Abstract : Discrete phase shifter of intelligent reflecting surface (IRS) generates phase quantization error (QE) and degrades the receive performance at the receiver. To make an analysis of the performance loss (PL) caused by IRS with phase QE, based on the law of large numbers, the closed-form expressions of signalto-noise ratio (SNR) PL, achievable rate (AR), and bit error rate (BER) are successively derived under line-of-sight (LoS) channels and Rayleigh channels. Moreover, based on the Taylor series expansion, the approximate simple closed form of PL of IRS with approximate QE is also given. The simulation results show that the performance losses of SNR and AR decrease as the number of quantization bits increases, while they gradually increase with the number of IRS phase shifter elements increases. Regardless of LoS channels or Rayleigh channels, when the number of quantization bits is larger than or equal to 3, the performance losses of SNR and AR are less than 0.23 dB and 0.08 bits/s/Hz, respectively, and the BER performance degradation is trivial. In particular, the performance loss difference between IRS with QE and IRS with approximate QE is negligible when the number of quantization bits is not less than 2.
Index terms : Intelligent reflecting surface, performance loss, quantization error, Taylor series, the law of large numbers.