The phase probability distribution of general Clarke model and its application in Doppler shift estimator

The phase probability density function (PDF) of the channel coefficients is analyzed for general Clarke channel model, and the close-form expressions are obtained under the von Mises/Tikhonov distribution. Then the simplified expressions for Rayleigh and Rice channels are derived. In addition, these expressions are applied to analyze the bias of a Doppler shift estimator based on phase difference proposed firstly by Sheng. The theoretic and simulation results show the good performance and consistency of this estimator.