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课题之一。本研究工作的目的主要有两个方面：（i）提出一种有用的方法来检测被高随机噪声污染的信号，以及（ii）开发一种有效的方法来估计噪声信号的未知参数。(I)基于小波变换的Wigner分布的提出：Wigner分布（WD）被公认为是检测随机噪声中信号的有力工具之一，能在时频域上刻画信号的集中图像，但WD的使用会产生交叉项或干扰项的问题。科普这一问题，本文提出了一种将小波变换与小波分解相结合的方法，即传统的小波分解是对观测数据的（裸）协方差进行傅立叶变换，而本文提出的小波分解则是对观测数据的协方差进行小波变换。通过仿真研究发现，所提出的小波小波基WD有相当好的行为方面的不良交叉项比传统的WD。(ii)有效参数估计的发展：在这项工作中的时间延迟和频率调制的接收信号作为未知参数进行检测。使用常规的WD是不可能的，以确定它们的精确值从时间-频率图片。在本研究中，一种新的方法，发展到这个问题，制定似然函数从WD随机场的实现。这种方法可以被认为是现有方法中最有效的，因为这对于诸如信噪比（SNR）-10[dB]的高噪声是如此坚韧。

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].