Linear Transmission for Rate Optimization in MIMO Broadcast Channels

In this paper, we study the linear transmission (or beamforming) techniques in MIMO broadcast channels (BC) and propose beamforming algorithms for rate optimization. Our method for algorithm design draws on ideas from the classic Arimoto-Blahut algorithm. Like Arimoto-Blahut algorithm, our algorithms operate iteratively in a two-stage manner, i.e., in one iteration, the first stage is for updating test conditional probabilities, the second for updating beamforming matrices, and both stages are composed of simple convex subproblems. Optimal transmit beamforming for weighted sum rate maximization, weighted rate balancing, and proportional fair rate allocation in MIMO BC are considered. We rediscover the weighted sum-rate beamforming weighted minimum mean square error (WSRBF-WMMSE) algorithm in for MIMO BC. And we apply our method together with uplink-downlink duality to optimal beamforming for weighted rate balancing and proportional fair rate allocation in MIMO BC. We show experimentally that our algorithm for rate balancing requires less computation time to converge than existing algorithms without performance loss, and the algorithm for proportional fair rate allocation can achieve the balance between sum rate maximization and minimum rate maximization.