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The implementation of optical communication and quantum communication technologies based on the free space has many advantages when compared with the implementation based on the optical fibers. However, the performance of communication systems can be deteriorated by the atmospheric turbulence when optical beams transmit through the free space, and it has been widely acknowledged that turbulence-induced pointing error is the one of the major performance-limiting factors. The pointing error model consists of two parts, one is the channel transmittance model and the other is radial model. To make the results more general, the Beckmann radial model can be assumed, and it is expressed in an integral form. Therefore, aiming to further analyze the performance of communication systems, researchers have proposed two kinds of modified Rayleigh distributions based on the moment matching method to approximate the Beckmann distribution. In this paper, we present a new variance estimation method of modified Rayleigh distribution based on the Kullback-Leibler divergence. The proposed method has two advantages when compared with the moment matching method proposed before: 1) The derived new variance can reduce the computational cost of gain parameter; 2) It leads to a better approximation to the Beckmann distribution in most scenarios according to the Kolmogorov-Smirnov goodness-of-fit statistical test results.
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