Spatial multiplexing in near field MIMO channels with reconfigurable intelligent surfaces

• Published in: IET signal processing Vol. 17; no. 3
• Main Authors: Bartoli, Giulio, Abrardo, Andrea, Decarli, Nicolo, Dardari, Davide, Di Renzo, Marco
• Format: Journal Article
• Language: English
• Published: John Wiley & Sons, Inc 01.03.2023; Institution of Engineering and Technology; Wiley
• Subjects: Communications equipment; Electromagnetism; Engineering Sciences; MIMO communication; MIMO communications; modulation; Numerical analysis; Signal and Image processing; modulation; MIMO communication
• DOI: 10.1049/sil2.12195
• ISSN: 1751-9675

We 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. In this paper, we have analysed the spatial multiplexing gains of RIS‐aided MIMO channels in the near field. We have proved that the best design for nearly‐passive RIS results in a non‐diagonal matrix of reflection coefficients. Due to the non‐negligible complexity of non‐diagonal designs for RIS, we have proposed a closed‐form diagonal design that is motivated and is proved to be optimal, from the end‐to‐end channel capacity standpoint, in line‐of‐sight channels and when the MIMO transmitter, RIS, and MIMO receiver are deployed according to the paraxial setup. In different network typologies and over fading channels, the proposed design is sub‐optimal. However, extensive simulation results in line‐of‐sight (free‐space) channels have confirmed that it provides good performance in non‐paraxial setups as well. Specifically, we have shown that the proposed diagonal design provides rates that are close to those obtained by numerically solving non‐convex optimization problems at a high computational complexity, as well as to those attained, in several considered network setups, by capacity‐achieving non‐diagonal RIS designs.