  Recently, grant-free transmission paradigm has been introduced for massive
Internet of Things (IoT) networks to save both time and bandwidth and transmit
the message with low latency. In order to accurately decode the message of each
device at the base station (BS), first, the active devices at each transmission
frame must be identified. In this work, first we investigate the problem of
activity detection as a threshold comparing problem. We show the convexity of
the activity detection method through analyzing its probability of error which
makes it possible to find the optimal threshold for minimizing the activity
detection error. Consequently, to achieve an optimum solution, we propose a
deep learning (DL)-based method called convolutional neural network
(CNN)-activity detection (AD). In order to make it more practical, we consider
unknown and time-varying activity rate for the IoT devices. Our simulations
verify that our proposed CNN-AD method can achieve higher performance compared
to the existing non-Bayesian greedy-based methods. This is while existing
methods need to know the activity rate of IoT devices, while our method works
for unknown and even time-varying activity rates
