Channel estimation for double IRS assisted communication for a mobile user

A single-user cellular communication system between a base station (BS) and a mobile user equipment (UE), assisted by intelligent reflecting surfaces is considered. The goal is to estimate the individual channels, i.e., BS-IRS-2, IRS-2-IRS-1 and UE-IRS-1. We propose a two-phase channel estimation (CE) algorithm wherein the BS-IRS-2 and IRS-1-IRS-2 channels are estimated simultaneously by utilizing the sparsity offered by mmWave channels in phase-1. In phase-2, in order to track the time-varying channel UE-IRS-1, we consider a channel model involving dynamic sparsity, and estimate it by using the dynamic turbo orthogonal approximate message passing (D-TOAMP) and dynamic compressive sensing AMP (DCS-AMP). Alternatively, we use Kalman-like filter (KLF) followed by Kalman filter (KF) to track UE-IRS-1 channel. Numerical results of phase-1 and phase-2 (for D-TOAMP, DCS-AMP) demonstrate the performance of our CE algorithm for double IRS assisted communication in terms of estimation error, computation time, and also provide a guideline for the choice of the appropriate version of the algorithm in each phase. Also, simulations of phase-2 (under KLF, KF) demonstrate the efficacy of our proposed KLF-KF algorithm over the Unscented Kalman filter (UKF)-KF in terms of estimation error.