Numerical Results on the Convergence of Relative Efficiencies

This paper considers the detection of a known constant signal in an additive non-Gaussian noise under the assumptions of discrete time and statistically independent noise samples. The objective is to determine how large sample size must be before the easily computed asymptotic relative efficiency becomes a valid measure of performance. The exact small-sample error probabilities are calculated for a Neyman-Pearson optimal nonlinear detector consisting of a zeromemory nonlinearity followed by summation and threshold comparison. "Large-tailed" noise having a double exponential distribution is used as an example. The exact distribution of the test statistics for a linear detector and for the Neyman-Pearson optimal detector are calculated. Then the relative efficiency of the Neyman-Pearson optimal detector, as compared to a linear detector, is computed in order to study the rate of approach of the relative efficiency to its asymptotic value.