This paper studies the performance of a single-input single-output (SISO) system enhanced by the assistance of an intelligent reflecting surface (IRS), which is equipped with a finite number of elements under Rayleigh fading channels. From the instantaneous channel capacity, we compute a closed-form expression of the coverage probability as a function of statistical channel information only. A scaling law of the coverage probability and the number of phase shifts is further obtained. The ergodic capacity is derived, then a simple upper bound to simplify matters of utilizing the symbolic functions and can be applied for a long period of time. Numerical results manifest the tightness and effectiveness of our closed-form expressions compared with Monte-Carlo simulations.

中文翻译：

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智能反射面增强通信系统的覆盖概率和遍历能力

本文研究了通过智能反射面 (IRS) 的辅助增强的单输入单输出 (SISO) 系统的性能，该系统在瑞利衰落信道下配备了有限数量的元素。根据瞬时信道容量，我们计算覆盖概率的闭式表达式，它仅作为统计信道信息的函数。进一步得到覆盖概率和相移次数的标度律。推导出遍历容量，然后是一个简单的上限，以简化使用符号函数的问题，并且可以长期应用。数值结果表明与蒙特卡罗模拟相比，我们的封闭形式表达式的紧密性和有效性。