Performance of coherent differential phase-shift keying free-space optical communication systems in M-distributed turbulence

In this paper, we investigate the error rate performance of a coherent free-space optical communication system with differential phase-shift keying over M-distributed turbulence channels. In our derivations, we express the probability density function of M distribution in terms of a series expansion. The coefficients of this series only include elementary and gamma functions. For numerical evaluation, this power series is truncated to a finite number of terms. An upper bound for the associated truncation error is provided and used for the convergence analysis of the series expansion. In the next step, using the moment generating function approach, we derive a bit error rate (BER) expression as a generalized infinite power series and demonstrate that existing BER results in the literature reported for gamma-gamma channels and K channels can obtained as special cases.