Jk. Breakall et al., THE MODELING AND MEASUREMENT OF HF ANTENNA SKYWAVE RADIATION-PATTERNSIN IRREGULAR TERRAIN, IEEE transactions on antennas and propagation, 42(7), 1994, pp. 936-945
The Method of Moments (MoM) was used in conjunction with the Geometric
Theory of Diffraction (GTD) for predicting the elevation-plane radiat
ion patterns of simple high-frequency (HF) vertical monopoles and hori
zontal dipoles situated in irregular terrain. The three-dimensional te
rrain was approximated by seven connected flat plates that were very w
ide relative to the largest wavelength of interest. The plate length a
long the terrain profile was the longest possible that still adequatel
y followed the shape of the path on the azimuth of the elevation patte
rn of interest and no shorter than 1 wavelength at the lowest frequenc
y of interest. The MoM model was used to determine the antenna current
s under the assumption that the terrain was planar (i.e., locally flat
) over the distance pertinent to establishing the input impedance. The
currents thus derived were used as inputs to the GTD model to determi
ne the gain versus elevation angle of the antennas for HF skywave when
situated in the irregular terrain. The surface wave solution for grou
ndwave was not included since this does not appreciably contribute any
effect to the skywave far-field patterns at HF in this case. The mode
l predictions were made using perfect electric conducting (PEC) plates
and using thin plates made, of lossy dielectric material with the sam
e conductivity and relative permittivity as measured for the soil. The
se computed results were compared with experimental elevation-plane pa
ttern data obtained using a single-frequency helicopter-borne beacon t
ransmitter towed on a long dielectric rope in the far field on a linea
r path directly over the antennas. The monopoles and dipoles were situ
ated in front of, on top of, and behind a hill whose elevation above t
he flat surrounding terrain was about 45 m. The patterns of all of the
antenna types and sitings exhibited diffraction effects caused by the
irregular terrain, with the largest effects being observed at the hig
hest measurement frequency (27 MHz). The results for the PEC plates an
d the lossy dielectric plates were essentially identical for the horiz
ontal dipoles, whereas the lossy dielectric plates were required to pr
operly match the measured results for the vertical monopoles. The gain
of the antennas in irregular terrain and the gain of the same antenna
s situated in flat, open terrain differed by up to 20 dB at the lower
elevation angles (eg., 3-degrees-5-degrees). This difference in gain i
s significant for most HF systems.