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Aiming at the key problems need to be solved, such as cascade channel sparse representation, time-varying channel parameter tracking and signal reconstruction, for time-varying cascade channels estimation of reconfigurable intelligent surface (RIS) assisted communication system, a Khatri-Rao and hierarchical Bayesian Kalman filter (KR-HBKF) algorithm was proposed.Firstly, the Khatri-Rao product and Kronecker product transformations were used to obtain the sparse representation of RIS cascaded channels based on the sparse characteristics of channels, thus the RIS cascaded channel estimation problem was transformed into a low-dimensional sparse signal recovery problem.Then, according to the state evolution model of RIS cascaded channel, the time correlation parameter was introduced into the prediction model of HBKF algorithm, and the improved HBKF was applied to solve the problem of time-varying channel parameter tracking and signal reconstruction for completing the time-varying cascaded channels estimation.The sparsity and time correlation of the channel were comprehensively considered in the KR-HBKF algorithm, thus better estimation accuracy could be obtained with small pilot overhead.Compared with the traditional compressed sensing algorithm, the simulation results show that the proposed algorithm has about 5 dB estimated performance improvement, and better robustness performance under different time-varying channel conditions.

Aiming at the key problems need to be solved, such as cascade channel sparse representation, time-varying channel parameter tracking and signal reconstruction, for time-varying cascade channels estimation of reconfigurable intelligent surface (RIS) assisted communication system, a Khatri-Rao and hierarchical Bayesian Kalman filter (KR-HBKF) algorithm was proposed.Firstly, the Khatri-Rao product and Kronecker product transformations were used to obtain the sparse representation of RIS cascaded channels based on the sparse characteristics of channels, thus the RIS cascaded channel estimation problem was transformed into a low-dimensional sparse signal recovery problem.Then, according to the state evolution model of RIS cascaded channel, the time correlation parameter was introduced into the prediction model of HBKF algorithm, and the improved HBKF was applied to solve the problem of time-varying channel parameter tracking and signal reconstruction for completing the time-varying cascaded channels estimation.The sparsity and time correlation of the channel were comprehensively considered in the KR-HBKF algorithm, thus better estimation accuracy could be obtained with small pilot overhead.Compared with the traditional compressed sensing algorithm, the simulation results show that the proposed algorithm has about 5 dB estimated performance improvement, and better robustness performance under different time-varying channel conditions.