Efficient Two-Level Block-Structured Sparse Bayesian Learning-Based Channel Estimation for RIS-Assisted MIMO IoT Systems

Reconfigurable intelligent surface (RIS)-assisted multiple-input multiple-output (MIMO) has recently emerged as a promising candidate to improve the energy and spectral efficiency of Internet of Things (IoT) systems. This paper aims to develop an efficient channel estimation scheme for RIS-assisted MIMO IoT systems within structured Bayesian learning framework. However, the high-dimensional channel matrix with considering its underlying structured sparsity makes efficient channel estimation scheme design a challenging task. To deal with it, we firstly formulate the cascaded RIS-assisted MIMO channel estimation as a generic sparse signal recovery problem with considering the constructed two-level block-structured sparsity of channels. Secondly, we design a flexible prior model to characterize such structured sparsity of channels, in which hierarchical hyperparameters are introduced, and the iterative Bayesian learning-based method is developed to autonomously estimate channels and the hyperparameters associated with the prior model. Thirdly, to relieve the high-computational complexity involving matrix inversion when calculating the posterior of channels, we develop efficient methods from two perspectives. On the one hand, an inverse-free method is developed by relaxed evidence lower bound (ELBO) maximization with an adjustable factor of reducing the gap between the standard ELBO and relaxed ELBO. On the other hand, a method of reducing the dimension of sparse representation matrix aided by external block-structured sparsity is developed. Finally, the computational complexity and convergence properties of the proposed methods are analyzed in detail. Simulation results are provided to verify the superiority of the devised channel estimation methods.