Approximate analysis of the convergence of relative efficiency to ARE for known signal detection

The limitations of the asymptotic relative efficiency (ARE) in predicting finite sample size detector performance have been noted in several previous studies. It has been observed that the finite-sample-size relative efficiency (RE) may converge very slowly to its asymptotic limit. In addition, in some cases the RE approaches the ARE from below, while in other cases the RE either starts above or overshoots the ARE and approaches it from above. Results indicate that both of these effects can be predicted for a useful class of detectors for known signals in additive noise. The prediction formula is developed for the generalized correlation detector structure. The result is then used to analyze some specific detectors. Among these are the sign detector, the dead-zone detector, the soft-limiter and the noise blanker. Calculations and simulations giving the relative efficiency as a function of sample size have been used to verify predictions