High-resolution beamforming by the Wigner-Ville distribution method

The Wigner-Ville distribution (WVD) function was originally proposed by Wigner in quantum mechanics and Ville applied it for signal analysis. This method has made it possible to represent a signal´s power density spectrum in the time-frequency domain as a natural extension of the Fourier transform method (FTM). Recently, it has attracted great interest for its validity to analyze time-varying signals accomplished by the development of high-speed digital signal processing, and it is used for analyzing nonstationary signals. Conventionally, a sonar beamformer is constructed using delay lines, but the development of the high-speed processor has made it possible to apply the FTM for sonar beamforming. However, the bearing resolution of the beamformer is not enough for discriminating small underwater objects on the sea bottom by this method. To solve this problem, we aim to apply the WVD method, which can represent finer structure of signals as a natural extension of the FTM, for sonar beamforming to obtain sharper beam patterns than those of the beamforming method by FTM. Simulation results by computational calculations to clarify the resolution by the WVD method, which is presented in this paper, becomes approximately twice as high as by conventional FTM. The results of an experiment at sea also show the performance of this method.