The asymmetric generalized Gaussian function: a new HOS-based model for generic noise pdfs

The work is addressed to provide realistic modelling of generic noise probability density functions (pdfs), in order to optimize signal detection in non-Gaussian environments. The target is to obtain a model depending on few parameters (quick and easy to estimate), and so general as to be able to describe many kinds of noise (e.g., symmetric or asymmetric, with variable sharpness). To this end, a new HOS-based model is introduced which derives from the generalized Gaussian function and depends on three parameters: kurtosis (fourth order), for representing variable sharpness, and left and right variances (whose combination provides the same information of skewness-third order) for describing deviation from symmetry. The model is applied in the design of a locally optimum detector test for detecting signals corrupted by real underwater acoustic noise in a low-frequency range.