Spatial multiplexing in near field MIMO channels with reconfigurable intelligent surfaces

Abstract

AbstractWe consider a multiple‐input multiple‐output (MIMO) channel in the presence of a reconfigurable intelligent surface (RIS). Specifically, our focus is on analysing 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 diagonalising 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, that is, 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.