IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 59, NO. 3, MARCH 2011 1217 Exploiting Long-Term Channel Correlation in Limited Feedback SDMA Through Channel Phase Codebook Yongming Huang, Member, IEEE, Luxi Yang, Member, IEEE, Mats Bengtsson, Senior Member, IEEE, and Björn Ottersten, Fellow, IEEE Abstract—Improving channel information quality at the base station (BS) is crucial for the optimization of frequency division duplexed (FDD) multi-antenna multiuser downlink systems with limited feedback. To this end, this paper proposes to estimate a particular representation of channel state information (CSI) at the BS through channel norm feedback and a newly developed channel phase codebook, where the long-term channel correlation is efficiently exploited to improve performance. In particular, the channel representation is decomposed into a gain-related part and a phase-related part, with each of them estimated separately. More specifically, the gain-related part is estimated from the channel norm and channel correlation matrix, while the phase-related part is determined using a channel phase codebook, constructed with the generalized Lloyd algorithm. Using the estimated channel representation, joint optimization of multiuser precoding and op- portunistic scheduling is performed to obtain an SDMA transmit scheme. Computer simulation results confirm the advantage of the proposed scheme over state of the art limited feedback SDMA schemes under correlated channel environment. Index Terms—Limited feedback, multi-antenna multiuser downlink, phase codebook, SDMA, user scheduling. Manuscript received August 14, 2009; revised March 24, 2010, September 30, 2010; accepted October 31, 2010. Date of publication November 22, 2010; date of current version February 09, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Dr. Martin Schubert. This work was supported in part by the NBRPC/973 under Grant 2007CB310603, the National Science and Technology Major Project of China under Grants 2011ZX03003-001 and 2011ZX03003-003, the NSFC under Grants 60902012 and 61071113, the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) and ERC grant agreement no. 228044, the Ph.D. Programs Foundation of Ministry of Education of China under Grants 20090092120013 and 20100092110010, and the Huawei Technologies Corporation. Part of this work was conducted when Y. Huang was visiting ACCESS Linnaeus Center, KTH Signal Processing Lab, Royal Institute of Technology, SE-100 44 Stockholm, Sweden. Y. Huang and L. Yang are with the School of Information Science and En- gineering, Southeast University, Nanjing 210096, China, and also with the Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing 210096, China (e-mail: huangym@seu.edu.cn; lxyang@seu.edu.cn). M. Bengtsson is with the ACCESS Linnaeus Center, KTH Signal Processing Lab, Royal Institute of Technology, SE-100 44 Stockholm, Sweden (e-mail: mats.bengtsson). B. Ottersten is with the ACCESS Linnaeus Center, KTH Signal Processing Lab, Royal Institute of Technology, SE-100 44 Stockholm, Sweden, and also with securityandtrust.lu, University of Luxembourg (e-mail: bjorn.otter- sten@ee.kth.se). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2010.2094190 I. INTRODUCTION I N multi-antenna multiuser downlink systems, space divi- sion multiple access (SDMA) may achieve a much larger system throughput compared to conventional time division multiple access (TDMA). The optimal capacity performance of SDMA can be achieved by a multiuser precoding scheme called dirty paper coding (DPC) [1]. In particular, when the number of users exceeds the number of transmit antennas at base station (BS), a linear increase of the capacity with can be achieved by DPC. However, in practical systems, DPC is difficult to implement due to intensive computational complexity especially when the number of users is large, and sensitivity to channel knowledge. To reduce the complexity, several suboptimal schemes have been developed recently, including the zero-forcing (ZF) precoding [2], block diago- nalized precoding [3], MMSE precoding [4], the generalized eigenvalue based solution [5] and the iterative method based solution [6] etc. These low-complexity schemes can achieve a large portion of the DPC capacity, but in the case of a large number of users they should be jointly designed with user scheduling algorithms [7], [8]. The main problem for the schemes above is that they all re- quire full channel state information (CSI) of all the users at the base station. This is difficult to realize in practical systems. In frequency division duplexed (FDD) systems, CSI can typi- cally be estimated only at receivers and must be fed back to the base station if needed. Unfortunately, the bandwidth of practical feedback channels is usually limited and must be shared by all the users. Thus, in most cases, only very limited channel infor- mation can be obtained at the base station. To address this issue, a number of SDMA schemes based on limited feedback have been proposed recently. In particular, a limited feedback SDMA scheme based on opportunistic scheduling [9] has been shown to asymptotically achieve the optimal capacity scaling when the user number tends to infinity. However, in networks where the number of users is limited, the performance of this scheme de- grades severely due to excessive mutual interference between multiple simultaneously active users. Later, a kind of improved SDMA scheme [10], [11] that uses a properly designed SDMA precoding codebook, instead of using a random unitary matrix as the precoder, is proposed to handle this problem. Alterna- tively, the method of CSI quantization can be used to reduce the feedback burden [12]–[14], which is effective especially when each user terminal is equipped with a single antenna. 1053-587X/$26.00 © 2010 IEEE