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

Optimum-distributed signal detection system design is studied for cases wit h statistically dependent observations from sensor to sensor. The common pa rallel architecture is assumed. Here, each sensor sends a decision to a fus ion center that determines a final binary decision using a nonrandomized fu sion rule. General L sensor cases are considered, A discretized iterative a lgorithm is suggested that can provide approximate solutions to the necessa ry conditions for optimum distributed sensor decision rules under a fixed f usion rule. The algorithm is shown to converge in a finite number of iterat ions, and the solutions obtained are shown to approach the solutions to the original problem, without discretization, as the variable step size shrink s to zero. In the formulation, both binary and multiple-bit sensor decision s cab es are considered. Illustrative numerical examples are presented for two-, three-, and four-sensor cases, in which a common random Gaussian sign al is to be detected in Gaussian noise, Some unexpected properties of distr ibuted signal detection systems are also proven to be true. In an L-sensor- distributed detection system, which uses L - 1 bits in the decisions of the first L - 1 sensors, the last sensor should use no greater than 2(L-1) bit s in its decision. Using more than this number of bits cannot improve perfo rmance. Further, in these cases, a particular fusion rule, which depends on ly on the number of bits used in the sensor decisions, can be used,without sacrificing any performance. This fusion rule can achieve optimum performan ce with the correct set of sensor decision rules.