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 |
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.
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');
Rate this article: 
(33 votes, average: 3.61 out of 5)
References
Topic in this chapter
- Introduction to Large scale propagation models
- Friis free space propagation model
- Log distance path loss model
- Two ray ground reflection model
- Modeling diffraction loss
- Hata Okumura model for outdoor propagation
Books by the author
 Wireless Communication Systems in Matlab Second Edition(PDF) Note: There is a rating embedded within this post, please visit this post to rate it. |  Digital Modulations using Python (PDF ebook) Note: There is a rating embedded within this post, please visit this post to rate it. |  Digital Modulations using Matlab (PDF ebook) Note: There is a rating embedded within this post, please visit this post to rate it. |
| Hand-picked Best books on Communication Engineering Best books on Signal Processing |
||
How can we calculate the shadowing effect Xsigma ? It is said that it zero mean gaussian random variable, but variance is considered in the equation. How is this possible?
The graph above was generated assuming mean=0 and sigma=2 dB for the underlying normal distribution.
log distance path loss model having a attenuation factor matlab code kindly help me
Dear Mr. Mathuranathan Sir,
May you please share the “log distance path loss matlab code” thanks
Mirza Ferdous Rahman
How i can generate Hata Model for (1) Urban (2)Rural area when ht=30m ,hr=1m ,f=800Mhz and distance is 10 t0 200m…. plz snd me coding
how I can generate the shadowing samples at different locations in a cell when they are not independent , there is a correlation distance between them .
Check this out
https://www.gaussianwaves.com/2014/07/generating-correlated-random-numbers/