Message Passing-Based Joint User Activity Detection and Channel Estimation for Temporally-Correlated Massive Access

This paper studies the temporally-correlated massive access system where a large number of users communicate with the base station sporadically and continue transmitting data in the following frames in high probability when being active. To exploit both the sparsity and the temporal correlations in the user activities, we formulate the joint user activity detection and channel estimation problem in multiple consecutive frames as a dynamic compressed sensing (DCS) problem. Particularly, the problem is proposed to be solved under Bayesian inference to fully utilize the channel statistics and the activity evolution process. The hybrid generalized approximate message passing (HyGAMP) framework is leveraged to design a HyGAMP-DCS algorithm, which can nearly achieve the Bayesian optimality with efficient computations. Specifically, a GAMP part for channel estimation and an MP part for activity likelihood update are included in the proposed algorithm, then the extrinsic information is exchanged between them for performance enhancement. Moveover, we develop the expectation maximization HyGAMP-DCS (EM-HyGAMP-DCS) algorithm to adaptively learn the hyperparameters during the estimation procedure when the system statistics are unavailable. Particularly, the analytical tool of state evolution is provided to find the appropriate hyperparameter initialization that ensures EM-HyGAMP-DCS to achieve satisfied performance and fast convergence. From the simulation results, it is validated that our proposed algorithm can significantly outperform the existing methods.