Distributed Detection of a Common Random Signal

We consider the problem of distributed detection of a common random signal. After evaluating the detection performance of the centralized detector, we propose two distributed detectors. Detector 1 employs energy detector at the local sensors and a monotone fusion rule at the fusion center (FC). Detector 2 uses a Sign detector at each local sensor and a two-sided test at the FC. Detector 1 performs better for the somewhat extreme cases where the number of sensors is very small. When the number of sensors is reasonably large, we prove that detector 2 outperforms detector 1 using the Kullback-Leibler divergence (KLD) and Stein's lemma. In fact, for sensor networks with a reasonable number of sensors, the performance of detector 2 is about √ 2/π equation as effective as the centralized case where no local quantization is made. We validate the derived results via numerical Monte Carlo Simulations.