Friss Free space model Archives

Hata Okumura model for outdoor propagation

Outdoor propagation models involve estimation of propagation loss over irregular terrains such as mountainous regions, simple curved earth profile, etc., with obstacles like trees and buildings. All such models predict the received signal strength at a particular distance or on a small sector. These models vary in approach, accuracy and complexity. Hata Okumura model is one such model.

In 1986, Yoshihisa Okumura traveled around Tokyo city and made measurements for the signal attenuation from base station to mobile station. He came up with a set of curves which gave the median attenuation relative to free space path loss. Okumura came up with three set of data for three scenarios: open area, urban area and sub-urban area. Since this was one of the very first model developed for cellular propagation environment, there exist other difficulties and concerns related to the applicability of the model. Okumura model can be adopted for computer simulations by digitizing those curves provided by Okumura and using them in the form of look-up-tables [1]. Since it is based on empirical studies, the validity of parameters is limited in range. The parameter values outside the range can be obtained by extrapolating the curves. There are also concerns related to the calculation of effective antenna height. Thus every RF modeling tool incorporates its own interpretations and adjustments when it comes to implementing Okumura model.

Hata, in 1980, came up with closed form expressions based on curve fitting of Okumura models. It is the most referred macroscopic propagation model. He extended the Okumura models to include effects due to diffraction, reflection and scattering of transmitted signals by the surrounding structures in a city environment.

Figure 1: Simulated distance vs. path loss using Hata model, for f_c = 1500 MHz , h_b = 70 m and h_m = 1.5 m

Chart for Hata Okumura path loss model distance vs propagation path loss — Figure 1: Simulated distance vs. path loss using Hata model, for f_c = 1500 MHz , h_b = 70 m and h_m = 1.5 m

The generic closed form expression for path loss (PL) in dB scale, is given by

where, the Tx-Rx separation distance (d) is specified in kilometers (valid range 1 km to 20 Km). The factors A,B,C depend on the frequency of transmission, antenna heights and the type of environment, as given next.

● f_c = frequency of transmission in MHz, valid range – 150 MHz to 1500 MHz
● h_b= effective height of transmitting base station antenna in meters, valid range 30 m to 200 m
● h_m=effective receiving mobile device antenna height in meters, valid range 1m to 10 m
● a(h_m) = mobile antenna height correction factor that depends on the environment (refer table below)
● C = a factor used to correct the formulas for open rural and suburban areas (refer table below)

Table of Parameters for Hata okumura model

The function to simulate Hata-Okumura model is given in the book – Wireless Communication Systems using Matlab. The simulated path loss in three types of environments are plotted in Figure 1. The simulated results are obtained over a range of distances for the following parameter values f_c=1500 MHz, h_b=70 m and h_m=1.5 m.

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References

[1] Masaharu Hata, Empirical formula for propagation loss in land mobile radio services, IEEE transactions on vehicular technology, vol. VT-29, no. 3, August 1980.↗

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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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Log Distance Path Loss or Log Normal Shadowing Model

Log distance path loss model

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.

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.

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 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.

*Table 1: Path loss exponent for various environments*

logNormalShadowing.m: Function to model Log-normal shadowing (Refer the book for the Matlab code – click here)

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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References

[1] Srinivasan, S.; Haenggi, M., Path loss exponent estimation in large wireless networks, Information Theory and Applications Workshop, pp. 124 – 129, Feb 2009.↗

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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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