  This paper studies the user activity detection and channel estimation problem
in a temporally-correlated massive access system where a very large number of
users communicate with a base station sporadically and each user once activated
can transmit with a large probability over multiple consecutive frames. We
formulate the problem as a dynamic compressed sensing (DCS) problem to exploit
both the sparsity and the temporal correlation of user activity. By leveraging
the hybrid generalized approximate message passing (HyGAMP) framework, we
design a computationally efficient algorithm, HyGAMP-DCS, to solve this
problem. In contrast to only exploit the historical estimations, the proposed
algorithm performs bidirectional message passing between the neighboring frames
for activity likelihood update to fully exploit the temporally-correlated user
activities. Furthermore, we develop an expectation maximization HyGAMP-DCS
(EM-HyGAMP-DCS) algorithm to adaptively learn the hyperparameters during the
estimation procedure when the system statistics are unknown. In particular, we
propose to utilize the analysis tool of state evolution to find the appropriate
hyperparameter initialization of EM-HyGAMP-DCS. Simulation results demonstrate
that our proposed algorithms can significantly improve the user activity
detection accuracy and reduce the channel estimation error.
