IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 54, NO. 9, SEPTEMBER 2006 1533 The Performance of Multiuser Diversity Scheduling for MIMO Channels With Spatially Correlated Fading Nan Zhang, Member, IEEE, and Branimir Vojcic, Senior Member, IEEE Abstract—We study a cellular network with one multiantenna base station and a number of multiantenna users. Correlated fading may exist at the base station or at the users, or at both sides. With time-varying fading, multiuser diversity is exploited by always allowing the base station to transmit to the user with the best channel. For this network, we find that if the number of transmitter antennas and the number of receiver antennas grow with a fixed ratio, the multiuser diversity gain will approximately remain constant. Index Terms—Multiple-input multiple-output (MIMO) systems, multiuser diversity, packet scheduling. I. INTRODUCTION M ULTIUSER diversity was introduced to exploit time-varying fading channels in multiuser systems [1], [2]. In a wireless network with multiple users and where each user is subject to independent fading, there is a high probability that one or several users have very good links with the base station. By providing them the channel access, the system throughput can be increased. In wireless communication, multiple-input multiple-output (MIMO) technology is often used to improve link preformance, and can achieve very high spectral efficiency. Since multiuser diversity and MIMO are used at different layers of a wireless network, it is natural to study the performance of the concate- nation of these two schemes. In [3], multiuser diversity was studied in MIMO channels when the linear receivers are used. Assuming antennas in the transmitter and -antenna users, the sum-rate capacity [achievable by using dirty-paper coding (DPC)] of the multiple-antenna broadcast channel is at most times the capacity of time-sharing to the user with the highest capacity [4]. DPC in multiuser multiantenna systems was also studied in [5] and [6]. Random beamforming in MIMO systems was investigated in [7]. Closed-form analytical expres- sions for the channel statistics (including the mean, standard de- viation, etc.) and scheduling gain for MIMO systems were de- rived in [10]. With asymptotic normality, a formula for the net- work capacity with multiuser diversity for MIMO channels with uncorrelated fading was proposed in [9]. Paper approved by D. I. Kim, the Editor for Spread Spectrum Transmission and Access of the IEEE Communications Society. Manuscript received April 3, 2005; revised September 14, 2005 and December 27, 2005. This work was sup- ported in part by the National Science Foundation under Grant CCF-04299228. This paper was presented in part at the 39th Annual Conference on Information Sciences and Systems, Baltimore, MD, March 2005. N. Zhang was with the Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052 USA. He is now with the San Diego Wireless Center, Texas Instruments, Inc., San Diego, CA 92123 USA (e-mail: nan.zhang@ti.com). B. Vojcic is with the Department of Electrical and Computer Engineering, The George Washington University, Washington, DC 20052 USA. Digital Object Identifier 10.1109/TCOMM.2006.881201 In this letter, we study the downlink transmission in a single cell of a network with a -antenna base station and -antenna users. Multiuser diversity is exploited by always allowing the base station to transmit to the user having a link with the highest mutual information. The capacity of such a network in corre- lated fading is evaluated in the limit as , , and is fixed. This analysis is facilitated by exploiting the asymptotic distribution of eigenvalues of covariance matrices of correlated fading at the transmitters and receivers. II. CAPACITY WITH MULTIUSER DIVERSITY We assume a block fading channel with coherence interval . For the downlink, the received signal of the th user can be modeled as (1) where is the channel gain matrix, is a vector representing the transmitted signal, and is a noise vector. When correlated fading at the transmitter and receivers are strictly local phenomenons, we use the Kronecker model for correlated fading and , where is an matrix with independent, identically distributed (i.i.d.) circularly symmetric complex Gaussian entries with zero mean and unit variance. and are covariance matrix for correlated fading at the receiver, and covariance matrix for correlated fading at the transmitter, respectively. stands for the Hermitian positive definite square root of matrix . As- suming no channel state information at the base station, the mutual information of the downlink channel from the base sta- tion to user is [13] b/s/Hz (2) where is the -dimension identity matrix, is the signal-to-noise ratio (SNR), and * denotes complex conju- gate-transpose. To achieve multiuser diversity, at the beginning of each time block , the base station will collect ’s of all users and transmit to the one with the highest . We should note that although by choosing only one user, this scheduling scheme may have smaller network capacity compared with the spatial multiplexing schemes found in [3] and [6], which select multiple users simultaneously, it has its own advantages such as less feedback information and a simpler scheduling algorithm, and particularly, a simpler system design, because only one user is active at a given time, which justifies the investigation of this scheduling scheme. 0090-6778/$20.00 © 2006 IEEE