Triple IRS-Aided Communications: Row-Column Sparsity Enhanced Bayesian Tensor Learning for Channel Estimation

Channel acquisition presents a major challenge in deploying intelligent reflecting surfaces (IRS) aided communication systems, due to massive reflective elements that create a complex multi-path channel and increase channel dimensions. For an IRS-aided communication system, complete channel includes three parts: From the users to IRS, from the IRS to BS, and from the BS back to the IRS. Thus, a generalized multi-IRS cascaded communication system with three cascaded IRSs is considered. Unfortunately, existing channel estimation methods focus on single or double IRS cascades, which is not applicable to the case of triple cascaded IRS channel estimation directly. In this paper, we study the uplink channel estimation for triple cascaded IRSs aided single-user single-input single-output (SISO) systems. Specifically, the triple IRS cascaded channel is typically sparse. It permits us to characterize the channel estimation as a problem of sparse matrix recovery. Then, the sparse learning is explored to achieve robust channel estimation with limited training overhead. Particularly, the sparse channel matrices of the cascaded triple IRS channels have a common row-column block sparsity structure. However, a unique challenge lies in characterizing and enhancing such a common row-column sparsity. To tackle this issue, we apply a random matrix prior to promote the common row-column-wise sparsity of the channel matrix, and then an efficient Bayesian tensor inference algorithm is proposed to estimate the IRS channel. Finally, simulation results confirm that the proposed scheme outperforms traditional counterparts in terms of accuracy.