Large Deviations Performance of Consensus+Innovations Distributed Detection with Non-Gaussian Observations

We establish the large deviations asymptotic performance (error exponent) of consensus+innovations distributed detection over random networks with generic (non-Gaussian) sensor observations. At each time instant, sensors 1) combine theirs with the decision variables of their neighbors (consensus) and 2) assimilate their new observations (innovations). This paper shows for general non-Gaussian distributions that consensus+innovations distributed detection exhibits a phase transition behavior with respect to the network degree of connectivity. Above a threshold, distributed is as good as centralized, with the same optimal asymptotic detection performance, but, below the threshold, distributed detection is suboptimal with respect to centralized detection. We determine this threshold and quantify the performance loss below threshold. Finally, we show the dependence of the threshold and performance on the distribution of the observations: distributed detectors over the same random network, but with different observations' distributions, for example, Gaussian, Laplace, or quantized, may have different asymptotic performance, even when the corresponding centralized detectors have the same asymptotic performance.Comment: 30 pages, journal, submitted Nov 17, 2011; revised Apr 3, 201

Distributed Detection over Noisy Networks: Large Deviations Analysis

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.Comment: 30 pages, journal, submitted August 2nd, 201