This study studies the performance of multihop free-space optical systems using the subcarrier binary phase-shift keying modulation over atmospheric turbulence channels. The authors propose a modified relaying strategy, termed 'amplify- decode-and-forward', realised by using avalanche photodiode (APD) receivers. The outage probability of the proposed system is analytically derived considering the atmospheric turbulence and the receiver noise, including APD shot noise and thermal noise. The analytical results are verified by Monte Carlo simulations, and a good agreement between the analytical and simulation results is confirmed. In the authors' analysis, they quantitatively discuss the impact of turbulence strength, number of relay nodes, relaying configuration, system bit rate and receiver parameters on the system outage probability. In addition, the optimal value of APD gain for achieving the lowest outage probability in different cases of relaying configuration, number of relays and receiver parameters is also discussed. [ABSTRACT FROM AUTHOR]