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.

翻译：复高斯分布已被广泛用作信号处理与通信中的基本频谱及噪声模型。然而，其高斯结构常限制其表征个体源信号中观测到的多样化幅度特征的能力。另一方面，许多现有基于超球面模型的非高斯幅度分布虽因具有幂律结构而能实现良好的经验拟合，但未能显式考虑复值观测固有的复平面几何特性。本文提出一种新的复值随机变量概率模型，可解释为功率加权非中心复高斯分布。与常规超球面幅度模型不同，该模型直接在复平面上构建，在保留复值观测几何结构的同时维持更高维度的解释性。模型通过单一形状参数引入非线性相位扩散，可连续控制分布几何形态从沿相位方向的弧状扩散到概率质量向原点集中。我们系统阐述了所提分布并分析了其诱导幅度分布的统计特性。导出的幅度分布与功率分布构建了一个统一框架，涵盖了信号建模中多种常用分布，包括莱斯分布、中上分布和伽马分布。在语音功率谱上的实验结果表明，所提模型在对数似然指标上持续优于常规分布。