Channel estimation for double IRS-assisted millimeter wave MIMO systems based on tensor decomposition and manifold optimization

The issue of channel estimation for a double intelligent reflecting surface (IRS) assisted millimeter wave multiple-input multiple-output (MIMO) system was addressed and a channel estimation scheme based on tensor decomposition and manifold optimization was proposed. Specifically, a tensor model was constructed based on the high-dimensional features of received signals, and the objective function of the channel estimation problem was formulated based on the Tucker2 decomposition of the tensor. Then, the channel estimation problem was decomposed into multiple sub-problems using alternating optimization theory, providing feasible solutions for estimating the channel of each hop in the double IRS scenario. Finally, considering the low-rank characteristics of the millimeter wave channel itself, each channel estimation sub-problem was transformed into an optimization problem on the complex fixed-rank matrix manifold, and a manifold optimization-based alternating channel estimation scheme was proposed by leveraging the advantages of fixed-rank manifold optimization in solving rank-constrained optimization problems. Unlike traditional schemes, the proposed scheme takes into account the low-rank characteristics of millimeter wave channels, accurately describes the channels, and effectively handles fixed-rank constraints using manifold optimization theory, thus improving the accuracy of channel estimation. Simulation results show that the proposed channel estimation scheme outperforms existing reference schemes in terms of estimation performance in different scenarios.