Ahead look sonar performance prediction via FFT

It is desired to predict the probabilities of detection and false alarm for an ahead look sonar providing N echoes from a cylindrical target. The signals are detected noncoherently and the targets are assumed to be bounded by, but not restricted to, the four Swerling cases. The clutter is assumed to be Rayleigh distributed. A computer algorithm is developed whose inputs are the number of echoes, the number of degrees of freedom, the multiple correlation of the echoes, and the average single‐ping signal‐to‐noise ratio. The outputs will be graphic representations of clutter and target probability density functions and a log‐log representation of their corresponding false alarm and detection probability distributions. The process is accomplished by calculating the characteristic function reversing and conjugating, and performing an FFT to obtain an estimate of the probability density functions.