Tag: propagation path model

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.

Log Normal shadowing or Log distance path loss 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.

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, Pr is the received signal power in Watts expressed as a function of separation distance (d meters) between the transmitter and the receiver, Pt is the power of the transmitted signal’s Watts, Gt and Gr 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 nth 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 PL, 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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