With the rise of wireless communications enabled by terahertz (THz), accurate channel modeling
is an essential requirement for any communication system. Various approximations have been
considered in modeling wave propagation at lower frequencies for the sake of simplicity. This
dissertation raises the question of the validity of such assumptions as the carrier frequency
increases and tries to deepen our understanding of the impact of common approximations on the newly investigated area of the electromagnetic field, the terahertz region.
The planar wavefront model is a common practice in line-of-sight channels, and the
scattering by rough surfaces is calculated using the Kirchhoff approximation, where the random
surface distribution is assumed to be Gaussian and the lateral roughness effect is neglected.
However, none of these simple assumptions reflect reality. For precise roughness profile
measurements, a mechanical profilometer and confocal microscope evaluated many indoor
materials. For the first time, we provide comprehensive histograms of sample height distribution
statistics. The roughness assessments include the first four moments of height distributions,
unlike most prior research, which dealt merely with the height standard deviation.
Non-Gaussian rough surface modeling techniques were explored. We generated several
random surfaces with statistical and spectral properties using the Johnson and Pearson families
of distributions. Comparing the produced surfaces’ statistics with the stated parameters confirms
the validity of modeling. Thereafter, the scattering by non-Gaussian rough surfaces is examined
analytically and numerically at THz frequencies. The roughness measurements show the non-
Gaussian nature of the height distribution of several materials, and a summary of prominent
indoor material data is provided. Intriguingly, statistical values with exceptionally high kurtosis
may lead to severe inaccuracies when modeling rough surfaces. Thereafter, the relation of
roughness parameters to the intensity and angular distribution of a reflected scattered wave
was discussed. The research findings address the fact that for a slightly rough surface, a
change in distribution has a minor effect on scattering behavior at the frequencies of interest
for communication applications. However, when a rough surface has standard height variances
in the scale of wavelength, the scattering profile is substantially altered, resulting in a distinct
distribution when all other scattering parameters are constant. The simulation findings accord
well with the analytical model and demonstrate that at THz frequencies, a normally distributed
surface model may present a very generic model to all random rough surfaces.
The next step was to examine the impact of changing the lateral roughness parameters. It has
been demonstrated that, under the assumption that the surface autocorrelation length is greater
than the wavelength, the surface roughness-induced diffuse scattering may be dramatically
enhanced. It has been proven that when this requirement is not met, the rough surface behaves
more like a reflector, resulting in a roll-off of specularity at higher frequencies. Statistically-
controlled rough samples were synthesized using Stereolithography, a three-dimensional printing
technique, and measurements were conducted on them to verify our findings.
Further, we employ our acquired knowledge in two real-world study cases. The first
proposed a method to include rough surfaces in a ray tracer for already-built roughness models,
while the other focused on designing, building, and implementing THz diffusers based on
well-known methods of optical diffusers.