A fundamental structure of all-optical free-space optical communication (FSO) system is presented. The system adopts subcarrier intensity modulation and all-optical amplify-and-forward relaying, and furthermore, it considers the effect of background noise and amplified spontaneous emission noise. A system model of the all-optical relaying FSO system under Gamma-Gamma turbulence condition is established. Two novel cooperative schemes, all-active relaying scheme and selective relaying scheme, are presented, and their corresponding power allocation modes are provided. The outage probability of the relay-assisted transmission is compared with that of the direct link, and the outage probability of the two schemes for different channel parameters and number of relays is analyzed by simulation. The simulation results show that the performance of the link can be improved obviously by the relayed transmission, and the performance of the selective relaying scheme is superior to that of the all-active relaying scheme.