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