# A Power-Weighted Noncentral Complex Gaussian Distribution

arXiv: https://arxiv.org/abs/2603.26344 · HTML: https://mlsanity.com/paper/2603.26344/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 20 references that are in the map.
- First posted on arXiv 27 Mar 2026.

## Builds on (most cited first, 1 of 1)

- [Independent Low-Rank Matrix Analysis Based on Complex Student's t-Distribution for Blind Audio Source Separation](https://mlsanity.com/paper/1708.04795/) (2017)

## Built on by (most cited first, 1 of 1)

- [PolarBM: Complex-valued Boltzmann Machine for Modeling Audio Signals in Polar and Log-polar Coordinates](https://mlsanity.com/paper/2607.12417/) (2026)

## Abstract (arXiv)

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 concentration of probability mass toward the origin. We formulate the proposed distribution and analyze the statistical properties of the induced amplitude distribution. The derived amplitude and power distributions provide a unified framework encompassing several widely used distributions in signal modeling, including the Rice, Nakagami, and gamma distributions. Experimental results on speech power spectra demonstrate that the proposed model consistently outperforms conventional distributions in terms of log-likelihood.