Closed-Form Approximation for the BEP of BDPSK Signals Over EW FSO Channel in Dual-Hop DF Relaying Systems

In this paper, we derive the closed-form expression of the bit error probability (BEP) for binary differential phase-shift keying (BDPSK) modulated signals over a single exponentiated Weibull (EW) free-space optical (FSO) fading channel. We simplify the calculations of an infinite integral by utilizing the second-order Taylor expansion as well as the second-order Binomial series approximation, and the expression is reduced to involve the gamma function only, with a high approximation accuracy. We further derive the explicit expression of the BEP for dual-hop decode-and-forward (DF) relaying systems. The comparisons between the approximate BEP and theoretical BEP for a single EW channel and a dual-hop EW channel are conducted via simulations with the appearance of weak, moderate and strong turbulences. The simulation results verify the accuracy and effectiveness of the proposed closedform approximate BEP expressions under various turbulence scenarios.