Joint IA Precoding and Active RIS Beamforming for Multi-User MIMO Systems: A Matrix Rank-Reduced Approach

Reconfigurable intelligent surface (RIS) can provide new ideas and methods for interference management. Particularly, applying interference alignment (IA) to RIS-aided interference networks can eliminate the interference completely and improve the system capacity enormously. However, the existing schemes solve the RIS-aided IA design problem by using iterative algorithms, which have high computational complexity. In this paper, we study the active RIS-aided IA design in closed form, for the multi-user multiple-input multiple-output (MIMO) system, comprising one active RIS and multiple transceiver pairs with multiple antennas. We first propose a novel framework of joint IA precoding and active RIS beamforming, to achieve the concurrent transmission of multiple interference-free data streams. Then, under the framework, the RIS beamforming is designed to minimize the rank of the MIMO interference channel, by using a matrix rank-reduced approach. After designing the RIS beamforming, the IA precoding at transmitter is designed to eliminate the interference completely. Furthermore, the proposed scheme can achieve the optimum degrees of freedom (DoF). Simulation results reveal that the proposed scheme outperforms the benchmark by 300% in terms of system sum-rate.