Parameter Estimation and Optimal Detection in Generalized Gaussian Noise

Modern signal processing algorithms need to work in complicated and variable noise environments. The generalized Gaussian distribution (GGD) can be used to accurately model noise in signal processing for telecommunication and other fields because the GGD covers a wide range of distributions. Three distributions widely used for the modeling of noise including the Laplace, Gaussian and uniform distributions are special cases of the GGD with the shape parameter p having values of 1, 2 and infinity respectively. In this thesis, estimation of the location parameter of the GGD is investigated. When the shape parameter p takes different values, three estimators are derived based on the maximum likelihood estimation theory. An optimal detector in the presence of generalized Gaussian distributed noise is proposed. The asymptotic performance of the optimal detector is analyzed by using the Gaussian approximation method.