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

In this paper, we investigate the robust beamforming for multi-user multiple-input single-output systems under quantized 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 performance. From the discussion of the non-robust optimal beamforming 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 approximate rank-one matrix solution and user equipments´ beamforming 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.