Iterative IA precoding and RIS beamforming based on rank-reduced MIMO interference channel

As a key technology for beyond 5G and 6G, reconfigurable intelligent surfaces (RIS) have been extensively studied for their application in wireless communication to enhance system performance. However, existing RIS-assisted interference alignment (IA) strategies predominantly utilize passive RIS to align interference in communication systems, and the amplified noise in active RIS-assisted communication systems cannot be overlooked. In this paper, we investigate the problems of interference cancellation and maximizing the system sum-rate performance in an active RIS-assisted multi-user multiple-input multiple-output (MIMO) communication system. We consider the issue of amplified noise introduced by the active RIS within the system model. To mitigate interference, we propose a matrix rank-reduced method for designing RIS beamforming, which aims to minimize the rank of the MIMO interference channel. Furthermore, we introduce a novel iterative minimum interference leakage (min-IL) and Riemannian conjugate gradient (RCG) algorithm based on the rank-reduced MIMO interference channel. The proposed algorithm can completely eliminate inter-user interference and maximize the system sum-rate. Various simulation experiments yielded numerical results that demonstrate the effectiveness and applicability of the proposed algorithm.