
Introduction


Deterministic models utilize physical phenomena in
order to describe the propagation of radio waves.
Herewith the effect of the actual environment is taken
into account by using
3D vector building data (plus terrain profile).
Generally deterministic propagation models are based on
rayoptical techniques. A radio ray is assumed to
propagate along a straight line influenced only by the
present obstacles which lead to reflection, diffraction
and the penetration of these objects. However for large
distances between transmitter and receiver, i.e.
especially for satellite transmitters, the computational
demand is still challenging. For some scenarios there is
no 3D vector data of the environment available but
clutter height
information describing the building heights in pixel
format. In both cases the knife edge diffraction model
provides an efficient approach for the coverage
prediction based on either vector or pixel data (incl.
building and topographical data).



Description


The transmitter is located at
(dT, 0, 0) and the receiver at (dR, 0, 0). A
diffracting knife edge (semi plane) is located
at x = 0 and has the height z = H (see figure on
the right). According to the principle of
Huygens every point in the semi plane z > H can
be considered as individual point source. The
transmitter as point source provides a field
strength F in the semi
plane x = 0 according to the following formula:
In order to compute the
field strength at the receiver location the
principle of Huygens can be applied and
accordingly every point above the absorbing semi
plane can be considered as point source. The
field strength at the receiver is computed as
superposition of all fields provided by the
point sources:

Modeling of a knife edge diffraction

There
are different modeling approaches for the
determination of the knife edges between the
transmitter and the receiver.
According to Epstein and Peterson the distance
between transmitter and receiver is separated in
different parts. The diffraction loss is then
computed in subsequent steps by applying the
formula between the transmitter
and Q2 and between Q1 and the receiver (see figure).
The parameters H1 and H2 hereby represent the
heights of the knife edge obstacles Q1 and Q2.
Modeling approach of Epstein
and Peterson
For the Deygout model
first the main obstacle in the vertical profile
is determined. This obstacle (Q1) is identified
by the point with the highest value for the
Fresnel parameter between transmitter and
receiver. For this obstacle the diffraction loss
is computed without consideration of the
remaining ones. In the next steps further
obstacles are determined, both before and after
the main obstacle Q1. This procedure is repeated
up to a certain value for the Fresnel parameter,
i.e. until no significant obstacle is
remaining. Finally all diffraction losses are
added. However, as this approach overestimates
the diffraction loss a correction term must be
considered for compensation.
Modeling approach of Deygout


Examples

The following examples show wave propagation
predictions with two different prediction models
with and without additional consideration of knife edge
diffraction. For the first example, the
Empirical Two Ray
model has been used to predict the field
strength in the area of Rimini (Italy) based on
topography
and clutter
databases in pixel format.
The second sample depicts a field strength
prediction with the
HataOkumura model in the area of Seoul
(Korea) based on topography and clutter
databases in pixel format.





Prediction of field strength
using Empirical Two Ray model
without Knife Edge diffraction

Prediction of field strength
using Empirical Two Ray model
with Knife Edge diffraction





Prediction of field strength
using HataOkumura model without
Knife Edge diffraction

Prediction of field strength
using HataOkumura model with
Knife Edge diffraction







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