Diagonal RIS Design to Approximate the Cascade Channel With Optimal Fully-Connected RIS

We consider two scenarios, single-user multipleinput multiple-output and multiuser multiple-input single-output transmissions with the support of a diagonal reconfigurable intelligent surface (RIS). We aim at optimizing the RIS configuration and the transmit beamformer to maximize the system capacity. We relax the optimization problem by removing the diagonal constraint on the RIS and relaxing its power constraint. This corresponds to optimizing a fully connected RIS, for which efficient solutions are available. Then, we iteratively optimize the transmit beamformer and the diagonal RIS to best approximate (according to a mean square error criterion) the cascade channel obtained with the fully connected RIS. Simulation results confirm the validity of our approach both in terms of capacity and computational complexity.