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Relay assisted transmission can compensate atmospheric turbulence, improve transmission distance, and realize communication between non-linear targets in free space optical communication (FSO) system. Space division multiplexing (SDM) greatly improves the channel capacity of FSO system. This paper focuses on the relay assisted transmission oriented to SDM wireless optical communication system. We develop a dual-hop SDM FSO communication model with two spatial mode channels. At the relay, the received optical signals are amplified by the few mode EDFA and forwarded to the destination. Simulation results show that the bit error rate (BER) of the dual-hop SDM system with a few mode EDFA based relay outperforms the single-hop SDM system. Under BER &#x003D; <inline-formula><tex-math notation="LaTeX">$1 \times {10}^{ - 5}$</tex-math></inline-formula>, the power budget is increased by 0.53 dB, 1.2 dB, and 4.88 dB, when <inline-formula><tex-math notation="LaTeX">${\boldsymbol{C}}_{\boldsymbol{n}}^2 = \ 4 \times {10}^{ - 15}$</tex-math></inline-formula>, <inline-formula><tex-math notation="LaTeX">$7 \times {10}^{ - 15}$</tex-math></inline-formula> and <inline-formula><tex-math notation="LaTeX">$1 \times {10}^{ - 14}$</tex-math></inline-formula>, respectively. Moreover, the BER performance is the best when the relay is (originally in the middle of the link) slightly closer to the source.

Relaying System Based on Few-Mode EDFA for Space Division Multiplexing Wireless Optical Communication