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 a CPD-based method for estimating the cascade channels associated with different subcarriers. The proposed method exploits the intrinsic low-rankness of the CPD formulation, which is a result of the sparse scattering characteristics of mmWave channels, and thus has the potential to achieve a significant training overhead reduction. Specifically, our analysis shows that the proposed method has 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 method attains mean square errors that are close to the Cramér-Rao bound (CRB) and present a clear advantage over the compressed sensing-based methods. In addition, the proposed joint beamforming method can effectively utilize the estimated channel parameters to achieve superior beamforming performance.

I. Introduction

Millimeter wave (mmWave) and terahertz (THz) communications are able to support extremely high data rate transmissions [1], [2], [3], [4]. Nevertheless, due to the reduced diffraction effect and high penetration loss, mmWave/THz systems require more antennas and active nodes such as access points (APs) and relays to improve the signal coverage [5], [6]. Deploying active nodes incurs an additional energy consumption and meanwhile presents a serious network interference issue. It is thus of practical significance to develop innovative technologies to address the coverage issue of future mmWave/THz wireless networks with a low cost and complexity.