Evaluating the detectability of Gaussian stochastic signals by steepest descent integration

The detection probability of Gaussian stochastic signals is computed by means of a numerical integration of the Laplace inversion integral involving either the characteristic function or the moment-generating function of the detection statistic. The path of steepest descent of the integrand, which is numerically determined as the integration proceeds, is used as the contour of integration. When the method is applied to the calculation of the performance of the optimum detector of a Gaussian stochastic signal in white noise, where the signals have an SNR that is different from that assumed in the design, results are obtained for narrowband signals with Lorentz and rectangular spectral densities. Of these, the former's detectability is the more sensitive to the value of the design SNR.