  In this paper, we investigate the downlink multiple-input-multipleoutput
(MIMO) broadcast channels in which a base transceiver station (BTS) broadcasts
multiple data streams to K MIMO mobile stations (MSs) simultaneously. In order
to maximize the weighted sum-rate (WSR) of the system subject to the
transmitted power constraint, the design problem is to find the pre-coding
matrices at BTS and the decoding matrices at MSs. However, such a design
problem is typically a nonlinear and nonconvex optimization and, thus, it is
quite hard to obtain the analytical solutions. To tackle with the mathematical
difficulties, we propose an efficient stochastic optimization algorithm to
optimize the transceiver matrices. Specifically, we utilize the linear minimum
mean square error (MMSE) Wiener filters at MSs. Then, we introduce the
constrained particle swarm optimization (PSO) algorithm to jointly optimize the
precoding and decoding matrices. Numerical experiments are exhibited to
validate the effectiveness of the proposed algorithm in terms of convergence,
computational complexity and total WSR.
