Improved Asymptotic Variance of the Associated Rician Phase Distribution

Whilst many common phase distributions have well-defined closed-form variance expressions, the well-known Rician phase (or Blachman-Bennett) distribution does not have any similar known expression. This Letter presents an asymptotic closed-form expression for the variance of the Rician phase distribution that is a significant improvement on existing expressions and straightforward to use. This new result takes advantage of the incomplete ${}_{3}\mathcal {F}_{1}$ hypergeometric function. We also introduce a normalized full-width half maximum (FWHM) figure of merit and the information theoretic-based Bhattarcharyya distance in a complementary way, in order to compare and characterize the Normal and the Rician phase noise distribution. MSC 2020: 41A60, 33B20, 33C90; OCIS: 060.5060, 120.3180,17 120.5050.