  The use of optical spatial modulation (OSM), which has been recently emerged
as a power and bandwidth efficient pulsed modulation technique for indoor
optical wireless communication, is proposed as a simple, low-complexity means
of achieving spatial diversity in coherent free space optical (FSO)
communication systems. In doing so, this paper makes several novel
contributions as follows. It presents a generic analytical framework for
obtaining the Average Bit Error Probability (ABEP) of uncoded OSM with coherent
detection in the presence of turbulence-induced fading.
  Although the framework is general enough to accommodate any type of models
based on turbulence scattering, the focus in this paper is the H-K
distribution. Although this distribution represents a very general scattering
model valid over a wide range of atmospheric conditions, it is has not been
considered in the past in conjunction with FSO systems possibly because of its
mathematical complexity. The proposed analytical framework yields exact
performance evaluation results for MIMO systems with two transmit- and an
arbitrary number of receive apertures. In addition, tight upper bounds are
derived for the error probability for OSM systems with an arbitrary number of
transmit apertures as well as for convolutionally encoded signals. The
performance of OSM is compared to that of well established coherent FSO
schemes, employing spatial diversity at the transmitter or the receiver only.
Specifically, it is shown that OSM can offer comparable performance with
conventional coherent FSO schemes while outperforming the latter in terms of
spectral efficiency and hardware complexity. Various numerical performance
evaluation results are also presented and compared with equivalent results
obtained by Monte Carlo simulations which verify the accuracy of the derived
analytical expressions.
