Circularity and Gaussianity Detection Using the Complex Generalized Gaussian Distribution

Knowing the statistical properties of a complex-valued signal is important in many signal processing applications by providing the necessary information for choosing the appropriate algorithm. In this paper, we provide generalized likelihood ratio tests (GLRT), based on the complex generalized Gaussian distribution (CGGD), for detecting two important signal properties: 1) the circularity of a complex random variable, not constrained to the Gaussian case and 2) whether a complex random variable is complex Gaussian. These tests can be combined to statistically determine if a complex random variable is, the often assumed, circular Gaussian. Simulations are used to quantify the performance of the detectors followed by application to communication signals and actual radar data.