Optimal Strategies for Distributed Sampling and Detection of Poisson Processes.

We study the problem of distributed sampling and detection of remote point processes. A remote source, modelled as a homogeneous Poisson counting process (PCP) is observed at multiple remote observers in noise. The observers have a sampling constraint which limits their ability to forward their observations to a centralized fusion center, or ‘detector’. More precisely, we assume that the remote observers can send any fixed fraction of their observation to the detector noiselessly; in addition, the overall time duration of the observation received, or the ON time, at the detector is limited. We refer to this constraint as a joint sampling/communication constraint, as it accounts for both of the following: (i) the finite energy available for sampling at the remote observers, and (ii) the finite capacity of the uplink toward the fusion center. Our main contribution is the complete characterization of optimal strategies for joint sampling and detection of the remote source. We first present optimal strategies when there are two samplers, and then extend the characterization for the K-sampler, K > 2, case. Our results reveal a fundamental tension in the design of distributed sampling strategies between (i) obtaining noisy observations of the remote source at multiple samplers so as to jointly ‘reject’ their individual observation noise at the detector, and (ii) observing noisy realization at exactly one appropriately chosen sampler over a longer time period to obtain a better estimate of the remote PCP source intensity. Our results also reveal the interesting fact that two simultaneously active samplers are necessary and sufficient for complete noise-rejection.