SNR Maximization in Beyond Diagonal RIS-assisted Single and Multiple Antenna Links

TL;DR

This paper investigates maximizing SNR in single and multiple antenna wireless links using advanced beyond-diagonal RIS architectures with symmetric unitary matrices, providing a closed-form solution applicable to various channel configurations.

Contribution

It introduces a novel SNR maximization approach for BD-RIS architectures with symmetric unitary matrices, deriving a closed-form solution using Takagi factorization for different channel types.

Findings

Closed-form SNR maximization solution derived.

Applicable to SISO, SIMO, and MISO channels.

Enhanced RIS flexibility with beyond-diagonal architectures.

Abstract

Reconfigurable intelligent surface (RIS) architectures not limited to diagonal phase shift matrices have recently been considered to increase their flexibility in shaping the wireless channel. One of these beyond-diagonal RIS or BD-RIS architectures leads to a unitary and symmetric RIS matrix. In this letter, we consider the problem of maximizing the signal-to-noise ratio (SNR) in single and multiple antenna links assisted by a BD-RIS. The Max-SNR problem admits a closed-form solution based on the Takagi factorization of a certain complex and symmetric matrix. This allows us to solve the max-SNR problem for SISO, SIMO, and MISO channels.