Feedback-based Differential Signaling for 2×2-FSO System under Atmospheric Turbulence Channel with Pointing Errors

In this paper, we propose a feedback-based differential signaling scheme (DSSFB) for the 2x2-free-space optical (FSO) system that is exposed to an atmospheric turbulence channel with pointing errors. We obtain closed-form expressions for the average bit error rate (BER) performance of DSSFB scheme using power series form of probability density function of channel, and then we compare it to differential signaling scheme (DSS), single-input dual-output system, and repetition coding (RC) scheme. Moreover, we obtain an approximation for the BER of the proposed scheme.  Numerical results, show that the proposed scheme, in contrast to the differential signaling scheme, can achieve full diversity gain, whereas in terms of coding gain it is even better than the repetition coding scheme. Finally, we investigate the effect of imperfect feedback on the performance, and we show that even with an erroneous feedback link, the DSSFB scheme outperforms the DSS scheme in terms of coding gain.