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 save 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 arising from IRS phase quantization error, in accordance with 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 double IRS-aided amplify-and-forward (AF) relay network, which are associated with the number of phase shifter quantization bits, are derived in the Rayleigh channels. In addition, 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, and increase with the number $k$ of IRS phase shift elements. The SNR and achievable rate performance losses of the system are smaller than 0.06dB and 0.03bits/s/Hz when $k$ is equal to 4 and 3, respectively.

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，智能反射面（IRS）近年来吸引了广泛关注。与传统中继系统相比，由IRS辅助的中继系统能够有效节省成本与能耗，并显著提升系统性能。然而，采用离散移相器的IRS所产生的相位量化误差可能会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，本文根据大数定律和瑞利分布，推导了双IRS辅助放大转发（AF）中继网络在瑞利信道下与移相器量化比特数相关的信噪比（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的闭式表达式。仿真结果表明，SNR和可达速率的性能损失随着量化比特数的增加而逐渐减小，并随IRS相位偏移单元数量k的增加而增大。当k分别等于4和3时，系统的SNR性能损失和可达速率性能损失分别小于0.06dB和0.03bits/s/Hz。