Performance of Subcarrier PSK Systems Using PSAM Maximum Likelihood Estimation in Turbulence Channels

A pilot-symbol assisted subcarrier phase-shift keying (PSK) free-space optical communication system is studied with maximum likelihood (ML) phase estimation. Using the phase error probability density function of ML estimation phase error, we study the error rate performance of the subcarrier PSK system with carrier phase error in lognormal and Gamma-Gamma turbulence channels. The closed-form expressions are derived for the asymptotic signal-to-noise ratio (SNR) performance loss for the imperfectly synchronized systems over turbulence channels, and the analytical expressions are verified with numerical results. These expressions reveal how the subcarrier PSK systems with ML estimated phase error are influenced by the pilot length and the modulation order in large SNR regimes.