A complex generalized Gaussian distribution: characterization, generation, and estimation

The generalized Gaussian distribution (GGD) provides a flexible and suitable tool for data modeling and simulation, however the characterization of the complex-valued GGD, in particular generation of samples from a complex GGD have not been well defined in the literature. In this study, we provide a thorough presentation of the complex-valued GGD by i) constructing the probability density function (pdf), ii) defining a procedure for generating random numbers from the complex-valued GGD, and iii) implementing a maximum likelihood estimation (MLE) procedure for the shape and covariance parameters in the complex domain. We quantify the performance of the MLE with simulations and actual radar data.