Performance of a two-stage nonparametric conditional detector for Rician density

A description is given of a constant-false-alarm-rate detector. A comparison is made between its performance and that of single-stage (fixed-sample-size) four-level conditional detector. It is assumed in a finite-sample comparison that the noise has a Rician probability density function, which is the probability density function of the output of an envelope detector in a radar receiver when the background noise is white Gaussian noise. In an asymptotic comparison the asymptotic relative efficiency (ARE) is defined, and expressions are given for its calculation. Both finite and asymptotic results reveal significant reduction in the average sample size in the no-signal case. The proposed two-stage detector is therefore suitable for signal detection in a situation where the no-signal hypothesis has a high a priori probability.