Remote Monitoring of Markov Sources over Random Access Channels: False Alarm and Detection Probability

We study the problem of remote source monitoring in an Internet of Things (IoT) system where a set of devices share a wireless channel to a common receiver. Each device observes an independent two-state Markov chain, with one of the states visited sporadically (modeling a critical event), and may transmit the current source value following a slotted ALOHA contention. We focus on protocols that set the transmission probability over a slot based on the value of the monitored process over the current and past slot. In turn, the receiver estimates the source state leveraging the channel outputs leaning either on a simple decode and hold approach, which requires no knowledge of the source statistics, or a maximum a posteriori estimator. For both approaches, we derive an analytical characterization of the system behavior in terms of false alarm and detection probability, deriving interesting insights and highlighting protocol design hints that depart from those commonly employed for throughput or age of information optimization.