Outage probability of the Gaussian MIMO free-space optical channel with PPM

Atmospheric effects can significantly degrade the reliability of free-space optical communications. One such effect is scintillation, caused by atmospheric turbulence, refers to random fluctuations in the irradiance and phase of the received laser beam. In this paper we investigate the use of multiple lasers and multiple apertures to mitigate scintillation. Since the scintillation process is slow, we adopt a block fading channel model and study the outage probability under the assumptions of orthogonal pulse-position modulation and non-ideal photodetection. Assuming perfect receiver channel state information (CSI), we derive the signal-to-noise ratio (SNR) exponents for the cases when the scintillation is lognormal, exponential and gamma-gamma distributed, which cover a wide range of atmospheric turbulence conditions. Furthermore, when CSI is also available at the transmitter, we illustrate very large gains in SNR are possible (in some cases larger than 15 dB) by adapting the transmitted power. Under a long-term power constraint, we outline fundamental design criteria via a simple expression that relates the required number of lasers and apertures for a given code rate and number of codeword blocks to completely remove system outages.