when adaptive subcarrier allocation is used withthat when uniform subcarrier allocation, i.e. ki = K/I , isused. The outage probability is the probability that there isno feasible solution for the problem (9). As shown in Fig.

2 4 6 8 10 12 14 160

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Rmax

(Mbps)

Out

age

Prob

abilit

y

Adaptive Subcarrier AllocationUniform Subcarrier Allocation

Fig. 4. Outage probability vs. capacity requirement

4, the outage probabilities in both cases increase with thecapacity requirement. For the same outage probability, higherergodic capacity requirement can be met by using the adaptivesubcarrier allocation. In other words, less power is needed toachieve the same ergodic capacity requirement.

VI. CONCLUSIONIn this paper, we studied the configuration of active RF

chains and resource allocation from the perspective of EE fordownlink MIMO-OFDMA systems. We first formulated theoptimization problem to minimize the total power consumedat the BS with the constraints on the maximum transmit powerand each users upper bound of ergodic capacity. Then a two-step algorithm was proposed, which first found the continuousvariable solutions and then discretized them to obtain thenumber of active RF chains and the number of subcarriersallocated to each user. Simulation results have shown thatboth the number of active RF chains and the overall transmitpower increase with the capacity requirement. Moreover, thereis a tradeoff between the number of active RF chains and theoverall transmit power, which depends on the circuit powerconsumed by each RF chain. The proposed algorithm can saveup to 60% power compared with the all-on RF chain schemewhen the required capacity is 4 Mbps and the circuit powerconsumed by each RF chain is 20 W. The adaptive subcarrierallocation consumes less power than the uniform subcarrierallocation for a given ergodic capacity requirement and a givenoutage probability.

APPENDIX ADERIVATION OF THE VARIANCE OF ijd

According to the property of singular value decomposition,we have

Dd=1

2ijd = Tr(HijHHij ), (16)

where Tr(A) denotes the trace of matrix A. After takingexpectation over both sides of ths equation, we obtain

E[D

d=1

2ijd] = Tr(E[HijHHij ]). (17)

Since all the singular values have the same variance due tothe i.i.d property of all the elements in Hij , we have

E[2ijd] = Tr(E[HijHHij ])/D = imN/D. (18)

APPENDIX BDERIVATION OF THE SOLUTION FOR SUBPROBLEM (S1)From mPt = in (14a), we know Pt = m . After

substituting it into problem (S1), the problem turns into

minm,Pt

m+ mPrf (19)

s. t. N m M (19a)m

Pmax. (19b)

When MPmax, this problem is feasible. Constraints(19a) and (19b) can be combined as follows,

Neq m M, (20)where Neq = max{ Pmax , N}.

It is readily shown that the objective function is mini-mized when m =

/PRF . When m >

/PRF , it

monotonically increases with m. When m M

Neq, MPmax and

Prf

< Neq.

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[2] S. Cui, A. J. Goldsmith, and A. Bahai, Energy-efficiency of MIMO andcooperative MIMO techniques in sensor networks, IEEE J. Select. AreasCommun., vol. 22, no. 6, pp. 10891098, Aug. 2004.

[3] O. Arnold, F. Richter, G. Fettweis, and O. Blume, Power consumptionmodeling of different base station types in heterogeneous cellular net-works, in Proc. Future Network Mobile Summit (FNMS), Jun. 2010.

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[5] H. Kim, C.-B. Chae, G. de Veciana, and J. R. W. Heath, A cross-layerapproach to energy efficiency for adaptive MIMO systems exploitingspare capacity, IEEE Trans. Wireless Commun., vol. 8, no. 8, pp. 42644275, Aug. 2009.

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