Beamforming Saturation in Two-Timescale RIS-assisted Communication

2025-07-29

AI Summary

This paper addresses the rapid saturation of dual-timescale beamforming gain with increasing RIS element count in RIS-assisted wireless communications. We identify the root cause as the decay rate of the channel’s power angular spectrum (PAS) in the angular domain: although the total captured power scales linearly with the number of elements, the spatial correlation among elements diminishes rapidly due to PAS decay, ultimately limiting re-radiated beamforming gain. Leveraging a stochastic channel model and a statistical beamforming framework, we analyze the angular-domain PAS and derive asymptotic performance bounds. For the first time, we establish a quantitative relationship between the PAS decay rate and the fundamental upper bound on beamforming gain. Our results provide a theoretical scaling law and novel design guidelines for RIS size optimization, challenging the conventional “more elements, higher gain” paradigm.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Search and Optimization: Distributed Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Security and Privacy: Large-scale security measurements
• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments

Abstract

This paper considers wireless communication assisted by a reconfigurable intelligent surface (RIS), focusing on the two-timescale approach, in which the RIS phase shifts are optimized based on channel statistics to mitigate the overheads associated with channel estimation. It is shown that, while the power captured by the RIS scales linearly with the number of its elements, the two-timescale beamforming gain upon re-radiation towards the receiver saturates rapidly as the number of RIS elements increases, for a broad class of power angular spectra (PAS). The ultimate achievable gain is determined by the decay rate of the PAS in the angular domain, which directly influences how rapidly spatial correlations between RIS elements diminish. The implications of this saturation on the effectiveness of RIS-assisted communications are discussed.

Problem

• Investigates beamforming saturation in RIS-assisted communication
• Analyzes two-timescale RIS phase shift optimization impact
• Explores PAS decay rate influence on spatial correlations

Innovation

• Two-timescale RIS phase optimization
• Beamforming gain saturation analysis
• PAS decay rate impact