Detection of Fractional Fourier Transform Rotated Chype Pulse with a Discrete Chype Transform

Many radar systems use linear chirp signals to locate targets. Detection is done by a matched filter (MF), which looks for a correlation peak between the received and transmitted signals. If targets move, Doppler in the reflected signal requires a cross-ambiguity function (CAF), which correlates across both frequency and time. But wide bandwidth signals can result in degradation of the CAF peak due to Doppler distortion in the received pulse. A hyperbolic chirp (chype) signal does not suffer from this performance loss. To detect the chype, a Discrete Chype Transform (DChyT) should be used instead of the CAF. But the DChyT is computationally complex, so we further propose to rotate the transmitted chype using a Fractional Fourier Transform (FrFT) to a domain where it may be transmitted by the radar and processed at the receiver by the DChyT with far fewer samples. We show both mathematically and by simulation that use of the FrFT rotated chype transmit signal and DChyT to detect it can be done efficiently with just 5 - 6% of the samples required by the chype, with up to 10 dB lower MSE than existing detection methods, at very low SNR (-20 < SNR < -10 dB), coming within a few dB of the Cramer-Rao Lower Bound (CRLB).