STUDIES ON DETECTION OF SIGNALS IN RANDOM NOISE USING WAVELET-BASED WIGNER DISTRIBUTION

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The signal detection in random noise is one of important topics in the signal processing community. The purpose of this research work was mainly twofold: (i) to propose a useful method of detecting signals which is contaminated by high random noise, and (ii) to develop an effective approach to problem of estimating the unknown parameters of the noisy signals.(I) Propose of Wavelet-based Wigner Distribution:The Wigner distribution (WD) is recognized as one of powerful tools to detect the signal in random noise, and can depicts the concentrated picture in time-frequency domain, However, the use of WD causes the problem of cross terms or interference terms. To cope with such problem, a useful method was proposed in this research works by incorporating the wavelet with WD ; that is, the conventional WD is the Fourier transform of the (naked) covariance of the observation data, while the proposed one is modified as the kind of wavelet transformation of covariance. By simulation studied it wasverfind that the proposed wavelet wavelet-based WD has considerably better behavior with regard to the undesirable cross terms than the conventional WD.(ii) Development of Effective Parameter Estimation:In this work the time-delay and frequency-modulation of the received signal taken as unknown parameters to be detected. The useof the conventional WD is impossible to determine their exact values from the time-frequency picture. In this research, a novel approach was developed to this problem by formulating the likelihood function from the realizations of WD random field. This approach can be considered to be the most effective among the existing methods, since this is so tough for high noise such as the signal-to-noise ratio (SNR) -10[dB].