Performance of various detectors in non-Gaussian noise and weak stochastic signal environment

Many locally optimum, sub-optimum and ad hoc detectors exploit knowledge of the noise probability density function (PDF) to obtain their test statistic for the detection of stochastic signals in non-Gaussian noise and appear to offer potential for highly improved performance for very small signal to noise ratios. The authors explore the realism of this conclusion by comparing performance of a locally optimum detector with that of the power detector and of the log-likelihood ratio detector by deriving analytical expressions for a performance measure using a double-sided exponential PDF as the dominant noise. The conclusion is that the performance of the generalized energy detector can become poorer than that of the power detector well within the practical range of signal to noise ratios, and the apparently large gains predicted by the asymptotic theory may not be reachable in practice.<>