Interference Minimization in Beyond-Diagonal RIS-Assisted MIMO Interference Channels

This paper proposes a two-stage approach for passive and active beamforming in multiple-input multiple-output (MIMO) interference channels (ICs) assisted by a beyond-diagonal reconfigurable intelligent surface (BD-RIS). In the first stage, the passive BD-RIS is designed to minimize the aggregate interference power at all receivers, a cost function called interference leakage (IL). To this end, we propose an optimization algorithm in the manifold of unitary matrices and a suboptimal but computationally efficient solution. In the second stage, users' active precoders are designed under different criteria such as minimizing the IL (min-IL), maximizing the signal-to-interference-plus-noise ratio (max-SINR), or maximizing the sum rate (max-SR). The residual interference not cancelled by the BD-RIS is treated as noise by the precoders. Our simulation results show that the max-SR precoders provide more than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$20\%$</tex-math></inline-formula> sum rate improvement compared to other designs, especially when the BD-RIS has a moderate number of elements and users transmit with high power, in which case the residual interference is still significant.