Rank-based detection of weak random signals in a multiplicative noise model

Abstract

Multiplicative noise is known to be useful in modeling some environment, which is difficult to describe by additive noise model. In this paper, nonparametric detection of weak random signals in multiplicative noise is considered. The locally optimum detector based on signs and ranks of observations is derived for good weak-signal detection performance under any noise probability density function. The detector has similarities to the locally optimum detector for random signals in multiplicative noise. It is shown that the nonparametric detector asymptotically has almost the same performance as the locally optimum detector.