A Large Deviation Analysis of Detection Over Multi-Access Channels with Random Number of Sensors

We consider the problem of distributed detection over a multi-access channel. Assuming a random number of sensors transmitting their observations using Type Based Multiple Access, we derive the detection performance using Large Deviations Principle as the mean number of sensors goes to infinity. We characterize the performance in terms of error exponents. We provide comparison with the case when the number of sensors is deterministic. We generalize this scheme to multiple collections, propose a Minimum Sum-Rate detector and characterize its error exponents.