This paper discusses signal intensity calculations for ionospheric HF radio waves using the geometrical optics approximation. To calculate the total signal intensity for an ionospheric channel, all the multipath and multimode amplitudes must be superimposed with their proper polarizations and phases. The basic method for calculating multipath interference with geometrical optics is presented. Using this method, the phenomenon of polarization fading is investigated and, in particular, the frequency-selective fading of a wideband HF channel due to the beating of the ordinary and extraordinary modes is calculated and compared with actual measured data.¿ 1997 American Geophysical Union