Noncoherent Detection of Sinusoidal Signals in Sinusoidal Clutter

Probability density expressions associated with the noncoherent detection of a sinusoidal signal have been obtained. The signal is assumed to be imbedded in sinusoidal clutter at the same frequency and narrow-band Gaussian noise. The density expressions are shown to be a function of the signal-to-noise power ratio and the clutter-to-noise power ratio. The expressions have been numerically evaluated for a number of conditions, and the results under each reception hypothesis are presented graphically. Under large-sample conditions, the probability density for a multisample test statistic is shown to be Gaussian, and the probability of detection expression is written such that commonly available tabulated data can be utilized to determine the probabilities.