Modeling diffraction loss
Propagation environments may have obstacles that hinder the radio transmission path between the transmitter and the receiver. Idealized models for estimating the signal loss associated with diffraction by such obstacles are available. The shape of the obstacles considered in these model are too idealized for real-life applications, nevertheless, these models can serve as a good reference.
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Single knife-edge diffraction model
The model depicted in Figure 1 considers two idealized cases where a sharp obstacle is placed between the transmitter and the receiver. Using all the geometric parameters as indicated in the figure, the diffraction loss can be estimated with the help of a single, dimension-less quantity called Fresnel-Krichhoff diffraction parameter – 
. Based on the availability of information, any of the following equation can be used to calculate this parameter [1].
After computing the Fresnel-Krichhoff diffraction parameter from the geometry, the signal level due to the single knife-edge diffraction is obtained by integrating the contributions from the unhindered portions of the wavefront. The diffraction gain (or loss) is obtained as
where, 
and 
are respectively the real and imaginary part of the the complex Fresnel integral 
given by
The diffraction gain/loss in the equation (2) can be obtained using numerical methods which are quite involved in computation. However, for the case where 
, the following approximation can be used [1].
The following function implements the above approximation and can be used to compute the diffraction loss for the given Fresnel-Kirchhoff parameter.
Program : diffractionLoss.m : Function to calculate diffraction loss/gain – Refer the book for Matlab code
The following snippet of code loops through a range of values for the parameter and plots the diffraction gain/loss (Figure 2).
Program : fresnel_Kirchhoff_diffLoss.m: Diffraction loss for a range of Fresnel-Kirchhoff parameter
v=-5:1:20; %Range of Fresnel-Kirchhoff diffraction parameter
Ld= diffractionLoss(v); %diffraction gain/loss (dB)
plot(v,-Ld);
title('Diffraction Gain Vs. Fresnel-Kirchhoff parameter');
xlabel('Fresnel-Kirchhoff parameter (v)');
ylabel('Diffraction gain - G_d(v) dB');
Finally, the single knife-edge diffraction model can be coded into a function as follows. It also incorporates equation 3 (given in this post) that help us find the 
Fresnel zone obstructed by the given obstacle. The subject of Fresnel zones are explained in the next section.
Program : singleKnifeEdgeModel.m : Single Knife-edge diffraction model – Refer the book for Matlab code
As an example, using the sample script below, we can determine the diffraction loss incurred for 
, 
and 
at frequency 
. The computed diffraction loss will be 
.
Program : Computing the diffraction loss using single knife-edge model
h=20; f=10e9;d1=10e3;d2=5e3;
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References
Topics in this chapter
- Introduction to Large scale propagation models
- Friis free space propagation model
- Log distance path loss model
- Two ray ground reflection model
- Modeling diffraction loss
- Hata Okumura model for outdoor propagation
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