Training Signal Design for Sparse Channel Estimation in Intelligent Reflecting Surface-Assisted Millimeter-Wave Communication

In this paper, the problem of training signal design for intelligent reflecting surface (IRS)-assisted millimeter-wave (mmWave) communication under a sparse channel model is considered. The problem is approached based on the Cram$\acute{\text{e}}$r-Rao lower bound (CRB) on the mean-square error (MSE) of channel estimation. By exploiting the sparse structure of mmWave channels, the CRB for the channel parameter composed of path gains and path angles is derived in closed form under Bayesian and hybrid parameter assumptions. Based on the derivation and analysis, an IRS reflection pattern design method is proposed by minimizing the CRB as a function of design variables under constant modulus constraint on reflection coefficients. Numerical results validate the effectiveness of the proposed design method for sparse mmWave channel estimation.