Performance analysis of MIMO free-space optical systems in gamma-gamma fading

Atmospheric turbulence induced fading is one of the main impairments affecting free-space optics (FSO) communications. In recent years, Gamma-Gamma fading has become the dominant fading model for FSO links because of its excellent agreement with measurement data for a wide range of turbulence conditions. However, in contrast to RF communications, the analysis techniques for FSO are not well developed and prior work has mostly resorted to simulations and numerical integration for performance evaluation in Gamma-Gamma fading. In this paper, we express the pairwise error probabilities of single-input single- output (SISO) and multiple-input multiple-output (MIMO) FSO systems with intensity modulation and direct detection (IM/DD) as generalized infinite power series with respect to the signal- to-noise ratio. For numerical evaluation these power series are truncated to a finite number of terms and an upper bound for the associated approximation error is provided. The resulting finite power series enables fast and accurate numerical evaluation of the bit error rate of IM/DD FSO with on-off keying and pulse position modulation in SISO and MIMO Gamma-Gamma fading channels. Furthermore, we extend the well-known RF concepts of diversity and combining gain to FSO and Gamma-Gamma fading. In particular, we provide simple closed-form expressions for the diversity gain and the combining gain of MIMO FSO with repetition coding across lasers at the transmitter and equal gain combining or maximal ratio combining at the receiver.