  This paper considers joint device activity detection and channel estimation
in Internet of Things (IoT) networks, where a large number of IoT devices exist
but merely a random subset of them become active for short-packet transmission
at each time slot. In particular, we propose to leverage the temporal
correlation in user activity, i.e., a device active at the previous time slot
is more likely to be still active at the current moment, to improve the
detection performance. Despite the temporally-correlated user activity in
consecutive time slots, it is challenging to unveil the connection between the
activity pattern estimated previously, which is imperfect but the only
available side information (SI), and the true activity pattern at the current
moment due to the unknown estimation error. In this work, we manage to tackle
this challenge under the framework of approximate message passing (AMP).
Specifically, thanks to the state evolution, the correlation between the
activity pattern estimated by AMP at the previous time slot and the real
activity pattern at the previous and current moment is quantified explicitly.
Based on the well-defined temporal correlation, we further manage to embed this
useful SI into the design of the minimum mean-squared error (MMSE) denoisers
and log-likelihood ratio (LLR) test based activity detectors under the AMP
framework. Theoretical comparison between the SI-aided AMP algorithm and its
counterpart without utilizing temporal correlation is provided. Moreover,
numerical results are given to show the significant gain in activity detection
accuracy brought by the SI-aided algorithm.
