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.
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.
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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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.
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.
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.
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
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.
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.
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.
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.
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 theFriis 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:
Log distance path loss model is an extension to the Friis free space model. It is used to predict the propagation loss for a wide range of environments, whereas, the Friis free space model is restricted to unobstructed clear path between the transmitter and the receiver. The model encompasses random shadowing effects due to signal blockage by hills, trees, buildings etc. It is also referred as log normal shadowing model.
Figure 1: Simulated results for log distance path loss model
In the far field region of the transmitter, for distances beyond , if is the path loss at a distance meters from the transmitter, then the path loss at an arbitrary distance is given by
where, is the path loss at an arbitrary distance meters, is the path loss exponent that depends on the type of environment, as given in Table below. Also, is a zero-mean Gaussian distributed random variable with standard deviation expressed in , used only when there is a shadowing effect. The reference path loss , also called close-in reference distance, is obtained by using Friis path loss equation (equation 2 in this post) or by field measurements at . Typically, to for microcell and for a large cell.
The path-loss exponent (PLE) values given in Table below are for reference only. They may or may not fit the actual environment we are trying to model. Usually, PLE is considered to be known a-priori, but mostly that is not the case. Care must be taken to estimate the PLE for the given environment before design and modeling. PLE is estimated by equating the observed (empirical) values over several time instants, to the established theoretical values. Refer [1] for a literature on PLE estimation in large wireless networks.
The function to implement log-normal shadowing is given above and the test code is given next. Figure 1 shows the received signal when there is no shadowing effect and the case where shadowing exists. The r
The function to implement log-normal shadowing is given above and the test code is given next. Figure 1 above shows the received signal power when there is no shadowing effect and the case when shadowing exists. The results are generated for an environment with PLE n = 2, frequency of transmission f = 2.4 GHz, reference distance d0 = 1 m and standard deviation of the log-normal shadowing σ = 2dB. Results clearly show that the log-normal shadowing introduces randomness in the received signal power, which may put us close to reality.
log_distance_model_test.m: Simulate Log Normal Shadowing for a range of distances
Pt_dBm=0; %Input transmitted power in dBm
Gt_dBi=1; %Gain of the Transmitted antenna in dBi
Gr_dBi=1; %Gain of the Receiver antenna in dBi
f=2.4e9; %Transmitted signal frequency in Hertz
d0=1; %assume reference distance = 1m
d=100*(1:0.2:100); %Array of distances to simulate
L=1; %Other System Losses, No Loss case L=1
sigma=2;%Standard deviation of log Normal distribution (in dB)
n=2; % path loss exponent
%Log normal shadowing (with shadowing effect)
[PL_shadow,Pr_shadow] = logNormalShadowing(Pt_dBm,Gt_dBi,Gr_dBi,f,d0,d,L,sigma,n);
figure;plot(d,Pr_shadow,'b');hold on;
%Friis transmission (no shadowing effect)
[Pr_Friss,PL_Friss] = FriisModel(Pt_dBm,Gt_dBi,Gr_dBi,f,d,L,n);
plot(d,Pr_Friss,'r');grid on;
xlabel('Distance (m)'); ylabel('P_r (dBm)');
title('Log Normal Shadowing Model');legend('Log normal shadowing','Friss model');
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