A low complexity approximation of the MIMO broadcast channel capacity region

Points on the boundary of the MIMO broadcast channel (BC) capacity region are achieved by a combination of dirty paper coding (DPC) and linear precoding. The linear precoding determines the covariance matrices of the transmitted signals. Determining the optimum covariance matrices may lead to an undesirably high computational complexity for systems of high dimension. In this paper, an approach to approximate the MIMO BC capacity region is proposed. The proposed method combines DPC with sub-optimum linear precoding matrices that can be computed with low complexity but provide close to optimum performance. Motivated by multiobjective optimization, an efficient algorithm developed for sum-rate maximization is generalized to computing an achievable rate region. Simulation results show that this rate region, which has low complexity in terms of computing the precoding matrices, well approximates the capacity region of the MIMO BC.