Employing fractional autocorrelation for fast detection and sweep rate estimation of pulse compression radar waveforms

Fractional autocorrelation of a signal defined for a fractional domain at an arbitrary angle of the time–frequency plane exactly corresponds to the radial slice of the radar ambiguity function (AF) of that signal at that particular angle. In other words, any radial cross-section of the radar AF, that itself serves as a two-dimensional correlation function, can be readily obtained by computing fractional autocorrelation, which is one-dimensional. In this manuscript, we employ a novel fast detection statistic derived utilizing this property of fractional autocorrelation for computationally efficient detection of pulse compression radar waveforms such as the step linear frequency modulated (SLFM) signal, Frank code, and P1 and P4 codes. As a byproduct, the detection algorithm also serves as an unbiased estimator of the sweep rate (chirp rate) of the considered radar waveforms. Through receiver operating characteristic (ROC) curves, we investigate the performance of the detection statistic and compare it against the matched filter and generalized likelihood ratio test (GLRT) detectors of the linear frequency modulated (LFM) signal. Performance of the accompanying sweep rate estimator is also demonstrated using mean square error (MSE) curves and compared with the optimum maximum likelihood (ML) estimator of the sweep rate parameter of the LFM signal.