Fractional Fourier Transform for Sonar Signal Processing

Abstract

In this paper we present an approach for processing of sonar signals with the ultimate goal of ocean bottom sediment classification. Work reported is based on sonar data collected by the volume search sonar (VSS) in the Gulf of Mexico, as well as on VSS synthetic data. The volume search sonar is a beam formed multibeam sonar system with 27 fore and 27 aft beams, covering almost the entire water volume (from above horizontal, through vertical, back to above horizontal). Our investigation is focused on the bottom-return signals since we are interested in determination of the impulse response of the ocean bottom floor. The bottom-return signal is the convolution between the impulse response of the bottom floor and the transmitted sonar chirp signal. The method developed here is based on fractional Fourier transform, a fundamental tool for signal processing and optical information processing. Fractional Fourier transform is a generalization of the classical Fourier transform. The traditional Fourier transform decomposes signal by sinusoids whereas Fractional Fourier transform corresponds to expressing the signal in terms of an orthonormal basis formed by chirps. In recent years, interest in and use of time-frequency tools have increased and become more suitable for sonar applications. The fractional Fourier transform requires finding the optimum order of the transform that can be estimated based on the properties of the chirp signal. The bottom impulse response is given by the magnitude of the fractional Fourier transform applied to the bottom return signal. The technique used in this work has been tested both on synthetic data and real sonar data collected by the VSS. The synthetic sonar return signal has been generated by the convolution between the Green function, which has been utilized to simulate the impulse response of the seafloor and the transmitted VSS chirp. A study is carried out to compare the performance of our method to a conventional method based on deconvolution in the frequency domain (using standard Fourier transform). The amplitude and shape of an acoustic signal reflected from the sea floor is determined mainly by the seabottom roughness, the density difference between water and the sea floor, and reverberation within the substrate. Since the distribution of seafloor types is a very important tool in different applications, a sediment classification has been implemented based on a statistical analysis of the obtained impulse response. In order to perform a robust analysis of the signal, a joint time-frequency analysis is necessary. In this paper the analysis has been evaluated using the Wigner distribution, which can be thought of as a signal energy distribution in joint time-frequency domain. Singular value decomposition of the Wigner distribution has been used in order to perform the seafloor sediment classification. A comparative analysis of the experimental results for classical deconvolution and fractional Fourier method is presented. Results are shown and suggestions for future work are provided