Compressed CPD-Based Channel Estimation and Joint Beamforming for RIS-Assisted Millimeter Wave Communications

We consider the problem of channel estimation and joint active and passive beamforming for reconfigurable intelligent surface (RIS) assisted millimeter wave (mmWave) multiple-input multiple-output (MIMO) orthogonal frequency division multiplexing (OFDM) systems. We show that, with a well-designed frame-based training protocol, the received pilot signal can be organized into a low-rank third-order tensor that admits a canonical polyadic decomposition (CPD). Based on this observation, we propose two CPD-based methods for estimating the cascade channels associated with different subcarriers. The proposed methods exploit the intrinsic low-rankness of the CPD formulation, which is a result of the sparse scattering characteristics of mmWave channels, and thus have the potential to achieve a significant training overhead reduction. Specifically, our analysis shows that the proposed methods have a sample complexity that scales quadratically with the sparsity of the cascade channel. Also, by utilizing the singular value decomposition-like structure of the effective channel, this paper develops a joint active and passive beamforming method based on the estimated cascade channels. Simulation results show that the proposed CPD-based channel estimation methods attain mean square errors that are close to the Cramer-Rao bound (CRB) and present a clear advantage over the compressed sensing-based method. In addition, the proposed joint beamforming method can effectively utilize the estimated channel parameters to achieve superior beamforming performance.