An exact expression for symbol-error rate of multipulse PPM technique in free-space optics with gamma-gamma channels

Atmospheric turbulence, also called scintillation, is one of the major challenges that face free space optics (FSO) communications. In this paper, we derive both exact and approximate expressions for the average symbol-error rate (SER) of free-space optics systems adopting multipulse PPM (MPPM) technique in gamma-gamma channels. Our expressions are then verified by getting the same results using lognormal and exponential channel expressions where lognormal and exponential distributions are valid only for weak and strong turbulence, respectively. As the computation of the exact expression is time consuming, we get an approximate expression based on Gauss-Laguerre quadrature. Both expressions produce almost the same results. Finally, we make a comparison between the average SER performance of MPPM and PPM assuming equal average energy per bit and equal data rate. We found that the performance of MPPM is better than that of PPM in case of weak turbulence but at strong turbulence both MPPM and PPM have nearly the same performance.