A probability distribution for the complex field of waves propagating in random media

A model for the joint probability density function is proposed for the quadrature components of waves propagating in random media (WPRM). The model is based on a further generalization of the model for the intensity distribution for WPRM proposed by Ewart [J. Acoust. Soc. Am. 86, 1490–1498 (1989)]. Both this distribution model and the intensity distribution model apply to the full range of scattering strengths and ranges. That is, from short ranges where the intensity probability density function (pdf) is lognormal, through the region of the medium focus, where the intensity moments 〈I^q〉 can be well above q!, to the saturation regime, where the moments approach exponential. Simulation of the complex fields used to test the model was accomplished by parabolic wave equation marching of the field through a medium with a fourth‐order power law transverse spectrum (usually termed the modified exponential). The fourth moment of the fields are accurately predicted using parabolic fourth moment theory—giving some confidence in the higher moments. The resulting joint pdf’s are parametrized in terms of the scattering strength γ and the scaled range X that parametrize the simulations. This work provides a necessary first step in the important quest to include highly non‐Gaussian quadrature component statistics in signal processing formulations.