Theoretical approaches for computing FAT spreads

FAT (frequency, angle, and time) spreading is approached theoretically through the Helmholtz integral equation for scattering from random rough surfaces. Using the Kirchhoff approximation, angle spread is readily found to be related to the probability of surface slopes. Various approximate evaluations are discussed for modeling time spread, from numerical ray tracing to integrals over pulse shapes. Solving for the half-power points of the intensity shows the link between angle and time spread. Frequency spread functions are discussed, illustrating the difficulty of using Fresnel phase approximations for higher-order corrections to the Doppler shift.