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

随机噪声中的信号检测是信号处理领域的重要研究课题之一。本研究的目的主要有两个：(1)提出一种有用的检测高随机噪声污染信号的方法；(2)开发一种有效的方法来估计噪声信号的未知参数问题。(1)基于小波的Wigner分布的提出：Wigner分布（WD）被认为是检测随机噪声中的信号的有力工具之一，它可以在时频域中描绘出信号的集中图像，但是使用WD会产生交叉项或干扰项的问题。为了解决这一问题，本研究提出了一种有效的方法，即将小波与WD相结合；即传统的WD是观测数据的（裸）协方差的傅里叶变换，而本文的WD被修改为协方差的一种小波变换。通过仿真研究，发现所提出的基于小波小波的WD在处理不良交叉项方面比传统WD具有明显更好的性能。（ii）有效参数估计的发展：在这项工作中，将接收信号的时间延迟和频率调制作为待检测的未知参数。使用传统的WD不可能从时频图中确定它们的确切值。本文提出了一种基于WD随机场实现的似然函数的求解方法。由于该方法在信噪比(SNR) -10[dB]等高噪声条件下很难实现，因此可以认为是现有方法中最有效的方法。

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].