Rank rule for signal detection in noise of unknown level

A locally most powerful rank rule is derived for signal detection against a noise background of unknown intensity. The rule is shown to be applicable to incoherent detection of both nonfluctuating and fluctuating signals, including signals that fluctuate according to the Rayleigh-Rice law. The rule possesses a parametric property in that it ensures an invariable false-alarm probability for any noise level or noise distribution, without requiring a change in threshold, and in that it maximizes the detection probability at small signal to noise ratios.