Channel Estimation for Intelligent Reflecting Surface Assisted Wireless Communications

TL;DR

This paper develops a closed-form MMSE channel estimation method for IRS-assisted wireless systems, providing bounds and asymptotic analysis, with numerical results demonstrating accuracy at moderate SNR and element counts.

Contribution

It introduces a novel MMSE estimation approach for IRS-assisted channels using a Gaussian scale mixture model and derives bounds and asymptotic behavior.

Findings

Upper and lower bounds on MSE are tight at medium SNR.

As the number of IRS elements increases, the MSE approaches the asymptotic limit.

Numerical results confirm the effectiveness of the proposed estimation method.

Abstract

In this paper, the minimum mean square error (MMSE) channel estimation for intelligent reflecting surface (IRS) assisted wireless communication systems is investigated. In the considered setting, each row vector of the equivalent channel matrix from the base station (BS) to the users is shown to be Bessel $K$ distributed, and all these row vectors are independent of each other. By introducing a Gaussian scale mixture model, we obtain a closed-form expression for the MMSE estimate of the equivalent channel, and determine analytical upper and lower bounds on the mean square error. Using the central limit theorem, we conduct an asymptotic analysis of the MMSE estimate, and show that the upper bound on the mean square error of the MMSE estimate is equal to the asymptotic mean square error of the MMSE estimation when the number of reflecting elements at the IRS tends to infinity. Numerical simulations show that the gap between the upper and lower bounds are very small, and they almost overlap with each other at medium signal-to-noise ratio (SNR) levels and moderate number of elements at the IRS.