## Abstract

In this paper, we study the performance of a space shift keying (SSK) scheme in a free-space optical (FSO) communication system under indoor and outdoor conditions. For the outdoor ${N}_{t}\times 1$ FSO-SSK system, where ${N}_{t}$ is the number of transmitters (Txs), a novel closed-form mathematical expression for the probability density function (pdf) of the difference between two weighted gamma-gamma random variables is derived. Using this pdf, a new analytical expression is obtained for the tight upper bound of the average bit error rate (ABER) of this system. We also study the analytical bit error rate (BER) of an indoor ${N}_{t}\times 1$ FSO-SSK system experiencing a deterministic channel. For this system, optimized values of transmit power weights are obtained by minimizing the analytical BER; it is observed that the optimized nonuniform power distribution is better than the uniform power distribution. However, for the outdoor FSO-SSK system, the best error performance can be achieved by employing uniform transmit power. An asymptotic BER analysis of uniformly weighted general outdoor FSO-SSK with an arbitrary number of Tx and receiver (Rx) apertures is also performed. Furthermore, the analytical coding gain and diversity order of the considered system are found based on the derived analytical BER expression. An interesting result observed from the coding gain analysis is that the performance of the outdoor FSO-SSK system remains unaltered from a moderate to a strong atmospheric turbulence regime, which makes the considered system nearly independent of turbulence. In addition, it is found by simulation and analysis that the considered system performs more poorly under the weak turbulence regime as compared to the other (strong and moderate) turbulence regimes. Our analysis also shows that the diversity order of the outdoor FSO-SSK system is ${N}_{r}/2$, where ${N}_{r}$ is the number of Rx apertures, irrespective of the number of optical sources and turbulence conditions. In addition, it is observed that the performance of the FSO-SSK system degrades with an increasing number of optical sources under both indoor and outdoor conditions. Therefore, a trade-off between spectral efficiency and ABER is observed.

© 2017 Optical Society of America

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