In this paper, three receiver designs for the detection of a known signal in an additive non-Gaussian noise process are considered. The noise process consists of white Gaussian noise modulated by a random-spectrum level. The first receiver considered is an optimum (likelihood) processor and the remaining two receivers are suboptimum designs consisting of a cross correlator and a likelihood correlator. The basic processing operations of the three receivers are investigated and compared on the basis of their effects in observation space. The performance of each receiver is evaluated and presented in terms of ROC curves. A comparison of the performance curves indicates a loss in optimum performance as compared to the Gaussian noise case and a significant loss in performance of the suboptimum receivers relative to the optimum receiver.
Treatment of detection problems from a Bayesian viewpoint implies the modeling of uncertain parameters as random variables with known a priori distributions. Attempts to compare performance of the certain parameter case with the uncertain parameter case become difficult because, for the former, performance is usually dependent on the value of the parameter in question, whereas for the latter, this dependence is removed by averaging. A method for a meaningful solution to this problem is proposed here. An auxiliary receiver, the Externally Sensed Parameter (ESP) receiver, is defined, and its performance is used as the standard for comparison purposes. The comparison is meaningful because the ESP receiver performance is independent of the value of any particular parameter in question and is an upper bound in the sense of perfect parameter information. The method appears to be particularly applicable to evaluating learning or adaptive acoustic signal processing systems and to determining the desirability of incorporating additional parameter estimation techniques in these systems.
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