Distributed Detection over Noisy Networks: Large Deviations Analysis

TL;DR

This paper analyzes the large deviations performance of distributed detection in noisy networks, showing that sensors can achieve exponential error decay through optimal weighting despite communication noise.

Contribution

It introduces a stochastic approximation-based distributed detector with an optimal weight sequence balancing noise and information flow, providing explicit performance bounds.

Findings

Sensors achieve exponential error decay even with noisy communication.

Optimal weight sequence balances information flow and communication noise.

A threshold on communication noise power determines when cooperation improves detection.

Abstract

We study the large deviations performance of consensus+innovations distributed detection over noisy networks, where sensors at a time step k cooperate with immediate neighbors (consensus) and assimilate their new observations (innovation.) We show that, even under noisy communication, \emph{all sensors} can achieve exponential decay e^{-k C_{\mathrm{dis}}} of the detection error probability, even when certain (or most) sensors cannot detect the event of interest in isolation. We achieve this by designing a single time scale stochastic approximation type distributed detector with the optimal weight sequence {\alpha_k}, by which sensors weigh their neighbors' messages. The optimal design of {\alpha_k} balances the opposing effects of communication noise and information flow from neighbors: larger, slowly decaying \alpha_k improves information flow but injects more communication noise. Further, we quantify the best achievable C_{\mathrm{dis}} as a function of the sensing signal and noise, communication noise, and network connectivity. Finally, we find a threshold on the communication noise power below which a sensor that can detect the event in isolation still improves its detection by cooperation through noisy links.