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. Some unexpected properties of distributed 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 2L-1 bits in its decision. Using more than this number of bits cannot improve performance. Further, in these cases, a particular fusion rule, which depends only on the number of bits used in the sensor decisions, can be used without sacrificing any performance. This fusion rule can achieve optimum performance with the correct set of sensor decision rules.
Bibliographical noteFunding Information:
Manuscript received March 24, 1997; revised November 14, 1997. This work was supported by The National Key Project and NNSF of China. This paper is based on work supported by the Office of Naval Research under Grant N00014-97-1-0774 and by the National Science Foundation under Grant MIP-9703730. Y. Zhu is with the Department of Mathematics, Sichuan University, Chengdu, Sichuan 610064, China. R. S. Blum is with the EECS Department, Lehigh University, Bethlehem, PA 18015-3084 USA. Z.-Q. Luo and K. M. Wong are with the Communications Research Laboratory, McMaster University, Hamilton, Ontario L8S 4K1 Canada. Publisher Item Identifier S 0018-9286(00)00397-4.
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