Abstract
Convexity properties of detection probability are investigated in generalized likelihood ratio test-based detection of one-sided composite signal corrupted by additive unimodal noise. It is shown that the detection probability of the corresponding threshold detector is a concave function of normalized signal power at low and high signal-to-noise ratio (SNR). For intermediate values of SNR, the behavior can be explicitly characterized based on the derivative of the logarithm of the channel noise density and the detector threshold. Optimal time-sharing strategies of average power-limited transmitters and jammers are established. Numerical examples are provided for Gaussian, Laplace, and Cauchy densities.
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