Per-Stream MSE Based Linear Transceiver Design for MIMO Interference Channels With CSI Error

This paper studies the linear transceiver design for multi-stream multiple-input-multiple-output (MIMO) interference channels with imperfect channel state information (CSI). Two CSI error models are considered. The same coding and modulation scheme is assumed for all users and data streams. In the first model, where the CSI error is statistical, we minimize the average maximum per-stream mean square error (MSE). In the second model, where the CSI error is norm bounded, the worst-case maximum per-stream MSE is optimized. Since the problems are not jointly convex, the alternate optimization approach is adopted to obtain suboptimal transceivers. For the statistical CSI error, a low-complexity algorithm utilizing Lagrangian duality is proposed, which has a semi-closed form solution and can be implemented distributively. Compared with the classical algorithm using the second-order-cone programming, the proposed algorithm significantly reduces the computational complexity without sacrificing the performance. For the bounded CSI error, we present two approaches. One uses S-procedure to obtain an equivalent problem and the other one solves an approximated problem. Simulation results demonstrate the robustness of the proposed algorithms and their improved performance over the sum-MSE and the maximum per-user MSE based methods. The lower complexity of the Lagrangian duality based algorithm is also verified numerically.