Fresnel zones

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

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