Optical communication in a turbulent atmosphere via the orbital angular momentum of a laser beam. II. Symbol error rate in a data line

A numerical simulation is applied to study the symbol error rate (SER) in an optical communication system with data modulation by the orbital angular momentum (OAM) of an optical beam propagating through a turbulent atmosphere. In this case, the OAM is calculated from pre-recorded powers of azimuthal modes, while the complex modes are the coefficients of expansion of the wave field of the beam into spiral harmonics. The SER is calculated as a function of turbulence conditions for the LG1 and LG4 beams and data line lengths, as well as the number of receiving channels (number of recorded powers of azimuthal modes) and size of the input aperture of the receiving telescope. It is shown that the range of angular harmonics can be optimized to diminish the SER. It is found that knowing the probability density of OAM fluctuations, with a pre-determined average OAM and its variance, we can estimate the SER without conducting special numerical tests.