In this paper, we develop a comprehensive theoretical framework for analyzing the performance of reconfigurable intelligent surfaces (RISs)-assisted communication systems over generalized fading channels and in the presence of phase noise. To this end, we propose the Fox's H model as a unified fading distribution for a large number of widely used generalized fading channels. In particular, we derive a unified analytical framework for computing the outage probability and for estimating the achievable diversity order of RIS-aided systems in the presence of phase shifts that either are optimally configured or are impaired by phase noise. The resulting expressions are general, as they hold for an arbitrary number of reflecting elements, and various channel fading and phase noise distributions. As far as the diversity order is concerned, notably, we introduce an asymptotic analytical framework for determining the diversity order in the absence of phase noise, as well as sufficient conditions based on upper bounds and lower bounds for ensuring that RIS-assisted systems achieve the full diversity order in the presence of phase noise. More specifically, if the absolute difference between pairs of phase errors is less than $\pi/2$, RIS-assisted communications achieve the full diversity order over independent fading channels, even in the presence of phase noise. The theoretical frameworks and findings are validated with the aid of Monte Carlo simulations.

中文翻译：

---

相位噪声下广义衰落信道上RIS辅助通信的性能评估和分集分析

在本文中，我们开发了一个综合的理论框架，用于分析在通用衰落信道上并且在存在相位噪声的情况下，可重构智能表面（RIS）辅助通信系统的性能。为此，我们提出了Fox的H模型作为大量广泛使用的广义衰落信道的统一衰落分布。特别是，我们推导了一个统一的分析框架，用于计算中断概率，并在存在最佳配置或受到相位噪声损害的相移的情况下，估算RIS辅助系统可实现的分集阶数。结果表达式是通用的，因为它们适用于任意数量的反射元素以及各种信道衰落和相位噪声分布。就多样性顺序而言，我们介绍了一种渐进分析框架，用于在不存在相位噪声的情况下确定分集阶数，以及基于上限和下限的充分条件，以确保RIS辅助系统在存在相位噪声的情况下实现完整的分集阶数。更具体地说，如果成对的相位误差之间的绝对差小于π/ 2，则即使在存在相位噪声的情况下，由RIS辅助的通信也能在独立的衰落信道上实现全分集阶数。理论框架和发现在蒙特卡洛模拟的帮助下得到了验证。以及基于上限和下限的充分条件，以确保RIS辅助系统在存在相位噪声的情况下达到完整的分集阶数。更具体地说，如果成对的相位误差之间的绝对差小于π/ 2，则即使在存在相位噪声的情况下，由RIS辅助的通信也能在独立的衰落信道上实现全分集阶数。理论框架和发现在蒙特卡洛模拟的帮助下得到了验证。以及基于上限和下限的充分条件，以确保RIS辅助系统在存在相位噪声的情况下达到完整的分集阶数。更具体地说，如果成对的相位误差之间的绝对差小于π/ 2，则即使在存在相位噪声的情况下，由RIS辅助的通信也能在独立的衰落信道上实现全分集阶数。理论框架和发现在蒙特卡洛模拟的帮助下得到了验证。