Structured Tensor Decomposition Based Channel Estimation and Double Refinements for Active RIS Empowered Broadband Systems

Channel parameter estimation is crucial for optimal designs of next-generation reconfigurable intelligent surface (RIS)-empowered communications and sensing. Tensor-based mechanisms are particularly effective, capturing the multi-dimensional nature of wireless channels, especially in scenarios where RIS integrates with multiple-antenna devices. However, existing studies assume either a line-of-sight (LOS) scenario or a blocked condition for non-RIS channel. This paper solves a novel problem: tensor-based channel parameter recovery for active RIS-aided multiple-antenna wideband connections in a multipath environment with non-RIS paths. System settings are customized to construct the received signals as a fifth-order canonical polyadic (CP) tensor. Four of the five-factor matrices unfortunately contain redundant columns, and the remaining one is a Vandermonde matrix, which fails to satisfy the Kruskal condition for tensor decomposition uniqueness. To address this issue, spatial smoothing and Vandermonde structured CP decomposition (VSCPD) are applied, making the tensor factorization problem solvable and providing a relaxed general uniqueness condition. A sequential triple-stage channel estimation framework is proposed based on the factor estimates. The first stage enables multipath identification and algebraic coarse estimation, while the following two stages offer optional successive refinements at the cost of increased complexity. The closed-form Cramer-Rao lower bound (CRLB) is derived to assess the estimation performance. Herein, the noise covariance matrix depends on multipath parameters in our active-RIS scenario. Finally, numerical results are provided to verify the effectiveness of proposed algorithms under various evaluation metrics.