Worst-Case Robust MIMO Transmission Based on Subgradient Projection

This letter studies robust multi-input multi-ouput (MIMO) transmission strategies, where the transmitter only has imperfect channel state information (CSI) and the transmission covariance matrix is designed to maximize the worst system capacity. We first extend Danskin's Theorem to complex spaces by the aid of Wirtinger's subgradients. Then, with the extended theorem, we propose a subgradient projection (SP) based algorithm to solve the covariance matrix, in which finding the worst channel error is key and can be formulated as a nonconvex minimization problem. We deploy the successive convex approximation (SCA) technique and create a sequence of convex problems to solve this problem. Simulation results demonstrate the robustness of the proposed algorithm.