A transformation approach for modeling and detecting non-Gaussian signals

We present a new approach to the modeling of non-Gaussian complex random signals. The method transforms an underlying complex white Gaussian sequence, whose magnitude is shaped by a zero memory non-linear (ZMNL) transformation. In this way, we match the magnitude PDF, and the power spectral density of the non-Gaussian output. The ZMNL technique has the additional benefits of synthesizing complex, positive, or real valued signals by keeping only portions of the complex signal. This provides a quick simulation capability. The JPDF of a multivariate sample is easily computed from our model. We use this to form a likelihood detector for the presence of our non-Gaussian versus a white Gaussian signal. The dramatic improvement of the likelihood detector compared with a Gaussian based quadratic detector is presented