Unexpected properties and optimum-distributed sensor detectors for dependent observation cases

Optimum-distributed signal detection system design is studied for cases with statistically dependent observations from sensor to sensor. The common parallel architecture is assumed. Here, each sensor sends a decision to a fusion center that determines a final binary decision using a nonrandomized fusion rule. General L sensor cases are considered. A discretized iterative algorithm is suggested that can provide approximate solutions to the necessary conditions for optimum distributed sensor decision rules under a fixed fusion rule. The algorithm is shown to converge in a finite number of iterations, and the solutions obtained are shown to approach the solutions to the original problem, without discretization, as the variable step size shrinks to zero. In the formulation, both binary and multiple-bit sensor decisions cases are considered. Illustrative numerical examples are presented for two-, three-, and four-sensor cases, in which a common random Gaussian signal is to be detected in Gaussian noise.