Spatial multiplexing in near field MIMO channels with reconfigurable intelligent surfaces

Abstract

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.

Channel Orthogonalization with Reconfigurable Surfaces

“…In [1], two further extended RS models are considered, amplitude-reconfigurable intelligent surface (ARIS), which corresponds to a variant of RIS which allows for amplitude reconfigurability (also contemplated to some extent in [22] and [31]), and fullyreconfigurable intelligent surface (FRIS), which considers the upper limit of having an unrestricted reflection matrix. In fact, considering the passive restriction, as well as the direct channel blockage assumption, the FRIS model leads to the capacity achieving reflection matrix derived in [33], which is given by an unconstrained unitary matrix. In this work, we will consider some of these RS technologies in the task of MU-MIMO channel orthogonalization towards OSDM.…”

“…2 The practicality of FRIS is doubtful, but it naturally arises as a limit case for upper bounding the capabilities of RS systems. In fact, this type of RS gives the capacity achieving reflection matrix in [33], where the non-symmetric reflection matrix is further restricted to be unitary, corresponding again to the lossless case, i.e., reflecting maximum power. In principle, a general reflection matrix, as given by (7), may be achieved by considering a passive non-reciprocal network, i.e., including elements such as passive circulators or isolators [37].…”

“…Input: H 0 , H r Output: β, U RS power minimization : 1: Select initial U and β, e.g., by (33) and (29).…”

“…We first analyze the performance of Algorithm 1, as well as its simplified version when U is directly fixed to (33) and [42,Table 2] is disregarded. We have considered a rich multipath propagation environment where H 0 , H 1 , and H 2 may be modelled as IID Gaussian matrices [6].…”

Communication Models for Reconfigurable Intelligent Surfaces: From Surface Electromagnetics to Wireless Networks Optimization

“…Therefore, they are referred to as beyonddiagonal RISs [31]. The information-theoretic optimality of non-diagonal scattering matrices for nearly passive RISs is proved in [32]. Recent contributions on beyond diagonal RISs include [33], [34], [35], [36].…”