Performance of coherent FSO systems with adaptive M-PSK modulation

We investigate the performance of a heterodyne detection system with adaptive modulation that employs M-ary phase shift keying (M-PSK) modulation for transmission over a strong turbulence channel modeled by Gamma- Gamma distribution. The spectral efficiency (SE) and bit-error-rate (BER) expressions of the considered adaptive system are derived, where a new exact expression for the BER in terms of bivariate Fox's H-function (BFHF) is presented. Furthermore, an asymptotic expression for the BER in terms of basic functions is introduced. The results show how much improvement in the SE that can be achieved when the adaptive system is used, where the modulation level is selected in accordance with the state of the channel, while maintaining the target BER. We also extend the adaptive system to a parallel-branches adaptive system employing the maximum ratio combining technique at the receiver, where the SE and BER are derived and analyzed to show the additional improvement in the SE when the number of branches is increased. Monte Carlo simulations are also provided to confirm the derived expressions.