The effects of transmission delay and channel errors on the performance of a distributed sensor system are studied. In a network of distributed sensors at a given time instant, the decisions from some sensors may not be available at the fusion center owing to networking and transmission delays. Assuming that the fusion center has to make a decision on the basis of the data from the rest of the sensors, provided that at least one peripheral decision has been received, it is shown that the optimal decision rule that maximizes the probability of detection for fixed probability of false alarm at the fusion center is the Neyman-Pearson test at the fusion center and the sensors as well. Furthermore, it is shown that, in the case of noisy channels, the decision made by each sensor depends on the reliability of the corresponding transmission channel. Moreover, the probability of false alarm at the fusion is restricted by the channel errors. For a given decision rule, the probability of any channel being in error must be kept at a certain level to achieve a desired probability of false alarm at the fusion. A suboptimal but computationally efficient algorithm is developed to solve for the sensor and fusion thresholds sequentially. Numerical results are provided to demonstrate the closeness of the solutions obtained by the suboptimal algorithm to the optimal solutions. © 1992.
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