Decentralized Cascaded Channel Estimation and Active User Detection for RIS-Assisted IoT Networks

Reconfigurable intelligent surface (RIS) is a promising technology for enhancing coverage and connectivity in Internet of Things (IoT) networks. However, the passive nature of RIS impedes the decoupling of the BS-RIS channel and RIS-user channels from the cascaded channel, making both channel estimation (CE) and active user detection (AUD) challenging in RIS-assisted IoT networks. To address this problem, this paper formulates the task of joint CE and AUD as a multi-layer sparse recovery problem by exploiting the sparsity structures in cascaded channels, as well as their joint scaling property whereby the cascaded channel of each user equipment (UE) can be normalized relative to that of an active reference UE through a diagonal matrix. Within the framework of variational Bayesian inference, the formulated problem is transformed into a Bethe free energy (BFE) minimization problem. To solve it effectively, we propose a low-complexity BFE-based hybrid message passing (BFE-HMP) algorithm that introduces various moment matching constraints. More importantly, two decentralized implementations of the proposed BFE-HMP algorithm are developed for the emerging decentralized base station (BS) architectures. Extensive simulation results validate the superiority of the proposed BFE-based algorithms in terms of normalized mean square error and the detection error probability over the existing state-of-the-art methods.