Power Minimization with Rate Constraints for Multi-User MIMO Systems with Large-Size RISs

This study focuses on the optimization of a single-cell multi-user multiple-input multiple-output (MIMO) system with multiple large-size reconfigurable intelligent surfaces (RISs). The overall transmit power is minimized by optimizing the precoding coefficients and the RIS configuration, with constraints on users' signal-to-interference-plus-noise ratios (SINRs). The minimization problem is divided into two sub-problems and solved by means of an iterative alternating optimization (AO) approach. The first sub-problem focuses on finding the best precoder design. The second sub-problem optimizes the configuration of the RISs by partitioning them into smaller tiles. Each tile is then configured as a combination of pre-defined configurations. This allows the efficient optimization of RISs, especially in scenarios where the computational complexity would be prohibitive using traditional approaches. Simulation results show the good performance and limited complexity of the proposed method in comparison to benchmark schemes.

Spatial Multiplexing in Near Field MIMO Channels with Reconfigurable Intelligent Surfaces

We consider a multiple-input multiple-output (MIMO) channel in the presence of a reconfigurable intelligent surface (RIS). Specifically, our focus is on analyzing the spatial multiplexing gains in line-of-sight and low-scattering MIMO channels in the near field. We prove that the channel capacity is achieved by diagonalizing the end-to-end transmitter-RIS-receiver channel, and applying the water-filling power allocation to the ordered product of the singular values of the transmitter-RIS and RIS-receiver channels. The obtained capacity-achieving solution requires an RIS with a non-diagonal matrix of reflection coefficients. Under the assumption of nearly-passive RIS, i.e., no power amplification is needed at the RIS, the water-filling power allocation is necessary only at the transmitter. We refer to this design of RIS as a linear, nearly-passive, reconfigurable electromagnetic object (EMO). In addition, we introduce a closed-form and low-complexity design for RIS, whose matrix of reflection coefficients is diagonal with unit-modulus entries. The reflection coefficients are given by the product of two focusing functions: one steering the RIS-aided signal towards the mid-point of the MIMO transmitter and one steering the RIS-aided signal towards the mid-point of the MIMO receiver. We prove that this solution is exact in line-of-sight channels under the paraxial setup. With the aid of extensive numerical simulations in line-of-sight (free-space) channels, we show that the proposed approach offers performance (rate and degrees of freedom) close to that obtained by numerically solving non-convex optimization problems at a high computational complexity. Also, we show that it provides performance close to that achieved by the EMO (non-diagonal RIS) in most of the considered case studies.