Closed-form expressions for the lower bound performance of variable weight multiple pulse-position modulation optical links through turbulent atmospheric channels

In this study, we derive the analytical expression for the lower-bound performance of the light intensity fading induced by turbulence for one of the most favourable signalling techniques used in atmospheric optical communications: the variable weight multiple pulse-position modulation (vw-MPPM). This lower-bound performance is obtained when the additive white Gaussian noise (AWGN) is not present in the system, showing that it only depends on both the fixed-threshold detection and the intensity of the atmospheric turbulence. In this sense, the statistical models employed to characterise the irradiance fluctuations are the lognormal and the Gamma–Gamma atmospheric channels. These ones have been chosen as two of the most representative distribution models for the irradiance. In addition, the starting point to obtain the lower-bound performance of a communication system using vw-MPPM is to calculate the one for an on–off keying modulation technique. As we have derived in the manuscript, and for the ideal condition of absence of AWGN, when the transmitted bit is a binary ‘0’ (the laser is turned off), then no photodetector errors occur. Thus, the inclusion of the appropriate transmission probability of a binary ‘1’ let us obtain the desired lower-bound performance expression of a vw-MPPM modulation technique through atmospheric turbulence channels. Numerical results using Monte-Carlo simulation confirm the analytical expressions derived in this study.