Distribution of the normalized periodogram detector

The detection problem for a radar receiver whose input signal is range-sampled Doppler-modulated sine waves in Gaussian noise of constant but unknown intensity is considered. The probability distribution for the likelihood ratio detector for this input is derived by applying a sequence of transformations. The distribution is a function of the signal-to-noise ratio and the error in the Doppler estimate. Several graphs are given illustrating this dependence. From this distribution the probability of detection and false alarm are found, and a typical case is plotted. This problem also has applications to a problem in diversity reception.