Applications of Fractional Fourier Transform in Sonar Signal Processing

Underwater scenario with all its complexities has been always very challenging for sonar signal processing. The -reverberation and the fast-fading nature of the channel make it necessary to use chirp waveforms for sonar transmissions. The conventional techniques based on Fourier transforms often fail to fully address the issues like Doppler estimation with chirp waveforms and low signal-to-noise ratio detection due to the vagaries of the medium. Alternately, the fractional Fourier transform (henceforth shortened as FrFT) can be used in sonar signal processing for improved chirp-detection performance. However, this useful signal-processing tool is largely unknown to the sonar signal processing community. This paper demonstrates the application of FrFT in active and intercept sonar signal processing. The motivation to adopt the proposed method is the ability of FrFT to process chirp signals better than the conventional Fourier transform. FrFT is a parameterized transform with parameter a, related to the chirp rate. Many active sonar systems choose to transmit chirp signals for better detection in the presence of reverberation. FrFT if used instead of FFT in the correlation receiver has great potential as it takes advantage of the knowledge of transmitted waveform and can be therefore implemented for the optimum order. In the simulations, performance of matched filtering with FrFT has been compared with performance using conventional FFT. In the case of intercept sonar, FrFT can be used to estimate the parameters of chirps from a multi-component signal. This paper presents a novel parameter-estimation procedure by which chirp parameters are calculated from the two primary estimates, namely, optimum order and FrFT peak position. Simulation results clearly demonstrate the potential advantages of the proposed methods.