Tag: knife-edge diffraction model

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.

Fresnal zone illustration
Figure 1: Fresnal zone illustration

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● 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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Modeling diffraction loss : Single knife-edge diffraction model

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].

Figure 1: Diffracting single knife-edge obstacle having (a) positive height and (b) negative height

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');
Figure 2: Loss of signal strength as a function of Fresnel-Kirchhoff diffraction parameter

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.↗

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Large scale propagation models – an introduction

Radio propagation models play an important role in designing a communication system for real world applications. Propagation models are instrumental in predicting the behavior of a communication system over different environments. This chapter is aimed at providing the ideas behind the simulation of some of the subtopics in large scale propagation models, such as, free space path loss model, two ray ground reflection model, diffraction loss model and Hata-Okumura model.

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.

Introduction

Communication over a wireless network requires radio transmission and this is usually depicted as a physical layer in network stack diagrams. The physical layer defines how the data bits are transferred to and from the physical medium of the system. In case of a wireless communication system, such as wireless LAN, the radio waves are used as the link between the physical layer of a transmitter and a receiver. In this chapter, the focus is on the simulation models for modeling the physical aspects of the radio wave when they are in transit.

Radio waves are electromagnetic radiations. The branch of physics that describes the fundamental aspects of radiation is called electrodynamics. Designing a wireless equipment for interaction with an environment involves application of electrodynamics. For example, design of an antenna that produces radio waves, involves solid understanding of radiation physics.

Let’s take a simple example. The most fundamental aspect of radio waves is that it travels in all directions. A dipole antenna, the simplest and the most widely used antenna can be designed with two conducting rods. When the conducting rods are driven with the current from the transmitter, it produces radiation that travels in all directions (strength of radiation will not be uniform in all directions). By applying field equations from electrodynamics theory, it can be deduced that the strength of the radiation field decreases by in the far field, where being the distance from the antenna at which the measurement is taken. Using this result, the received power level at a given distance can be calculated and incorporated in the channel model.

Radio propagation models are broadly classified into large scale and small scale models. Large scale effects typically occur in the order of hundreds to thousands of meters in distance. Small scale effects are localized and occur temporally (in the order of a few seconds) or spatially (in the order of a few meters). This chapter is dedicated for simulation of some of the large-scale models. The small-scale simulation models are discussed in the next chapter.

The important questions in large scale modeling are – how the signal from a transmitter reaches the receiver in the first place and what is the relative power of the received signal with respect to the transmitted power level. Lots of scenarios can occur in large-scale. For example, the transmitter and the receiver could be in line-of-sight in an environment surrounded by buildings, trees and other objects. As a result, the receiver may receive – a direct attenuated signal (also called as line-of-sight (LOS) signal) from the transmitter and indirect signals (or non-line-of-sight (NLOS) signal) due to other physical effects like reflection, refraction, diffraction and scattering. The direct and indirect signals could also interfere with each other. Some of the large-scale models are briefly described here.

The Free-space propagation model is the simplest large-scale model, quite useful in satellite and microwave link modeling. It models a single unobstructed path between the transmitter and the receiver. Applying the fact that the strength of a radiation field decreases as in the far field, we arrive at the Friis free space equation that can tell us about the amount of power received relative to the power transmitted. The log distance propagation model is an extension to Friis space propagation model. It incorporates a path-loss exponent that is used to predict the relative received power in a wide range of environments.

In the absence of line-of-sight signal, other physical phenomena like refection, diffraction, etc.., must be relied upon for the modeling. Reflection involves a change in direction of the signal wavefront when it bounces off an object with different optical properties. The plane-earth loss model is another simple propagation model that considers the interaction between the line-of-sight signal and the reflected signal.

Diffraction is another phenomena in radiation physics that makes it possible for a radiated wave bend around the edges of obstacles. In the knife-edge diffraction model, the path between the transmitter and the receiver is blocked by a single sharp ridge. Approximate mathematical expressions for calculating the loss-due-to-diffraction for the case of multiple ridges were also proposed by many researchers [1][2][3][4].

Of the several available large-scale models, five are selected here for simulation:

Figure 1: Friis free space propagation model (large scale propagation model)

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References

[1] K. Bullington, Radio propagation at frequencies above 30 megacycles, Proceedings of the IRE, IEEE, vol. 35, issue 10, pp.1122-1136, Oct. 1947.↗

[2] J. Epstein, D. W. Peterson, An experimental study of wave propagation at 850 MC, Proceedings of the IRE, IEEE, vol. 41, issue 5, pp. 595-611, May 1953.↗

[3] J. Deygout, Multiple knife-edge diffraction of microwaves, IEEE Transactions on Antennas Propagation, vol. AP-14, pp. 480-489, July 1966.↗

[4] C.L. Giovaneli, An Analysis of Simplified Solutions for Multiple Knife-Edge Diffraction, IEEE Transactions on Antennas Propagation, Vol. AP-32, No.3, pp. 297-301, March 1984.↗

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