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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.