A Worst-Case Robust MMSE Transceiver Design for Nonregenerative MIMO Relaying

Abstract—Transceiver designs have been a key issue in guaranteeing the performance of multiple-input multiple-output (MIMO) relay systems, which are, however, often subject to imperfect channel state information (CSI). In this paper, we aim to design a robust MIMO transceiver for nonregenerative MIMO relay systems against imperfect CSI from a worst-case robust perspective. Specifically, we formulate the robust transceiver design, under the minimum mean-squared error (MMSE) criterion, as a minimax problem. Then, by decomposing the minimax problem into two subproblems with respect to the relay precoder and destination equalizer, respectively, we show that the optimal solution to each subproblem has a favorable channel-diagonalizing structure under some mild conditions. Based on this finding, we transform the two complex-matrix subproblems into their equivalent scalar forms, both of which are proven to be convex and can be efficiently solved by our proposed methods. We further propose an alternating algorithm to jointly optimize the precoder and equalizer that only requires scalar operations. Finally, the effectiveness of the proposed robust design is verified by simulation results. Index Terms—Multiple-input multiple-output (MIMO) relay systems, minimum mean-squared error (MMSE), worst-case transceiver design, imperfect channel state information (CSI). I