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.