Worst-case weighted sum-rate maximization in multicell massive MIMO downlink system for 5G communications

In this paper, we present a robust beamforming design to examine the weighted sum-rate maximization (WSRM) problem in a multicell massive MIMO downlink system for 5G communications. This work assume imperfect channel state information (CSI) by adding uncertainties to channel matrices with worst-case models i.e. singular value uncertainty model (SVUM) and ellipsoidal uncertainty model (EUM). In SVUM, WSRM problem is formulated subject to the transmit power constraints. While, the problem is devised in EUM by alternatively considering its dual power minimization problem subject to the worst-case signal-to-interference-plus-noise ratio (SINR) constraints for all mobile stations. The designed problem for both SVUM and EUM are known as non-deterministic polynomial (NP) problem which is difficult to solve. We propose an iterative algorithm established on majorization minimization (MM) technique that solves and achieves convergence to stationary point of these two problems. In EUM, the convergence point is obtained after converting the infinite number of SINR constraints into linear matrix inequalities (LMI) by employing S-Procedure. Extensive numerical results are provided to show that the proposed iterative algorithm significantly increases performance in terms of sum-rate and also attains faster convergence as compared with the conventional polynomial time algorithm.