Phase-modulated Rice model for statistical distributions of complex signals

The basic Rice model is commonly used to describe complex signal statistics from randomly scattered waves. It correctly describes weak (Born) scattering, as well as fully saturated scattering, and smoothly interpolates between these extremes. However, the basic Rice model is unsuitable for situations involving scattering by random inhomogeneities spanning a broad range of spatial scales, as commonly occurs for sound scattering by turbulence in the atmospheric boundary layer and other scenarios. In such scenarios, the phase variations are often considerably stronger than those predicted by the basic Rice model. Therefore, the basic Rice model is extended to include a random modulation in the signal phase, which is attributable to the influence of the largest, most energetic inhomogeneities in the propagation medium. Various joint and marginal distributions for the complex signal statistics are derived to incorporate the phase-modulation effect. Approximations of the phase-modulated Rice model involving the Nakagami distribution for amplitude, and the wrapped normal and von Mises distributions for phase, are also developed and analyzed. The phase-modulated Rice model and various approximations are shown to greatly improve agreement with simulated data for sound propagation in the near-ground atmosphere.