The average bit error rate （BER） performance of a free-space optical （FOS） system based on the multi-hop parallel decode-and-forward cooperative communication method with an M-ary phase shift keying subcarrier intensity modulation is studied systematically. With the max-min criterion as the best path selection scheme, the probability density function and the cumulative distribution function of the gamma-gamma distribution random variable signal-to-noise ratio are derived. The analytical BER expression is then obtained in terms of the Gauss-Laguerre quadrature rule. Monte Carlo simulation is also provided to confirm the validity of the presented average BER model.
