Quantized Zero-Energy RIS: Residual Phase Modeling and Outage Analysis

2026-04-17

AI Summary

This work addresses the performance limitations of zero-energy reconfigurable intelligent surfaces (zeRIS) under finite phase resolution, where the coupling between energy harvesting and signal reflection constrains system efficiency. To tackle this challenge, the authors develop a unified analytical framework that integrates quantized phase shifts with the harvest-and-reflect (HaR) mechanism. For the first time, the statistical characteristics of residual phase errors induced by quantization are explicitly incorporated into the model. Leveraging stochastic geometry theory along with time-switching and element-partitioning strategies, closed-form expressions for outage probability and energy efficiency are derived. The analysis unveils a non-trivial trade-off between phase resolution and HaR design, offering critical theoretical guidance for optimizing phase precision and HaR configuration in practical zeRIS deployments.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Machine Learning: Calibration & Uncertainty Quantification
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Energy management for devices in mobile Web and WoT environments
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

Abstract

Zero-energy reconfigurable intelligent surfaces (zeRISs) have recently emerged as a promising solution for enabling energy-efficient and scalable programmable wireless environments (PWEs) by harvesting their operational energy from impinging radio-frequency signals. However, the operation of zeRIS-assisted systems is inherently constrained by the coupling between energy harvesting and signal reflection, a dependency that becomes more intricate under practical hardware limitations such as finite-resolution phase control. In this paper, we develop a comprehensive analytical framework for zeRIS-assisted communication systems operating under quantized phase shifts and harvest-and-reflect (HaR) schemes. Specifically, we analyze the joint energy-data rate outage probability and the energy efficiency under time switching and element splitting schemes, considering both transmitter-side and user-side deployment scenarios. By explicitly modeling the residual phase error induced by quantization and incorporating its statistical properties into the analysis, we show that quantization jointly affects energy harvesting and signal reflection, thereby inducing non-trivial trade-offs. As a result, the presented framework enables accurate performance evaluation and reveals critical design trade-offs for the selection of the phase resolution, and the applied HaR scheme in zeRIS-assisted wireless networks.

Problem

• zero-energy RIS
• phase quantization
• energy harvesting
• outage probability
• residual phase error

Innovation

• quantized phase shift
• zero-energy RIS
• residual phase error
• harvest-and-reflect
• outage probability