Wireless Beacon Enabled Hybrid Sparse Channel Estimation for RIS-Aided mmWave Communications

The inability of reconfigurable intelligent surfaces (RISs) to signal processing has become a critical bottleneck in terms of the precise capture of cascaded channels. There exists a pair of critical issues: 1) the high-dimensional cascaded channel to be estimated, which always entails substantial pilot overhead typically proportional to RIS elements and 2) the high possibilities of false alarms and unfaithful angle detection during cascaded channel estimates, referred to as the angular distortion, particularly in the case of conventional fully-passive RIS systems. To circumvent these issues, we investigate in this paper a multi-user multiple-input multiple-output (MIMO) system assisted by a wireless beacon (WB) enabled RIS over millimeter wave (mmWave) frequency. Specifically, WB is a functionally independent hardware that attaches parasitically to the RIS using only one radio frequency chain for broadcasting pilots, allowing for the accurate acquisition of partial cascaded channel information, e.g., some of angles of arrival/departure (AoA/AoDs) and complex gains. This efficiently eliminates the angular distortion effect and thus facilitates high precision recovery of sparse cascaded mmWave channels. Then, a hybrid structured sparsity (HSS) model is presented to capture hybrid sparse priors and approximate exact posterior distributions associated with RIS-aided twin-hop channels. We conceive of channel estimation as a compressive sensing problem in contrast to its conventional copy due to the presence of an unknown sensing matrix. To tackle this problem, an expectation-maximization (EM)-based algorithm, i.e., HSS-EM, is developed in order to fully employ the sparse priors encapsulated by the proposed HSS model for a robust and accurate recovery of the cascaded channels. Numerical results validate our analytical claims and demonstrate the significant improvement in terms of the normalized mean square error (NMSE) performance over conventional designs.