Performance Analysis of Fractional Fourier Transform-Based Chype Pulse for Doppler Variant Systems

Linear chirp signals used for target detection in radar or sonar systems suffer performance degradation when using a matched filter (MF) or cross-ambiguity function (CAF) to detect them in the presence of Doppler, especially with a fast moving target. One solution to this problem is to use a hyperbolic chirp (chype) signal, that does not suffer from Doppler induced CAF performance loss. However, performing a CAF with the chype is computationally intense. Recently, a computationally efficient solution that uses the chype and the Fractional Fourier Transform (FrFT) to rotate the chype signal prior to transmission into a domain using far fewer samples was proposed. In this paper, we compare the CAF output signal-to-noise ratio (SNR) to that of the matched filter (MF) output and the ideal MF SNR, i.e. in the absence of Doppler distortions. We also compare the SNR of the FrFT-based chype signal to that of the linear chirp, FrFT-based linear chirp, and original chype. The SNR analysis shows the robustness of the FrFT rotated chype signal over a large Doppler range with less than 1 − 2.5 dB loss with just 1 − 12% of the samples, whereas the MF degrades significantly for large Doppler.