The analysis and simulation of the detectors based on FRFT statistic performance

The task to analyze the statistic performance of the detectors based on the Fractional Fourier Transform (FRFT) is simplified via the way to research the statistic properties of the random variables located at the peak of the FRFT envelop and intensity. Their ROC curve and output SNR are obtained. It is shown that under great input SNR, the detection performance of this kind nonlinear detector is close to the optimal receiver -matched filter. Their ROC curves and output SNR only depend on the input SNR and the product of the receiver time-width and frequency-bandwidth, but have nothing to do with the peak value and position of the FRFT envelop or intensity. So the detectors have excellent adaptive capability to the signal parameters, including phase, time-delay, frequency-shift, central frequency and the rate of frequency modulation etc. The computer simulation has been carried out with the Monte Carlo simulation method, and the experimental ROC is consistent well with the theoretic ones. Compared to the matched filter, the detectors based on FRFT have better future in the case of motion target or motion target maneuvers with different acceleration being detected.