IRS Parameter Optimization for Channel Estimation MSE Minimization in Double-IRS Aided Systems

We consider the channel estimation problem in double intelligent reflecting surface (IRS)-aided single-user single-input-multiple-output systems. We focus on scenarios with less observations (training slots) {T} than number of IRS antennas {L} , exploiting channel spatial correlations. Unlike existing works, we reformulate the problem and obtain an equivalent signal model that is tractable for numerical optimization of the IRS parameters in the {T} < {L} regime. We first derive the linear minimum-mean-square-error (MMSE) channel estimates of all links, then optimize the parameters of both IRSs to minimize the channel estimation sum MSE via an alternating optimization and projected gradient descent framework, exploiting channel spatial correlations as side information. Simulation results show superior channel estimation and data rate performance to literature approaches based on configuring the IRS parameters with discrete Fourier transform coefficients.