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.

翻译：零能量可重构智能表面（zeRIS）近年来通过从入射射频信号中采集运行能量，成为实现高能效、可扩展可编程无线环境（PWE）的一种有前景的解决方案。然而，zeRIS辅助系统的运行本质上受限于能量采集与信号反射之间的耦合关系，这种依赖关系在有限分辨率相位控制等实际硬件限制下变得更加复杂。本文针对采用量化相移及“采能-反射”（HaR）方案的zeRIS辅助通信系统，开发了一个全面的分析框架。具体而言，我们分析了时间切换和元素分裂方案下的联合能-数率中断概率和能效，并考虑了发射端侧和用户侧两种部署场景。通过对量化引起的残余相位误差进行显式建模，并将其统计特性纳入分析，我们揭示了量化会同时影响能量采集和信号反射，从而引发不容忽视的权衡。因此，所提出的框架能够实现精确的性能评估，并揭示了在zeRIS辅助无线网络中选择相位分辨率和应用HaR方案时的关键设计权衡。