“…Li et al [5] developed a mathematical model for a heterodyne detection system for partially coherent Gaussian Schell beams under the Tatarskii turbulence spectrum in 2015. Furthermore, some of the authors of this paper investigated the effect of signal beam propagation in atmospheric turbulence on heterodyne detection, e.g., angle-of-arrival fluctuation [3], beam mode of the partially coherent Gaussian Schell-model beam [1,2], irradiance and phase fluctuations [13] and wavefront correction [10]. However, these works were based on the vector theory of partially coherent light fields or Gaussian beam.…”