Through-Wall Imaging With UWB Radar System - KEMT FEI TUKE

4.2 Measurements of the Wall Parameters by Reflectometry 58
4.2.2 Model of the Wave Propagation in the Wall
The main idea of the wall parameter estimation is to use time domain reflectometry.
The Fresnel equations at the wall interfaces and plane wave propagation within
the wall are applied. This idea was firstly introduced in [155]. However, here a
time consuming iterative error minimization process that solves inverse problem
for multilayer medium has to be processed. In addition, as a multiple reflection
reduction technique a low effective time gating was chosen. Therefore, a wall
with thickness only 12 cm was measured to prove the method’s functioning. A
time domain reflectometry was chosen for wall parameter estimation also in [119].
However, the piece of wall has to be placed in anechoic chamber room and measured
with and without a metal plate behind it, what can not be done in a dangerous
environment. The reflectometry principle was also used in [80]. However, only the
theoretical approach was tested there on simulated data and an extensive iteration
algorithm was used to estimate the wanted parameters. Furthermore, the whole
wave propagation was assumed to be planar. This is not practical since it requires
a large distance between the wall and the radar device.
Our approach permits spherical wave propagation. But within the wall we
also simplify to planar waves in order to keep simple. An error made by that
approximation is negligible since it only neglects the spreading losses in the wall.
That is, the conductivity would be slightly overestimated. For our wall model, we
suppose, as in [155] and [80], a flat wall surface, a homogeneous wall structure, and
normal incidence of the sounding waves. Frequency independent wall permittivity
εw and wall conductivity σw are also supposed. Moreover, it can be assumed that
the relative permeability of common wall material will be µrw = 1 and the wave
attenuation would not be extremely strong at the applied radar frequencies.
Fig. 4.2.1 illustrates the wave propagation within a wall. Obviously, we have
to deal with the reflections in both wall surfaces and the wave propagation within
the wall. As demonstrated below, the reflections depicted in blue would be used
to determine the wall parameters and the transmitted wave (green line) should
sound the targets behind the wall. Reflections of higher order are not of interest
(depicted as green dotted lines). Their amplitudes are negligible.
Fresnel’s equations give ratios between the incident wave and the scattered
respectively transmitted electrical field at a flat boundary for normal incident
waves:
√
εa −
Γ = ±
√ εw
√
εa + √ ,
εw
T = 2 4√ εaεw
√
εa + √ =
εw
√ 1 − Γ2 (4.2.1)
where Γ is a reflection coefficient, T is a transmission coefficient, and εa is the
permittivity of the air or vacuum. The positive sign in Γ holds for the propagation
air to a wall and the negative sign has be to applied if the wave moves from a wall
to the air.
The wave propagation within the wall is characterized by the propagation