Transmitter Optimization for Multiuser MIMO Systems

Multiple transmit and receive antennas are a means to increase wireless capacity [1, 2]. Recently, there has been considerable research in exploiting the space dimension through transmit diversity, and spatial multiplexing which is used to transmit multiple data streams that can be separated using receiver signal processing, e.g., [3–5]. Spatial multiplexing can significantly benefit from transmit precoding when the channel is known at the transmitter side in addition to the receiver side. In such cases, designing the appropriate precoding strategy has been studied under a variety of system objectives, see [5] and references therein. All of these studies, as most of the MIMO system analysis, have been done for a single user system that transmits multiple data streams. Optimum or near optimum transmit strategies that maximize the information theoretic sum capacity of vector multiple access channels have been investigated recently [6, 7]. Transmit and receiver beamforming for multiuser systems when each user is transmitting a single data stream have also been studied extensively up to date, see [8] and references therein. Algorithms that identify transmit and receiver beamforming strategies and the corresponding transmit power assignments are investigated in [8] with the aim of maximizing the minimum achievable SIR or providing each user with its SIR target. The algorithms suggested were numerically shown to enhance system performance, but were observed to converge to local optima. Our aim in this work is to design algorithms that converge to the optimum transmitters and receivers for all users in a multiuser MIMO system, when users transmit possibly multiple data streams. We assume linear precoders and decoders for all users. We work with a system-wide performance measure for the joint optimization of precoders and decoders, namely the system-wide mean squared error (MSE). In contrast to receiver optimization for fixed transmitters, e.g. in [9], optimization of the individual MSEs is not equivalent to total MSE optimization. However, one can construct iterative algorithms that monotonically decrease the total MSE under the given system constraints. The proposed algorithms converge to the best precoder-decoder pairs under the given power constraints, and result in enhanced performance for all users. We consider the uplink of a single cell synchronous system with K users. The receiver employs NR antennas. We assume that the ith user multiplexes Mi data streams through its NTi transmit antennas employing a linear precoder. Similar to the notation in [5], the received vector is