Analysis on Functions and Characteristics of the Rician Phase Distribution
Zhongtao Luo, Yanmei Zhan, Edmond Jonckheere
Abstract
For a complex variable consisting of the deterministic signal and the zero-mean complex Gaussian noise, the module and phase follow the Rice distribution and the Rician phase distribution, respectively. This paper discusses the distribution functions and numerical characteristics of the Rician phase distribution. For the unwrapped noise and the wrapped noise, we present the noise distributions and then develop the functions of probability density and cumulative distribution. The formulas of the mean and the variance are derived. Besides, the variance of the unwrapped noise is approximated in closed-form. The relationship between the characteristics and the parameters are analyzed. This paper provides fundamental analysis and preparation for signal processing in the phase domain.