Dual-Polarized Beyond Diagonal RIS

TL;DR

This work analyzes dual-polarized BD-RIS to establish fundamental limits for RIS-aided links under Rayleigh and LoS conditions. By deriving $P_R^{\mathrm{Single}}$ and $P_R^{\mathrm{Fully}}$ and the BD-RIS gain $G$, the authors show that dual-polarized BD-RIS yields notable gains over conventional D-RIS, with $G$ depending on the cross-polarization factor $\chi$. In LoS scenarios, a group-connected BD-RIS with group size 2 achieves the full performance bound with reduced circuit complexity, and the paper provides a general optimal architecture for intermediate complexities $C = N+n$, yielding the Pareto frontier between performance and hardware cost. These insights offer practical guidance for designing low-complexity, high-performance BD-RIS deployments in dual-polarized wireless systems.

Abstract

Beyond diagonal reconfigurable intelligent surface (BD-RIS) is a family of RIS architectures more flexible than conventional RIS. While BD-RIS has been primarily analyzed assuming uni-polarized systems, modern wireless deployments are dual-polarized. To address this gap, this paper investigates the fundamental limits of dual-polarized BD-RIS-aided systems. We derive the scaling laws governing the performance of BD-RIS and the Pareto frontier of the trade-off between performance and circuit complexity enabled by BD-RIS. Theoretical results show that the group-connected RIS with group size 2 provides remarkable gains over conventional RIS in both Rayleigh and line-of-sight (LoS) channels, while maintaining a reduced circuit complexity.

Figures (3)

• Figure 1: Dual-polarized RIS-aided system where and have opposite polarization.
• Figure 2: Gain of BD-RIS over D-RIS $G$ as a function of $\chi$, when the and have the same/opposite polarization, and with Rayleigh/ channels.
• Figure 3: Pareto frontier of the performance-complexity trade-off achieved by dual-polarized BD-RISs, with $N=64$.

Theorems & Definitions (4)

• Proposition 1
• proof
• Proposition 2
• proof