Channel Shaping Using Beyond Diagonal Reconfigurable Intelligent Surface: Analysis, Optimization, and Enhanced Flexibility

2024-07-21

arXiv.org

AI Summary

Conventional diagonal reconfigurable intelligent surfaces (RISs) can only modulate signal phase, lacking independent control over channel singular values. Method: This paper proposes a novel non-diagonal RIS architecture—block-diagonal RIS (BD-RIS)—enabling joint dynamic reshaping of both amplitude and phase in MIMO channels. We formulate a non-diagonal phase response model, develop a geodesic-optimization-based framework to characterize singular-value regions, and integrate alternating optimization with singular-value bounding theory for rigorous analysis. Contributions/Results: BD-RIS significantly expands the dynamic range and trade-off space of individual singular values. It enables multi-stream transmission even at low SNR, approaching the theoretical degrees-of-freedom limit. Moreover, BD-RIS delivers pronounced rate gains in high-dimensional MIMO and large-scale RIS deployments, while supporting energy-efficient multi-stream communication under low-power constraints.

Technology Category

• Search and Optimization: Non-convex Optimization
• Intelligent Robots: Multi-Robot Systems
• Multiagent Systems: Mechanism Design

Application Category

• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

This paper investigates the capability of a passive Reconfigurable Intelligent Surface (RIS) to redistribute the singular values of point-to-point Multiple-Input Multiple-Output (MIMO) channels for achieving power and rate gains. We depart from the conventional Diagonal (D)-RIS with diagonal phase shift matrix and adopt a Beyond Diagonal (BD) architecture that offers greater wave manipulation flexibility through element-wise connections. Specifically, we first provide shaping insights by characterizing the channel singular value regions attainable by D-RIS and BD-RIS via a novel geodesic optimization. Analytical singular value bounds are then derived to explore their shaping limits in typical deployment scenarios. As a side product, we tackle BD-RIS-aided MIMO rate maximization problem by a local-optimal Alternating Optimization (AO) and a shaping-inspired low-complexity approach. Results show that compared to D-RIS, BD-RIS significantly improves the dynamic range of all channel singular values, the trade-off in manipulating them, and thus the channel power and achievable rate. Those observations become more pronounced when the number of RIS elements and MIMO dimensions increase. Of particular interest, BD-RIS is shown to activate multi-stream transmission at lower transmit power than D-RIS, hence achieving the asymptotic Degrees of Freedom (DoF) at low Signal-to-Noise Ratio (SNR) thanks to its higher flexibility of shaping the distribution of channel singular values.

Problem

• Explores RIS reshaping MIMO channels for better wireless performance.
• Derives bounds for BD-RIS impact on channel DoF and capacity.
• Proposes optimization methods for MIMO rate maximization using BD-RIS.

Innovation

• Beyond Diagonal RIS enhances MIMO channel shaping
• Local-optimal Alternating Optimization for rate maximization
• BD-RIS activates multi-stream at lower power