On the Asymptotic Efficiencies of Robust

Two methods are considered for comparing the asymptotic efficiencies of robust detectors in the problem of detecting coherent signals in additive noise. The first of these methods considers the relative detector sample sizes for a fixed value of the detector power, while the second method considers the relative detector sample sizes for a fixed value of the local detector power, as measured by the local values of the slopes or curvatures of the detector power functions. These measures of efficiency are variations of the asymptotic relative efficiencies (ARE'S) of Pitman and Blomqvist, respectively, adapted to the robust detection problem. These two approaches are used to compare the performance of robust nonlinear correlators to that of robust M-detectors in both one-sided and two-sided detection problems, under an +contaminated mixture model for uncer- tainty in the noise statistics. Both measures of ARE, fixed-power and ked-local-power, indicate that the robust nonlinear correla- tor outperforms the robust M-detector for this type of model. However, the fixed-local-power ARE is shown to be more useful in measuring the degree to which the robust nonlinear correlator is more efficient. This analysis motivates a new evaluation of the performance of robust detectors relative to their nominally optimum counterparts on the basis of fixed-local-power ARE. Index Terms-Signal detection, robust detection, asymptotic relative efficiency, Pitman efficiency, Blomqvist efficiency.