Performance of Coherent Optical MPSK in Underwater Turbulent Channels With Phase Errors

Compared to intensity modulation with direct detection, coherent detection offers superior receiver sensitivity, higher spectral efficiency, and better background noise suppression. However, research on coherent detection in underwater wireless optical communication (UWOC) systems is relatively limited. This paper investigates the average bit error rate (BER) performance of coherent UWOC systems employing different phase-shift keying schemes in the presence of phase errors. The underwater turbulent channel is characterized by the mixture exponential-generalized gamma distribution, taking into account the impact of pointing errors as well. Phase errors are modeled by a Gaussian distribution. Specifically, we first derive the average BER expressions for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula>-ary phase-shift keying (MPSK) under ideal carrier phase estimation. Then, we derive the exact average BER expressions for binary phase-shift keying and quadrature phase-shift keying, as well as tight approximations for MPSK, considering the influence of phase errors. Additionally, we provide asymptotic BER expressions in the high signal-to-noise ratio region and the BER floor expression. Finally, these expressions are validated through Monte Carlo simulations.