Sparse Bayesian Learning Based Channel Extrapolation for RIS Assisted MIMO-OFDM

Reconfigurable intelligent surface (RIS) is a revolutionary technology and can be used to assist communication systems by adaptively manipulating the wireless environment. In this paper, we propose a novel cascaded channel estimation algorithm for the RIS-assisted multiple-input multiple-output orthogonal frequency division multiplexing systems. Inspired by the channel compression idea, we can obtain a sub-sampled channel by turning off a fraction of RIS elements and then extrapolate it to the complete one, by which the pilot overhead is greatly reduced. The problem of channel extrapolation is transformed into recovering the physical parameters of the cascaded channel from the partial channel observations and is then formulated by the sparse Bayesian learning (SBL) framework. In order to circumvent the curse of high dimensional matrices inversion in the vector-matrix system, we further introduce the tensor structure into the SBL framework. Specially, by leveraging of the channel sparsity over the angle domain and delay domain, we derive the virtual channel expression in tensor form and model a Kronecker-structured prior distribution for the virtual channels. The multi-domain sparse properties of the virtual channel tensor can be effectively captured by a group of low-dimensional hyper-parameters, and thus reduce the computational complexity. In addition, the Cramer-Rao lower bound is derived for the proposed channel extrapolation. Simulation results show the superior performance of the proposed scheme.