Temporally-correlated massive access: joint user activity detection and channel estimation via vector approximate message passing

In the paper, we investigate a massive machine-type communication (mMTC), where numerous single-antenna users communicate with a single-antenna base station while being active. However, the status of user can undergoes multiple transitions between active and inactive states across whole consecutive intervals. Then, we formulate the problem of joint user activity detection and channel estimation within the dynamic compressed sensing (DCS) framework, considering the temporally-correlated user activity across the entire consecutive intervals. To be specific, we introduce a new hybrid vector approximate message passing algorithm for DCS (HyVAMP-DCS). The proposed algorithm comprises a VAMP block for estimating channel and a loopy belief propagation (LBP) block for detecting user activity. Moreover, these two blocks can exchange messages, enhancing the performance of both channel estimation and user activity detection. Importantly, compared to the fragile GAMP algorithm, VAMP is robust and applicable to a much broader class of large random matrices. Furthermore, the fixed points of VAMP's state evolution align with the replica prediction of the minimum mean-squared error. The simulation results illustrate the superiority of HyVAMP-DCS, demonstrating its significant outperformance over HyGAMP-DCS.