Knife Edge Diffraction Extension

The half deterministic way to consider hilly terrain in Rural Prediction Models



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 ray-optical 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). 




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



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 Hata-Okumura 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 Hata-Okumura model without Knife Edge diffraction
Prediction of field strength
using Hata-Okumura model with Knife Edge diffraction


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