Tag: fresnal zone

An important consideration for propagation models are the existence of objects within what is called the first Fresnel zone. Fresnel zones, referenced in Figure 1 are ellipsoids with the foci at the transmitter and the receiver, where the path length between the direct path and the alternative paths are multiples of half-wavelength (). Rays emanating from odd-numbered Fresnel zones cause destructive interference and the rays from the even-numbered Fresnel zones cause constructive interference.

This article is part of the book ● Wireless Communication Systems in Matlab (second edition), ISBN: 979-8648350779 available in ebook (PDF) format and Paperback (hardcopy) format.

For large-scale propagation geometry, the path difference between the LOS and the diffracted rays is

The radius of the (n^{th}) Fresnel zone is approximated as

Given the height of the obstruction (refer Figure 1 given in the single knife-edge diffraction model), we can find out which Fresnel zone is obstructed by the obstruction. Setting in equation (2) and solving for (n) by using equation (1).

As general rule of thumb for point-to-point communication, if of the first Fresnel zone is clear of obstructions, the diffraction loss would be negligible. Any further Fresnel zone clearance does not significantly alter the diffraction loss.

Program 1: FresnalZone.m : Compute radius of a Fresnel zone and safe clearance at first Fresnel zone – Refer the book for Matlab code

As an example, we would like to measure the radius of the first Fresnel zone at the midpoint between the transmitter and receiver that are separated by a distance of and operating at the frequency . The script results in the following output. The radius of the first Fresnel zone will be . It will also inform us that if at-least of the first Fresnel zone is clear of any obstruction, then any calculated diffraction loss can be safely ignored.

Program 2: FresnelzoneTest.m: Computing the diffraction loss using single knife-edge model

d=25e3; %total distance between the tx and the Rx
f=12e9; %frequency of transmission
n=1;% Freznel zone number - affects r_n only
d1=25e3/2; d2=25e3/2; %measurement at mid point
%r_n = radius of the given zone number
%r_clear = clearance required at first zone
[r_n,r_clear] = Fresnelzone(d1,d2,f,1)

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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
  • Single knife-edge diffraction model
  • Fresnel zones
• Hata Okumura model for outdoor propagation

Books by the author

Wireless Communication Systems in Matlab Second Edition(PDF) (173 votes, average: 3.66 out of 5) $14.99 – Add to Cart Checkout Added to cart	Digital Modulations using Python (PDF ebook) (127 votes, average: 3.58 out of 5) $14.99 – Add to Cart Checkout Added to cart	Digital Modulations using Matlab (PDF ebook) (134 votes, average: 3.63 out of 5) $14.99 – Add to Cart Checkout Added to cart
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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.

This article is part of the book ● Wireless Communication Systems in Matlab (second edition), ISBN: 979-8648350779 available in ebook (PDF) format and Paperback (hardcopy) format.

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;
[L_dB,n]=singleKnifeEdgeModel(h,f,d1,d2)

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References

[1] Recommendation ITU-R P.526.11, Propagation by diffraction, The international telecommunication union, Oct 2009.↗

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
  • Single knife-edge diffraction model
  • Fresnel zones
• Hata Okumura model for outdoor propagation

Books by the author

Wireless Communication Systems in Matlab Second Edition(PDF) Note: There is a rating embedded within this post, please visit this post to rate it. $14.99 – Add to Cart Checkout Added to cart	Digital Modulations using Python (PDF ebook) Note: There is a rating embedded within this post, please visit this post to rate it. $14.99 – Add to Cart Checkout Added to cart	Digital Modulations using Matlab (PDF ebook) Note: There is a rating embedded within this post, please visit this post to rate it. $14.99 – Add to Cart Checkout Added to cart
Hand-picked Best books on Communication Engineering Best books on Signal Processing