Outage probability of the Gaussian free space optical channel with pulse-position modulation

The main drawback in communicating via the free space optical channel is the detrimental effect the atmosphere has on a propagating laser beam. Atmospheric turbulence causes random fluctuations in the irradiance of the received optical laser beam, commonly referred to as scintillation. The scintillation fading process is slow compared to the large data rates typical of optical transmission. As such, we adopt a quasi-static block fading model and study the outage probability of the channel under the assumption of orthogonal pulse-position modulation. Non-ideal photodetection is also assumed such that the combined shot noise and thermal noise are considered as signal-independent additive Gaussian white noise. Two channel state information (CSI) scenarios are considered: CSI at the receiver only, and CSI at both transmitter and receiver. We compute the signal-to-noise ratio exponents with receiver CSI for the cases when the scintillation is lognormal and exponential distributed, corresponding to weak and strong turbulence regimes respectively. When CSI is also known at the transmitter we show that large gains are possible by using power allocation techniques to minimise the outage probability.