Electromagnetic Macro Modeling of Propagation in Mobile Wireless Communication: Theory and Experiment

A Novel Asymptotic Solution to the Sommerfeld Radiation Problem: Analytic Field Expressions and the Emergence of the Surface Waves

“…Asymptotic expressions (17) and (31) for the direct and scattered field respectively, represent outgoing spherical waves. Now the conditions for the generation of the, well-known in the literature, surface waves are studied [1][2][3][4][5][6]19]. As their name imply, these waves are constrained close to the the planar interface, so a reasonable choice is to examine the field's behavior at sliding observation angles, ie at θ 2 → π/2.…”

“…Further analysis of (30), revealed useful insights as for the nature of the EM field. Far away from the ground -air interface, (32) holds and the scattered field takes the form of an outgoing spherical wave (which of course resembles a plane wave at very large distances from the source) and together with the LOS field of (17), form what is frequently called in the literature as "space wave" [5,19]. On the contrary, at sliding observation angles, that is at observation points that are far away from the source and simultaneously very close to the ground (so as θ 2 ≃ π/2), the space wave diminishes.…”

“…The "Sommerfeld radiation problem" is a well-known problem in the area of propagation of electromagnetic (EM) waves above flat and lossy ground with important applications in the area of wireless and mobile telecommunications [1][2][3][4][5][6][7][8][9][10][11][12]. The original Sommerfeld solution to this problem is provided in the physical space by using the "Hertz potentials" and it does not end up with closed form analytical solutions.…”

A closed — Form analytical solution to the radiation problem from a short dipole antenna above flat ground using spectral domain approach

“…The classical Sommerfeld solution to this problem is provided in the physical space by using the so-called 'Hertz potentials' and it does not endup with closed form analytical solutions. K. A. Norton [3] concentrated in subsequent years more in the engineering application of the above problem with obvious application to wireless telecommunications, and provided approximate solutions to the above problem, which are represented by rather long algebraic expressions for engineering use, in which the so -called 'attenuation coefficient' for the propagating surface wave plays an important role.…”

“…Geometry of the radiation problem considered in this paper, namely radiation from a vertical Hertzian dipole at position (x 0 ,0,0) above infinite, flat and lossy ground, as an interface situated at plane x=0 (Sommerfeld problem [1]-[3]). III.…”