Imperfect-quantized-feedback-based beamforming for an FSO MISO system over Gamma-Gamma fading with pointing errors

In this paper, we propose an imperfect-quantized-feedback-based beamforming scheme for a generalized multiple-input single-output (MISO) free space optical (FSO) system over Gamma-Gamma fading channels with pointing error. It is well known that a feedback-based beamforming scheme aids channel adaptive signaling in wireless communication systems and provides large performance gain. If the feedback information is always decoded error free, then the beamforming technique reduces to a best transmit aperture selection scheme [termed error free optimal weighting scheme (EFOWS)]. However, due to a practically unguided environment, the feedback link is prone to error and leads to incorrect aperture selection, due to which diversity gain is lost. Therefore, a signal-to-noise ratio (SNR) adaptive error tolerant weighting (ETW) scheme is introduced and is optimized according to the SNR of the feedback link. In comparison to the considered arbitrarily fixed SNR-based ETW scheme, the proposed SNR adaptive ETW scheme provides significant performance gain (coding gain) almost equivalent to EFOWS. Closed-form expressions for the upper bound of the asymptotic average bit-error rate (BER) and the ergodic capacity of the proposed schemes are obtained with the help of order statistics. By minimizing the derived average BER, optimized transmit weights for the transmit apertures are achieved under erroneous feedback over Gamma-Gamma fading with pointing errors. Further, numerical results show that the proposed new error tolerant scheme outperforms the well-known repetition coding (referred to as the uniformly weighted scheme).