[2603.26344] A Power-Weighted Noncentral Complex Gaussian Distribution

Statistics > Machine Learning arXiv:2603.26344 (stat) [Submitted on 27 Mar 2026] Title:A Power-Weighted Noncentral Complex Gaussian Distribution Authors:Toru Nakashika View a PDF of the paper titled A Power-Weighted Noncentral Complex Gaussian Distribution, by Toru Nakashika View PDF HTML (experimental) Abstract:The complex Gaussian distribution has been widely used as a fundamental spectral and noise model in signal processing and communication. However, its Gaussian structure often limits its ability to represent the diverse amplitude characteristics observed in individual source signals. On the other hand, many existing non-Gaussian amplitude distributions derived from hyperspherical models achieve good empirical fit due to their power-law structures, while they do not explicitly account for the complex-plane geometry inherent in complex-valued observations. In this paper, we propose a new probabilistic model for complex-valued random variables, which can be interpreted as a power-weighted noncentral complex Gaussian distribution. Unlike conventional hyperspherical amplitude models, the proposed model is formulated directly on the complex plane and preserves the geometric structure of complex-valued observations while retaining a higher-dimensional interpretation. The model introduces a nonlinear phase diffusion through a single shape parameter, enabling continuous control of the distributional geometry from arc-shaped diffusion along the phase direction to concentratio...