A Model for the Statistics of Field Fluctuation, Phase Front Aberration, and Field Spatial Covariance of Electromagnetic Waves Propagating in Rain

This article presents a model for the statistics of field fluctuations, phase aberration, and field spatial covariance of electromagnetic waves propagating in the rain at millimeter-wave frequencies as a function of range and rain rate. This statistical model is derived based on a full-wave S-matrix approach and using the fact that the fluctuating component of the field is a Gaussian process. The model is useful in the performance evaluation of coherent communication systems and imaging radars, such as multiple-input multiple-output (MIMO) and synthetic aperture (SAR) systems. The mean field component is represented by a field propagating in a medium with an effective refractive index characterized by the S-matrix approach. It is shown that the statistical behavior of the magnitude and phase of the fluctuating field at any point on the wavefront with respect to a reference point on the wavefront can be described by only one parameter. The statistics of the magnitude of the fluctuation field at the reference point can also be described by one more parameter. In this article, the effective refractive index of the medium for estimating the mean field and the two required parameters for describing the fluctuating field at a given point and its covariance with that of an adjacent point are given for different rain rates in the range 2-50 mm/h and at 77 GHz. Simple algebraic expressions for the parameters for describing the fluctuating field and its covariance are provided that are valid for propagation ranges of up to 500 m and the separation distance (between any point on the wavefront and the reference point) of up to eight wavelengths.