Block-Level Interference Exploitation Precoding for BD-RIS-Aided Communication Systems

The constructive interference (CI)-based block-level precoding (CI-BLP) approach reduces computational complexity compared to conventional CI-based symbol-level precoding (CI-SLP) and provides additional design flexibility due to its relaxed block-level design. However, using a constant precoding matrix within each block limits the system’s degrees of freedom (DoFs), resulting in significant performance degradation for large block lengths. To overcome this limitation, we propose using a reconfigurable intelligent surface (RIS) to enhance the propagation environment and offer extra DoFs. We jointly optimize the BLP matrix and the block-level RIS scattering matrix for active RIS and passive beyond-diagonal RIS (BD-RIS) aided communication systems using an alternating optimization (AO) algorithm. The BLP subproblem admits a closed-form solution and can be reformulated as a quadratic programming (QP) problem. For active RIS, two architectures are considered: uniform-amplitude and adaptive-amplitude, where the scattering subproblems are approximated as convex, and two different projection methods are employed to ensure feasibility. Furthermore, to reduce power consumption and increase design flexibility, we formulate a block-level passive BD-RIS scattering optimization subproblem, which is solved using an alternating direction method of multipliers (ADMM) algorithm. Simulation results demonstrate that RIS-aided CI-BLP designs significantly outperform conventional approaches without RIS. In particular, BD-RIS achieves higher CI gains than active RIS, benefiting from more available design flexibility, albeit at the cost of increased computational complexity.