On the Performance of Training-Based IRS-Assisted Communications Under Correlated Rayleigh Fading

The channel state information (CSI) is crucial in communication systems assisted by intelligent reflecting surfaces (IRSs). This paper is on the phase estimation of individual channels in IRS-assisted communication systems with single-antenna transceivers under the correlated Rayleigh fading. We consider both the fully-active-IRS where all IRS elements are active and the hybrid-IRS where partially IRS elements are active, where an active IRS element is equipped with a sensing device for pilot signal reception. We derive the maximum likelihood (ML) estimator for channel phases of all IRS elements based on the observations on active IRS elements. This estimator is also proved to be the minimum mean square error (MMSE), maximum a posterior (MAP) and minimum mean absolute error (MMAE) estimators. Then we conduct performance analysis in terms of the gain and the capacity of the cascaded transmitter-IRS-receiver channel with perfectly known and estimated individual channel phases. Numerical results are provided to show that the performance of IRS-assisted communication systems with our proposed phase estimator is close to that with perfect CSI and validate our theoretical analysis.