High-resolution beamforming by Wigner-Ville distribution method

The Wigner-Ville distribution (WVD) function was proposed by Wigner (1932) in quantum mechanics and Ville (1948) applied it for a signal analysis. This method has made it possible to represent signal´s power density spectrum in time-frequency domain as a natural extension of the Fourier transformation 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, 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 spatial 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 that of the beamforming method by FTM. Simulation results by the computational calculations clarify that resolution by WVD method, which is presented in this paper, becomes about twice as high as by conventional FTM. The result of experiment at sea also shows the performance of this method