As a new technology to reconfigure wireless communication environment by signal reflection controlled by software, intelligent reflecting surface (IRS) has attracted lots of attention in recent years. Compared with conventional relay system, the relay system aided by IRS can effectively reduce the cost and energy consumption, and significantly enhance the system performance. However, the phase quantization error generated by IRS with discrete phase shifter may degrade the receiving performance of the receiver. To analyze the performance loss caused by IRS phase quantization error, based on the law of large numbers and Rayleigh distribution, the closed-form expressions for the signal-to-noise ratio (SNR) performance loss and achievable rate of the IRS-aided amplify-and-forward (AF) relay network, which are related to the number of phase shifter quantization bits, are derived under the line-of-sight (LoS) channels and Rayleigh channels, respectively. Moreover, their approximate performance loss closed-form expressions are also derived based on the Taylor series expansion. Simulation results show that the performance losses of SNR and achievable rate decrease with the number of quantization bits increases gradually. When the number of quantization bits is larger than or equal to 3, the SNR performance loss of the system is smaller than 0.23dB, and the achievable rate loss is less than 0.04bits/s/Hz, regardless of the LoS channels or Rayleigh channels.

翻译：作为一种通过软件控制信号反射来重构无线通信环境的新技术，智能反射表面（IRS）近年来引起了广泛关注。与传统中继系统相比，IRS辅助的中继系统能有效降低成本和能耗，并显著提升系统性能。然而，采用离散相位偏置器的IRS产生的相位量化误差可能降低接收端的接收性能。为分析IRS相位量化误差导致的性能损失，基于大数定律和瑞利分布，分别在视距（LoS）信道和瑞利信道下推导了与相位偏置器量化比特数相关的IRS辅助放大转发（AF）中继网络信噪比（SNR）性能损失和可达速率的闭式表达式。此外，基于泰勒级数展开还推导了其近似性能损失闭式表达式。仿真结果表明，SNR和可达速率的性能损失随量化比特数增加逐渐减小。当量化比特数大于或等于3时，无论是在LoS信道还是瑞利信道下，系统的SNR性能损失均小于0.23dB，可达速率损失小于0.04bits/s/Hz。