IEEE ICC 2012 - Wireless Communications Symposium
Joint Transceiver Beamforming Design and Power Allocation for Multiuser MIMO Systems Qian Liu
Chang Wen Chen
Department of Computer Science and Engineering State University of New York at Buffalo Buffalo, NY, 14260
[email protected]
Department of Computer Science and Engineering State University of New York at Buffalo Buffalo, NY, 14260
[email protected]
Abstract— Multi-user multiple input multiple output (MUMIMO) system is an excellent choice for the next generation broadband communications because of its great potential in enhancing MIMO system capacity. One major challenge of such system is the jointly optimal transceiver beamforming design that maximizes the sum capacity under a total power constraint. Existing approaches have provided convex optimization solution by exploiting the duality between transmitter and receiver. However, with high computation complexity, these approaches are ineligible of practical implementation. In this paper, we aim to provide complexity efficient transceiver beamformer and power allocation design in MU-MIMO downlink (broadcast) channels. We first develop an iterative sub-optimal algorithm based on cyclic self-SINR-maximization (CSSM) beamforming design and waterfilling power allocation. Comparing to convex-optimization-based (COB) approaches, the proposed solution (i.e. CSSM-WF algorithm) have insignificant sum-rate degradation but very low computational complexity and extremely fast converging speed. Trying to improve the performance of CSSM-WF algorithm, we then introduce another algorithm denoted as efficient COB (ECOB) algorithm in which CSSM-WF algorithm is used to generate a good start point for optimal COB approaches. Simulation results prove the efficiency of both proposed algorithms. Keywords- Multiuser MIMO, beamforming, sum-rate, power allocation, cross-layer optimization
I.
INTRODUCTION
Multiuser multiple input multiple output (MU-MIMO) systems promise significant capacity improvements in rich scattering fading wireless communication links relative to singleinput single-output (SISO) systems [1]. More recently, researchers have investigated the achievable capacity region and the optimal transmission policy of MU-MIMO Gaussian broadcast (BC) channels is characterized in an information theoretic context [2]-[6]. Among them, dirty paper coding (DPC) has been shown to achieve the sum-rate capacity of the Gaussian MIMO BC channel. However, DPC is of high complexity and has not yet been implemented in practical systems. Exploiting linear beamforming in both transmitter and receiver is a common strategy and has been implemented in practical system design. One feasible design on such linear beamformers is the joint transmit-receive beamforming vector design and power allocation to maximize the sum-rate of the entire system under a total transmitting power constraint. Howev-
er, this design generally leads to a non-convex optimization so that its global optimum is intrinsically intractable. By utilizing the uplink-downlink SINR duality, it has been noticed that the original non-convex optimization problem can be decomposed into a series of convex optimization problems that can then be efficiently solved. For example, a general approach for joint design of transmitting and receiving beamforming vectors according to weighted sum-rate maximization is developed in [7]. However, geometric programming solver proposed in this approach for computing power allocation [8] introduces high computational complexity. Other solutions [9][13] have also been proposed based on variations of convex optimization criteria, including sum of mean square error (MSE) minimization, minimum signal-to-interference-plusnoise ratio (SINR) maximization and sum of power minimization under a minimum SINR constraint. However, they all suffer from similar complexity problem as in [7]. In this paper, we aim to achieve reduced complexity as well as to speed up the converging speed through developing a novel approach based on the joint design of cyclic self-SINRmaximization (CSSM) beamforming and water-filling (WF) power allocation. We name this approach CSSM-WF algorithm in which the overall optimization is decomposed into several sub-problems and is solved in an iterative fashion. As a result, CSSM-WF algorithm generally converges to a local optimum. However, the proposed algorithm is capable of achieving satisfactory sum-rate performance with extremely fast converging speed and very low computational complexity. Such algorithmic characteristics in low complexity and fast convergence are ideal for some MU-MIMO systems that constrained by computational resource and/or by real-time adaptation requirement. Furthermore, this scheme can also provide a quick initial estimate for a corresponding convex-optimization-based (COB) algorithm to converge to an optimal solution. We develop in this research an efficient COB (ECOB) algorithm in which the CSSM-WF is first executed to obtain good initial estimate. The estimate is then used as the input to the COB algorithm to obtain the optimal solution for the joint design. This ECOB algorithm has been confirmed by the simulation results that it can obtain the optimum solution with much less computation complexity and much faster converging speed than the exiting COB algorithms.
This research is supported by NSF Grant 0915842 and Gift Funding from Huawei Technologies.
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The rest of this paper is organized as follows. In Section II, the system model for joint transceiver beamforming design in MU-MIMO is described. CSSM-WF algorithm is presented in Section III, and ECOB algorithm is introduced in Section IV. Section V demonstrates the simulation results to confirm the proposed algorithms. Finally, Section VI concludes the paper with a summary. The following notations are used throughout this paper. All boldface letters indicate vectors (lower case) or matrices (upper case). , and stand for Hermitian transpose, matrix inversion, and Frobenius norm, respectively. Matrix denotes identity matrix and , denotes the (, )-th entry of the matrix . The notation , indicates complex Gaussian distribution with mean and covariance. denotes the set of m n complex matrices. E denotes statistical expectation. II.
! $ ∑' 1 () *+( ,( - ( where +( " . , ,( " , - ( " # denote the average energy per symbol, the information symbol with unit energy, and the beam vector, respectively (e.g. for user 0 , E,( $ 0 , E|,( |3 $ 1, - ( - ( $ 1, 4 0 $ 1,2, … , ). Assume that the channel between BS and mobile user 0 is flat Rayleigh fading and represented by 7( " 8# , where 7( , represents the channel gain from transmit antenna to antenna of user 0. We assume for now that both BS and users have full knowledge of channel matrix 7( , 0 $ 1, … , . The signal vector received by user 0 is /
9( $ 7( ! : ;( $ 7( - ( ,( *+( : 7( ∑
