On the characterization, generation, and efficient estimation of the complex multivariate GGD

Abstract

The complex multivariate generalized Gaussian distribution (CMGGD) is a flexible parametrized distribution suitable for a variety of applications. Previous work in this area is either limited to the univariate case or, in the multivariate case, restricts the complex vectors, unjustifiably, to be circular. In both cases, algorithms for parameter estimation also suffer from convergence or accuracy limitations over the complete range of their parameters. In this work, we develop the probability density function (PDF) for CMGGD that properly describes noncircular complex data. We then develop a fixed-point algorithm for the estimation of parameters of the CMGGD that is both rapid in its convergence and accurate for the complete shape parameter range. We quantify performance against other algorithms while varying noncircularity, shape parameter and data dimensionality and demonstrate robustness and gains in performance, especially for noncircular data.