large scale propagation Archives

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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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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Two ray ground reflection model

Friis propagation model considers the line-of-sight (LOS) path between the transmitter and the receiver. The expression for the received power becomes complicated if the effect of reflections from the earth surface has to be incorporated in the modeling. In addition to the line-of-sight path, a single reflected path is added in the two ray ground reflection model, as illustrated in Figure 1. This model takes into account the phenomenon of reflection from the ground and the antenna heights above the ground. The ground surface is characterized by reflection coefficient – which depends on the material properties of the surface and the type of wave polarization. The transmitter and receiver antennas are of heights and respectively and are separated by the distance of meters.

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● Wireless Communication Systems in Matlab (second edition), ISBN: 979-8648350779 available in ebook (PDF) format and Paperback (hardcopy) format.

The received signal consists of two components: LOS ray that travels the free space from the transmitter and a reflected ray from the ground surface. The distances traveled by the LOS ray and the reflected ray are given by

Depending on the phase difference () between the LOS ray and reflected ray, the received signal may suffer constructive or destructive interference. Hence, this model is also called as two ray interference model.

where, is the wavelength of the radiating wave that can be calculated from the transmission frequency. Under large-scale assumption, the power of the received signal can be expressed as

where is the product of antenna field patterns along the LOS direction and is the product of antenna field patterns along the reflected path.

The following piece of code implements equation 3 and plots the received power () against the separation distance (). The resulting plot for , , , , is shown in the Figure 2. In this plot, the transmitter power is normalized such that the plot starts at . The plot also contains approximations of the received power over three regions.

twoRayModel.m: Two ray ground reflection model simulation (refer book for Matlab code – click here)

Figure 2: Distance vs received power for two ray ground reflection model and approximations**

** the approximations are shifted down in the plot for clarity, otherwise they will ride on top of the two ray model

The distance that is denoted as in the plot, is called the critical distance. It is calculated . For the region beyond the critical distance, the received power falls-off at rate. For the region where , the received power falls-off at rate and it can be approximated by free space loss equation. Table 1 captures the approximate expressions that can be applied for the three distinct regions of propagation as identified in the plot above.

Table 1: Approximate expressions for three different scenarios of separation distance

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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:

Friis free space propagation model: to model propagation path loss (Figure 1 shown below)
Log distance path loss model: incorporates both path loss and shadowing effect
Two ray ground reflection model, also called as plane-earth loss model
Single knife-edge diffraction model – incorporates diffraction loss
Hata – Okumura Model – an empirical model

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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Friis Free Space Propagation Model

Friis free space propagation model is used to model the line-of-sight (LOS) path loss incurred in a free space environment, devoid of any objects that create absorption, diffraction, reflections, or any other characteristic-altering phenomenon to a radiated wave. It is valid only in the far field region of the transmitting antenna [1] and is based on the inverse square law of distance which states that the received power at a particular distance from the transmitter decays by a factor of square of the distance.

Figure 1: Received power using Friis model for WiFi transmission at ***f=2.4 GHz*** and ***f=5 GHz***

The Friis equation for received power is given by

where, P_r is the received signal power in Watts expressed as a function of separation distance (d meters) between the transmitter and the receiver, P_t is the power of the transmitted signal’s Watts, G_t and G_r are the gains of transmitter and receiver antennas when compared to an isotropic radiator with unit gain, λ is the wavelength of carrier in meters and L represents other losses that is not associated with the propagation loss. The parameter L may include system losses like loss at the antenna, transmission line attenuation, loss at various filters etc. The factor L is usually greater than or equal to 1 with L=1 for no such system losses.

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.

The Friis equation can be modified to accommodate different environments, on the reason that the received signal decreases as the n^th power of distance, where the parameter n is the path-loss exponent (PLE) that takes constant values depending on the environment that is modeled (see Table below} for various empirical values for PLE).

*Table 1: Path loss exponent for various environment*

The propagation path loss in free space, denoted as P_L, is the loss incurred by the transmitted signal during propagation. It is expressed as the signal loss between the feed points of two isotropic antennas in free space.

The propagation of an electromagnetic signal, through free space, is unaffected by its frequency of transmission and hence has no dependency on the wavelength λ. However, the variable λ exists in the path loss equation to account for the effective aperture of the receiving antenna, which is an indicator of the antenna’s ability to collect power. If the link between the transmitting and receiving antenna is something other than the free space, penetration/absorption losses are also considered in path loss calculation. Material penetrations are fairly dependent on frequency. Incorporation of penetration losses require detailed analysis.

Usually, the transmitted power and the receiver power are specified in terms of dBm (power in decibels with respect to 1 mW) and the antenna gains in dBi (gain in decibels with respect to an isotropic antenna). Therefore, it is often convenient to work in log scale instead of linear scale. The alternative form of Friis equation in log scale is given by

Following function, implements a generic Friis equation that includes the path loss exponent, , whose possible values are listed in Table 1.

FriisModel.m: Function implementing Friis propagation model (Refer the book for the Matlab code – click here)

For example, consider a WiFi (IEEE 802.11n standard↗) transmission-reception system operating at f =2.4 GHz or f =5 GHz band with 0 dBm (1 mW) output power from the transmitter. The gain of the transmitter antenna is 1 dBi and that of receiving antenna is 1 dBi. It is assumed that there is no system loss, therefore L = 1. The following Matlab code uses the Friis equation and plots the received power in dBm for a range of distances (Figure 1 shown above). From the plot, the received power decreases by a factor of 6 dB for every doubling of the distance.

Friis_model_test.m: Friis free space propagation model

%Matlab code to simulate Friis Free space equation
%-----------Input section------------------------
Pt_dBm=52; %Input - Transmitted power in dBm
Gt_dBi=25; %Gain of the Transmitted antenna in dBi
Gr_dBi=15; %Gain of the Receiver antenna in dBi
f=110ˆ9; %Transmitted signal frequency in Hertz d =41935000(1:1:200) ; %Array of input distances in meters
L=1; %Other System Losses, No Loss case L=1
n=2; %Path loss exponent for Free space
%----------------------------------------------------
[PL,Pr_dBm] = FriisModel(Pt_dBm,Gt_dBi,Gr_dBi,f,d,L,n);
plot(log10(d),Pr_dBm); title('Friis Path loss model');
xlabel('log10(d)'); ylabel('P_r (dBm)')

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References

[1] Allen C. Newell, Near Field Antenna Measurement Theory, Planar, Cylindrical and Spherical, Nearfield Systems Inc.↗

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