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Chirp, Clutter, Fractional Fourier Transform, Radar.

The Fractional Fourier Transform (FrFT) is a powerful tool that utilizes the time-frequency plane to separate signals-of-interest (SOIs) from interference and noise in non-stationary environments. This requires estimation of the rotational parameter ‘a’, which is typically chosen as the value that minimizes the mean-square error between the desired SOI and its estimate or that minimizes the overlap of the projection of the signal and noise onto the axis ‘ta’. The FrFT has successfully been used in many applications, but it is most suited for applications in which the time and frequency content of an SOI and the undesired interference are different, and it has been shown to greatly outperform the conventional Fast Fourier Transform (FFT). In this paper, we develop a simple algorithm that applies the FrFT to separate multiple moving targets in a radar system from each other, as well as from the clutter filled environment. The algorithm utilizes the fact that echoes from moving targets are chirps, and therefore project onto the optimum rotational axis in the FrFT domain just as a single CW tone projects in the FFT domain. By searching for peaks and notching them out, we can remove high power moving targets, enabling us to extract low power ones. This algorithm is robust in clutter because clutter does not correlate with the chirp signal in the FrFT domain, and thus does not impair our ability to estimate the chirp signal peaks. We show that the performance of the proposed algorithm is robust using up to three simultaneous moving targets in clutter for signal-to-clutter ratios (SCRs) of SCR = 0 and 10 dB when the weakest target is 8 and 20 dB below the strongest one, respectively.