Improved beamforming for FSO MISO system over gamma-gamma fading with pointing errors

In this paper, we study the problem of feedback based beamforming for multiple-input single-output free space optical (FSO) system with pointing errors. For a 2 × 1 FSO system, it is shown by analysis that any arbitrary beamforming scheme performs poorer than the repetition coding scheme but achieves full diversity over the Gamma-Gamma fading with pointing errors. Then we study a beamforming scheme for 2 × 1 FSO system which employs one bit feedback from receiver to the transmitter. Erroneous feedback leads to loss in diversity for this beamforming scheme as established by the bit error rate (BER) analysis. For avoiding the loss in diversity, an improved one bit feedback based beamforming scheme is proposed which outperforms the repetition coding. The average BER of this scheme is obtained by using the order statistic and it is minimized to find the optimized transmit weights for the transmit apertures under the erroneous feedback over Gamma-Gamma fading with pointing errors.