Interference Alignment Transceiver Design by Minimizing the Maximum Mean Square Error for MIMO Interfering Broadcast Channel

An interference alignment (IA) transceiver design scheme for multiple-input–multiple-output (MIMO) multicell multiuser wireless communication systems is proposed by minimizing the maximum mean square error (MSE) of the received symbols to improve fairness among users. The formulated Min-Max MSE optimization problem is not jointly convex on the transmit precoders and receive filters and, thus, is very difficult to solve directly. An iterative method is proposed to solve the optimization problem to get a suboptimal solution instead. Considering that if the receive filters are fixed, the Min-Max MSE problem can be reformulated as a second-order cone programming problem, and if the transmit precoders are fixed, the closed-form receive filters minimizing the receive MSE can be easily obtained, and the formulated Min-Max MSE problem is solved by alternatively optimizing the transmit precoders and the receive filters. The convergence of the proposed algorithm is proved, which shows its feasibility. Furthermore, a robust Min-Max MSE algorithm is proposed to counter the channel uncertainty. Simulation results show that the proposed Min-Max MSE algorithm can achieve IA when the antennas are configured to be strong IA proper and when the users in the network are of the same signal-to-noise ratio (SNR). Analysis indicates that the proposed Min-Max IA transceiver design scheme can significantly improve user fairness with a possible cost of sum-rate reduction. Results also show that the proposed robust design algorithm provides better performance when lacking perfect channel state information (CSI).