1-bit feedback-based beamforming scheme for an uplink FSO-NOMA system with SIC errors

In this paper, we study the effect of a beamforming scheme for a multiple-input-single-output (MISO) uplink free-space optical (FSO) communication system with nonorthogonal multiple access (NOMA) over negative exponential fading channels. 1-bit feedback about the channel state information is required by the proposed beamforming scheme. The feedback is considered to be error-free in this work; however, an error due to successive interference cancellation (SIC) is taken into consideration. It is inferred by bit error rate (BER) analysis that a higher weight given to the channel with higher channel gain and a slightly lower weight given to the channel with lower channel gain gives the best performance as compared to all arbitrary schemes in a 2×1 FSO-NOMA system. Further, it is also analytically shown that using a 1-bit feedback-based beamforming scheme in an FSO-NOMA system suppresses the effect of SIC error; hence the BER performance of both the transmitters (TXs) is the same, which is not the case for a conventional NOMA scheme. A simplified asymptotic upper bound of BER of the proposed scheme is obtained by using the order statistics, and an optimized beamforming vector is found by minimizing this upper bound. It is then established analytically as well as through simulations that the beamforming vector is independent of average signal-to-noise ratio as long as the two channels remain independent and identically distributed. We further compare the proposed scheme with an FSO-NOMA system without feedback and beamforming and with single-input single-output FSO system using 4-ary pulse amplitude modulated signaling. It is shown by simulations that the proposed scheme outperforms both of them and has a huge coding gain advantage. A numerical analysis of this scheme is also provided for gamma-gamma (GG) and log-normal (LN) turbulence regime. The proposed scheme is extended to 3×1 and 4×1 MISO systems, and it is revealed that the performance of the system degrades as the number of TX increases.