Polyblock Algorithm-Based Robust Beamforming for Downlink Multi-User Systems With Per-Antenna Power

Abstract—In this paper, we investigate the robust beamforming for multi-user multiple-input single-output systems under quan-tized channel direction information (CDI) with per-antenna power constraints. The robustness of the considered beamforming design is achieved in the sense that the stochastic interference leakage is below a certain level by a given probability. Our design objective is to maximize the expectation of the weighted sum-rate per-formance. From the discussion of the non-robust optimal beam-forming based on the polyblock algorithm, we propose a robust beamforming scheme for the quantized CDI case with per-antenna power constraints. In the proposed beamforming scheme, we use Jensen’s inequality to generate a tractable feasibility problem for the polyblock algorithm and apply the semi-definite programming relaxation, as well as the randomization technique to find its ap-proximate rank-one matrix solution and user equipments ’ beam-forming vectors. Simulation results show that substantial gains can be achieved by the proposed scheme compared with the existing schemes in terms of the average weighted sum-rate performance. Although very high complexity is required for the implementation of the proposed scheme, it stands as a good benchmark for robust beamforming designs. Index Terms—Multi-user, robust beamforming, per-antenna power constraints, quantized CDI, polyblock algorithm, weighted sum-rate. I