Mix-and-Conquer: Beamforming Design with Interconnected RIS for Multi-User Networks

TL;DR

This work introduces an interconnected RIS (I-RIS) architecture that enables inter-element signal sharing via binary RF switches, producing a non-diagonal RIS matrix and enabling more efficient multi-user scaling than standard RIS (S-RIS). It formalizes the channel model with Rician Tx→RIS and Rayleigh RIS→Rx links, along with CSI estimation errors, and defines a cell-based I-RIS with $cd$ switches per arrival element to realize the mixing and redistribution of incident signals. The core contribution is a beamforming design framework that optimizes RIS configurations to maximize the sum-rate; it develops two optimization approaches for S-RIS—sigmoid filled function (SFF) and semi-definite binary optimization (SBO)—and shows that I-RIS is best handled by SFF due to coupling in the interconnections. Numerical results show that I-RIS with appropriate cell sizes can substantially outperform S-RIS in sum-rate (e.g., up to $81\%$ gain for $M=64$) and reduce the required number of elements to achieve the same performance, highlighting practical advantages for space-constrained nodes like UAVs. The findings underscore the potential of switch-based interconnections to improve multi-user RIS performance while offering a clear path for scalable deployment and optimization in future wireless networks.

Abstract

We propose a new reconfigurable intelligent surface (RIS) structure, referred to as interconnected RIS (I-RIS), which allows the RIS elements to be interconnected and share the incident signals using simple binary radio frequency (RF) switches and mix them into the reflecting signals. This structure enables multi-user scaling and requires fewer elements (i.e., a compact structure) compared to standard RIS (S-RIS), which assumes no interconnection between the elements. The I-RIS compact design makes it practical for deployment on space-limited nodes, e.g., unmanned aerial vehicles (UAVs). Hence, in this work, we propose a beamforming design based on I-RIS in a multi-user network, where we use binary RF switches as RIS elements. We show that our switch-based I-RIS offers a higher gain compared to an S-RIS using phase shifters. Finally, we introduce two optimization methods, sigmoid filled function (SFF) and semi-definite binary optimization (SBO), to optimize the RIS elements and evaluate their performance in terms of sum-rate and complexity.

Figures (5)

• Figure 1: A SISO network with an RIS assisting multi-user communications.
• Figure 2: (a) A $32$-element S-RIS, where the $m^{\mathrm{th}}$ RIS element uses an RF switch to either reflect or block its incident signal; (b) An I-RIS with $32$ elements and eight cells of size $(2,2)$; (c) The $m^{\mathrm{th}}$ arrival element uses $cd$ RF switches and a power splitter to share its incident signal; (d) The reflected signal from the $m^{\mathrm{th}}$ departure element includes a combination of the incident signals at all arrival elements.
• Figure 3: Sum-rate against $\log(M)$ using S-RIS, I-RIS $(2,1)$, and I-RIS $(2,2)$.
• Figure 4: A comparison between a switch-based S-RIS, two cases of switch-based I-RIS, and a PS-based S-RIS using the SFF method.
• Figure 5: A Sum-rate comparison between the SFF, SBO, and SR methods.