  This paper considers the joint device activity detection and channel
estimation problem in a massive Internet of Things (IoT) connectivity system,
where a large number of IoT devices exist but merely a random subset of them
become active for short-packet transmission in each coherence block. In
particular, we propose to leverage the temporal correlation in device activity,
e.g., a device active in the previous coherence block is more likely to be
still active in the current coherence block, to improve the detection and
estimation performance. However, it is challenging to utilize this temporal
correlation as side information (SI), which relies on the knowledge about the
exact statistical relation between the estimated activity pattern for the
previous coherence block (which may be imperfect with unknown error) and the
true activity pattern in the current coherence block. To tackle this challenge,
we establish a novel SI-aided multiple measurement vector approximate message
passing (MMV-AMP) framework. Specifically, thanks to the state evolution of the
MMV-AMP algorithm, the correlation between the activity pattern estimated by
the MMV-AMP algorithm in the previous coherence block and the real activity
pattern in the current coherence block is quantified explicitly. Based on the
well-defined temporal correlation, we further manage to embed this useful SI
into the denoiser design under the MMV-AMP framework. Specifically, the
SI-based soft-thresholding denoisers with binary thresholds and the SI-based
minimum mean-squared error (MMSE) denoisers are characterized for the cases
without and with the knowledge of the channel distribution, respectively.
Numerical results are given to show the significant gain in device activity
detection and channel estimation performance brought by our proposed SI-aided
MMV-AMP framework.
