Tensor-Based Joint Channel Estimation and Activity Detection for Reconfigurable Intelligent Surface-Assisted Massive Connectivity

Reconfigurable intelligent surface (RIS) has gained much attention as a cost-effective solution to enhance connectivity and coverage in massive machine-type communication. However, the passive nature of RIS poses fundamental challenges to decoupling and estimating base station (BS)-RIS and RIS-device channels, as well as identifying active devices. To effectively tackle this issue, we cast the joint channel estimation and activity detection for RIS-assisted Internet-of-Things networks as a tensor-based two-layer problem by exploiting the channel sparsity and a multi-frame pilot training structure. The first layer involves the Canonical Polyadic (CP) decomposition of a third-order tensor observation, while the second layer addresses compressive sensing (CS)-based simple measurement vector (SMV) and multiple measurement vector (MMV) problems. Then, by leveraging the Bayesian inference framework, we propose a tensor-based approximate message passing (TAMP) algorithm to estimate one-hop BS-RIS channel, one-hop RIS-device channels, and active IoT devices simultaneously. Furthermore, we conduct the state evolution (SE) analysis of TAMP to theoretically characterize its MSE. Numerical results corroborate the superior estimation and detection performance of TAMP and demonstrate that our SE analysis perfectly predicts the actual MSE.