A Notion of Diversity Order in Distributed Radar Networks

We introduce the notion of diversity order in distributed radar networks. Our goal is to analyze the tradeoff between distributed detection, using K sensors, and centralized detection, using collocated antennas. The diversity order is representative of the degrees of freedom available in the system. In contrast with the asymptotically high signal-to-noise ratio (SNR) definition in wireless communications, we define the diversity order of a distributed radar network as the slope of the probability of detection (P_D) versus SNR curve at P_D = 0.5. We analyze an optimal joint detection system and prove that its corresponding Neyman-Pearson (NP) test statistic follows a Gamma distribution and that, for large K, its diversity order grows as ¿K. For a fully distributed system using the NP fusion rule, we prove that the test statistic follows a binomial distribution and that the diversity order is also on the order of ¿K. In more practical systems where the fusion center uses a fixed fusion rule, the largest growth in diversity order is achieved by the OR rule, and it only grows as log(K). We provide the results of simulations to confirm the theory developed.