Abstract

We consider downlink transmission whereby a multiantenna base station simultaneously transmits data to multiple single-antenna users. We focus on slow flat fading channel where the channel state information is imperfect, the channel estimation error is unbounded and its statistics are known. The aim is to design beamforming vectors such that the sum rate is maximized under the constraints on probability of successful transmission for each user and maximum transmit power. The optimization problem is intractable due to the chance constraints. To this end, we propose an efficient solution drawn upon stochastic optimization. In particular, we first use the step function and its smooth approximation to get an approximate nonconvex stochastic program of the considered problem. We then develop an iterative procedure to solve the stochastic program based on the stochastic successive convex approximation framework. The numerical results show that the proposed solution can achieve remarkable sum rate gains compared to the conventional one.