Joint interference alignment and beyond diagonal RIS design for maximizing SNR in MIMO device-to-device communications

As a novel and flexible branch of RIS architectures, beyond-diagonal reconfigurable intelligent surface (BD-RIS) has been proposed recently to manipulate wireless environment and expand the coverage benefits. One efficient BD-RIS has been realized in the form of a unitary and symmetric RIS matrix in the existing research. However, it is still not clear whether interference alignment can improve BD-RIS aided system performance yet. In this paper, the joint optimization of interference alignment (IA) beamforming and phase-shift matrix of BD-RIS is investigated to maximize the signal-to-noise ratio (SNR), where a K-user RIS-aided multiple-input multiple-output (MIMO) device-to-device (D2D) communications system is considered. Numerical results show that the proposed algorithm can achieve a higher sum-rate compared to that of the conventional diagonal RIS and without RIS strategies.