A Novel Approximation for K Distribution: Closed-Form BER Using DPSK Modulation in Free-Space Optical Communication

A new analytical approximate expression for K distribution is proposed by expanding it in terms of orthogonal associated Laguerre polynomial. The expansion is truncated after first three terms, which yields a fairly close approximation to K distribution. The advantage of the proposed approximation is that the analytical closed form expression for bit error rate can be easily derived. KL measure is used to show the accuracy of the proposed approximation. The proposed approximate probability density function and bit error rate work well within the desired range of the channel parameter $\alpha$ , which is $1 < \alpha < 2$ and corresponds to the scintillation index value ranging from 2 to 3. We have also demonstrated the utility of our approximation for other quality of service metric such as fade probability.