Use of the Chype Pulse and the Fractional Fourier Transform for Performance and Efficiency in Doppler Variant Radar Applications

Active radar systems often transmit linear chirp signals to locate targets. These types of signals provide better range resolution than sinusoidal pulses. The chirp bounces off of a target, returns to the receiver, and is detected. Detection may be done by a matched filter (MF), which correlates the received signal with a locally generated version of the transmitted signal, and searches over time for a correlation peak. Due to Doppler in the reflected signal, the search may need to be expanded to include a frequency range as well as time. If frequency range is included, we refer to this MF as a cross-ambiguity function (CAF). A problem arises if a target is moving fast, because now the reflected pulse gets distorted from the frequency dependent Doppler shifts, resulting in the degradation of the CAF peak. In the worst case, high speeds or high chirp bandwidths can result in failure of the CAF to detect the target. But high bandwidths are desirable for better target range resolution. A solution to this problem is replacing the linear chirp with a hyperbolic chirp (aka chype signal) that does not suffer from performance loss due to Doppler. However, a CAF with the chype is computationally intense, making its use impractical, especially for real-time applications. In this paper, we propose a computationally efficient solution that uses the chype in conjunction with the Fractional Fourier Transform (FrFT) to rotate the chype signals prior to transmitting into a domain where they may be detected by a cross-ambiguity function (CAF) without much performance loss and with far fewer samples for processing efficiency. We demonstrate that this method can detect targets with just 1-2 dB loss compared to the original chype, using only 3-5% of the samples required by the chype signal.