Diffraction theory of tropospheric propagation near and beyond the radio horizon: Part I--Theory

By means of the earth-flattening approximation, the problem of radio diffraction by the earth is treated as that of refraction in an atmosphere with a linear profile of modified index. Use is made of the saddle point method, whose special case, known as the method of stationary phase, proves useful for analysis of the normal propagation within the horizon. It is found that the classical diffraction theory is as valid at ranges beyond the horizon as in its neighborhood, if account is taken of the contribution of other terms than the first of the residue series, and that exclusive use of the saddle point method makes it possible to deal systematically with the tropospheric propagation for all regions within, nears and beyond the horizon. Theoretical derivations are presented in Part I. Part II gives a comparison of the theory with experiments, showing a fairly good agreement between them.