**7.4. Pulse separation**

36 Will-be-set-by-IN-TECH

microwave range. The estimation of the dielectric characteristics, especially the permittivity and the emissivity are based on the ratio of the reflected power measured at two orthogonal polarizations. The orientation of the polarization is defined with regard to the plane of incidence. The plane of incidence is orthogonal to the surface of the object and is spanned by the incoming and the reflected ray. In Fig. 36 a drawing of the functional principle is given.

Rx Tx

Distance from border in meter −→

<sup>+</sup> sin2 *<sup>θ</sup><sup>i</sup>* and *<sup>e</sup>* <sup>=</sup> <sup>1</sup> <sup>−</sup>

  <sup>1</sup> <sup>−</sup> <sup>√</sup>*�*<sup>r</sup> <sup>1</sup> <sup>+</sup> <sup>√</sup>*�*<sup>r</sup>   2

. (16)

0 0.1 0.2 0.3 0.4

The calculation of the permittivity is performed by the inverse application of the Fresnel-formulas. Assuming a material with a relative permeability *μ*<sup>r</sup> = 1, the expressions for the calculation of the relative permittivity *�*r and the emissivity *e* can be written as follows,

Here, it is important to note that the given expression for the emissivity *e* is valid for a straight monitoring of the hot spot. The additional information about the hot spot dimension and distance e.g. to a radiometer can be supplied by the UWB radar. So, an estimation of the hot

**Figure 37.** Permittivity (blue) and simulation values (red) as a function from the distance from the

*θi θi*

objects surface

**Figure 36.** Schematic representation of the functional principle.

*�r* −→

border.

*�*<sup>r</sup> =

spot temperature is possible.

sin2 *θ<sup>i</sup>*

cos *θ<sup>i</sup> E*<sup>⊥</sup> *<sup>E</sup>*� <sup>+</sup> <sup>1</sup> 

2

with *E* as the received electric field strength for each polarization:

<sup>2</sup>

 *E*<sup>⊥</sup> *<sup>E</sup>*� <sup>−</sup> <sup>1</sup> 

2.5

3

3.5

The fundamental problem common to all super-resolution approaches is the precise extraction of the round trip time of UWB pulses. While this approach can easily be performed for single reflection measurements, things become challenging when the distance between multiple scattering centers drops below the range resolution. Constructive and destructive interferences are caused, and the shape of the resulting superposed pulses is distorted massively. Common algorithms for this purpose were analyzed, evaluated and extensively tested under various circumstances. In most cases, they can hardly resolve richly interfered pulses which overlap almost the whole pulse width or have vast computational load. Often, to some extent a priori information is necessary (e.g. the number of pulses to be separated), otherwise these algorithms suffer from inflexible termination conditions or need huge post-processing.

Within the CoLOR project a novel wavefront extraction algorithm called Dynamic Correlation Method (DCM) was proposed, [51]. The DCM is based on a correlation search using a set of two differently shifted reference pulses. Thus, the resulting correlation coefficients are no more just a function of one temporal parameter but rather of two parameters which result in a matrix of correlation coefficients. DCM does not ignore the interfering signature of backscattered pulses and provides a pair of pulses taking the interference pattern of them into account. Additionally, it terminates adaptively to different power levels which enables the detection of weak reflections and avoids post-processing. For a further detailed description and a comparison with alternative methods, see [51].
