A Power-Weighted Noncentral Complex Gaussian Distribution
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 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.
The following analysis is generated by AI and may contain errors. It is separate from the authors’ abstract and is not peer review.
Research summary
The main contribution of this paper is the introduction of a novel complex-valued probabilistic model that effectively captures the geometric relationship between amplitude and phase in signal processing. This work significantly advances the field by providing a flexible framework for modeling complex-valued data, addressing limitations of existing models, and demonstrating superior performance in empirical evaluations.
Methodology
The paper introduces a novel probabilistic model termed the power-weighted noncentral complex Gaussian distribution, which is formulated directly on the complex plane. This approach addresses the limitations of traditional Gaussian models by incorporating a nonlinear phase diffusion mechanism and allowing for flexible control over the distributional geometry. The methodology is theoretically grounded, with a systematic formulation and analysis of statistical properties, including moments and sampling methods. The proposed model's ability to unify various existing distributions (e.g., Rice, Nakagami, gamma) enhances its applicability in signal processing.
Results & evaluation
The experimental validation is robust, utilizing the TIMIT speech corpus to demonstrate the model's effectiveness in modeling speech power spectra. The results indicate a consistent improvement in log-likelihood over conventional distributions, suggesting that the proposed model captures the underlying statistical characteristics of speech signals more effectively. However, the paper could benefit from additional metrics and comparisons with a broader range of existing models to further substantiate its claims.
Reproducibility
The paper outlines the theoretical foundations and provides a detailed description of the sampling methods, including the Metropolis-Hastings algorithm and finite discrete distribution approximation. However, the lack of a publicly accessible code repository limits reproducibility. Including implementation details or a link to a codebase would enhance the reproducibility of the results.
Limitations
One limitation is the focus on speech power spectra, which may restrict the model's generalizability to other types of complex-valued data. Additionally, while the model shows improved performance over existing distributions, the paper does not explore the computational complexity or efficiency of the proposed sampling methods in depth, which could be critical for real-time applications.
Broader impact
The proposed model has significant implications for various fields, including signal processing, communications, and audio analysis. Its ability to accurately model complex-valued data could lead to advancements in applications such as speech synthesis, sound source separation, and medical imaging. The potential for extending the model to incorporate phase information further enhances its relevance across diverse engineering problems. The main contribution of this paper is the introduction of a novel complex-valued probabilistic model that effectively captures the geometric relationship between amplitude and phase in signal processing. This work significantly advances the field by providing a flexible framework for modeling complex-valued data, addressing limitations of existing models, and demonstrating superior performance in empirical evaluations.
Author of this paper? Send a correction.