Detection of weak secondary signals with the aid of already detected strong primary signals

We consider a problem of detecting a weak secondary signal in noise with the aid of an already detected strong primary signal. Such a problem arises in classification or identification of signal sources. Because of unknown signal parameters, which are the relative strength and the frequency ratio of the secondary to the primary, the usual likelihood ratio cannot be used for the optimum detection. We propose to use in its place the maximum likelihood estimate of the relative strength and develop an efficient iterative method of obtaining the estimate. The detection performance using the estimate is numerically evaluated by using simulated data for various values of signal-to-noise ratio and data size. We also derive an asymptotic approximation of the estimate for large data, and show that the detectors using the estimate and its approximation become asymptotically perfect in the Neyman-Pearson sense.