A simple way to approximate average robust multiuser MISO transmit optimization under covariance-based CSIT

Abstract

This paper focuses on an average robust transmit beamforming optimization problem for the multiuser multiple-input-single-output (MISO) downlink scenario. In this problem, the channels are modeled as Gaussian variables with mean zero and with known covariance at the transmitter. The design criterion is to maximize the sum of the users' average rates with respect to the channels, subject to the total transmission power constraint. The challenge of this problem is that the average rate function generally admits a complex expression. Such an issue can be tackled by stochastic approximation (SA) approaches, but SA may require a large number of samples, or iterations, to provide reasonable performance. In this work, a simple deterministic approximation scheme is proposed. First, we propose a closed-form surrogate of the per-user average rate function. The proposed surrogate function is shown to have an approximation accuracy within 0.8314 bits from the true average rate. Then, we utilize the proposed surrogate function to establish an algebraically simple alternating optimization algorithm for the beamforming problem. Simulation results show that the proposed algorithm is computationally much more efficient than an SA-based state-of-the-art algorithm when they are compared under similar sum rate performance levels.