On the Performance of IRS-Assisted Communications with joint Phase Estimation Errors and Discrete Phase Control

In intelligent reflecting surface (IRS)-assisted communications, the ultimate gain is achieved when the phases of the reflected signals are optimally selected to maximize the signal-to-noise ratio (SNR). However, practical hurdles, particularly the imperfect phase estimation and quantization can reduce the potential gain. Therefore, this work aims at evaluating the impact of applying a quantized phase in the presence of phase estimation errors. Towards this goal, we derive the probability density function (PDF) of the estimated quantized phase, then using the sinusoidal addition theorem (SAT), the PDF of the received signal envelope is derived and used to derive closed-form expressions of the symbol error rate (SER) and outage probability (OP). The obtained analytical and simulation results show that the SER and OP jointly depend on the SNR, phase estimation accuracy, number of IRS elements, and number of quantization levels. The imperfect phase and quantization demonstrated several counterintuitive results. In particular, it is shown that increasing the number of IRS elements or the number of quantization levels may degrade the system performance. Moreover, the results reveal that the impact of phase quantization increases as the phase estimation accuracy decreases. The results also show that the performance is susceptible to phase errors with an even number of reflectors and binary quantization levels.