Distributed detection of weak signals from multiple sensors with correlated observations

The authors extend the memoryless detection of a known weak signal in dependent noise to the case of distributed two-sensor detection from correlated sensor observations. The correlation of noise across time and/or sensors is characterized by m-dependent or φ-mixing models. The authors devise two-dimensional Chernoff bounds on the average error probability of the two detectors and from those obtain performance measures resembling (although distinctly different from) the asymptotic relative efficiency (ARE) for the two-sensor problem. Optimization of this performance measure leads to linear integral equations whose solutions provide the optimal memoryless nonlinearities used by the sensors. The results are applicable to cases of both symmetric and asymmetric correlated noise. Simulation results suggest that, regarding the average error probability of the two sensors, using memoryless nonlinearities that take into account the correlation in the samples of the two detectors is always better than using the locally optimal nonlinearity that ignores the dependence between samples