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Intelligent Reflecting Surface (IRS) holds promise for enhancing wireless channel propagation, especially in high-frequency bands like millimeter-wave (mmWave) that are prone to significant propagation losses and blockage effects. However, channel estimation poses significant challenges due to passive nature of the IRS, high dimension of channel matrix, and need to consider superposition of direct channel between transceivers and reflective channel through the IRS. In this study, we explore adaptive and robust estimator for time-varying mmWave channels, considering the use of more general arbitrarily shaped IRS, in contrast to classical regular IRS elements arranged on a grid. Firstly, we establish a consistent-sparse-subspace relationship between direct and reflective channels using linearly modified atomic norm minimization. Secondly, we formulate joint estimation as a low-dimensional and robustly sparse matrix reconstruction programming, resolving efficiently through alternating optimization and alternating direction method of multipliers. Additionally, to reduce complexity, we propose a learning-based solver using fixed-point iteration and a cascaded deep-learning network framework. This solver can adjust its network depth according to the time-varying channel, achieving linear convergence and reduced complexity. Simulation results demonstrate that both proposed channel estimation methods outperform current state-of-the-art techniques.
Chu et al. (Mon,) studied this question.