Generalized complex elliptical distributions

We introduce a new class of distributions called generalized complex elliptically symmetric distributions. Several distributions commonly used in the literature, for example, the multivariate complex normal and Cauchy and the generalized complex normal distribution, are prominent members of this class. The treatment covers both proper and improper random vectors and goes beyond second-order concepts in defining the distribution model. Some properties of these distributions are studied and illustrative examples of their applications in multichannel signal processing are presented such as tests for circularity.