Distributed Detection Over Noisy Networks: Large Deviations Analysis

We study the large deviations performance of consensus+innovations distributed detection over noisy networks, where agents at a time step cooperate with their immediate neighbors (consensus) and assimilate their new observations (innovation.) We show that, under noisy communication, all agents can still achieve an exponential error rate, even when certain (or most) agents cannot detect the event of interest in isolation. The key to achieving this is the appropriate design of the time-varying weight sequence {α_k = b₀/(a + k)} by which agents weigh their neighbors´ messages. We and a communication payoff threshold on the communication noise power, i.e., the critical noise power below which cooperation among neighbors improves detection performance and above which the noise in the communication among agents overwhelms the distributed detector performance. Numerical examples illustrate several tradeoffs among network parameters and between the time (or number of measurements) needed for a reliable decision and the transmission power invested by the agents.