The Gaussian free space optical MIMO channel with Q-ary pulse position modulation

The main drawback in communicating via the free space optical (FSO) 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. This paper investigates the use of multiple lasers and multiple apertures to mitigate the effects of scintillation. In particular, the FSO multiple-input multiple-output (MIMO) channel with Q-ary pulse position modulation (QPPM) and transmit repetition under the assumption of non-ideal photodetection is analyzed in terms of its uncoded bit error rate (BER) and ergodic channel capacity. This analysis is based, in part, on the use of irradiance fluctuation samples that were obtained from a laser range experiment that was conducted in the presence of moderate turbulence conditions. Expressions are derived for the log-likelihood ratio (LLR) of a received bit, uncoded BER and ergodic capacity. Using these results it is shown that large gains are possible with the use of MIMO combined with strong coding techniques.

I. Introduction

THE free space optical (FSO) channel offers an attractive alternative to the radio frequency (RF) channel for the purpose of transmitting data at very high rates. By utilizing a high carrier frequency in the optical range, digital communication on the order of gigabits per second is achievable. In addition, FSO links are difficult to intercept and are immune to interference or jamming from external sources. The use of FSO links has been proposed as a solution to the ‘connectivity bottleneck’ problem which has arisen from the ever increasing demand for high bandwidth metropolitan networks on short deployment time-lines [1].