Robust linear transceivers for downlink multi-user multiple-input multiple-output systems using second-order cone programming optimisation

This study addresses the joint robust linear transceiver design problems for a downlink multi-user multiple-input multiple-output (MIMO) antenna system in the presence of imperfect channel state information (CSI). The uncertainty in the channel is characteried by a norm-bounded region, and two robust optimal design problems are considered. One is aimed at minimising the total transmitter power subject to users´ mean square error (MSE) constraints in the presence of channel uncertainty, the other is to minimise the worst-case sum-mean square error (sum-MSE) under power constraints for all admissible uncertainties. For these two problems, the authors propose two iterative algorithms based on second-order cone programming (SOCP) formulations, which can be efficiently solved and have less computational complexity than their semi-definite programming (SDP) counterparts. Simulation results also illustrate that the proposed robust design approaches can significantly reduce the computational complexity while achieving almost the same performance as the robust SDP methods.