International audienceFor indoor Wireless LAN systems planning, an accurate propagation modelling is required. Semi-empirical models represent an efficient approach to the coverage prediction. Based on measurement results, the model parameters are derived. In this paper we present the influence of the measurement point choice on the accuracy of the parameters estimation and thus on the model robustness

Guillet, Valery

Pajusco, Patrice

Tahri, Rida

Thiriet, Jean-Yves

English

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Measurements and calibration method for WLAN
indoor path loss modelling
Rida Tahri, Valery Guillet, Jean-Yves Thiriet, Patrice Pajusco
To cite this version:
Rida Tahri, Valery Guillet, Jean-Yves Thiriet, Patrice Pajusco. Measurements and calibration method
for WLAN indoor path loss modelling. IEE Sixth international conference on 3G and beyond, Nov
2005, Washington, United States. pp.1 - 4. ￿hal-02379345￿
MEASUREMENTS AND CALIBRATION METHOD FOR 
WLAN INDOOR PATH LOSS MODELLING 
R. Tahri, V. Guillet, J. Y. Thiriet and P. Pajusco
France Télécom 6, avenue des Usines - BP 382 - 90007 Belfort, France 
{ rida. tahri, valery. guillet, j ean-yves. thiriet, patrice. pajusco }@francetelecom.co m 
Keywords: Indoor 
measurements, WLAN. 
Abstract 
propagation, modelling, 
For indoor Wireless LAN systems planning, an accurate 
propagation modelling is required. Semi-empirical models 
represent an efficient approach to the coverage prediction. 
Based on measurement results, the model parameters are 
derived. In this paper we present the influence of the 
measurements points choice on the accuracy of the parameters 
estimation and thus on the model robustness. 
1 Introduction 
Over the last few years, the market for wireless service has 
grown at an unprecedented rate. The commercial success 
achieved by the introduction of cellular mobile radio 
telephones has generated strong interest in the development of 
other wireless communications systems. Recently, there has 
been an increasing interest in providing wireless local area 
networks (WLAN) working in the 2.4 GHz ISM unlicensed 
band. The performance of this system depends on the radio 
propagation environment. For planning indoor wireless LAN 
systems working around 2.4 GHz, the signal propagation 
characteristics prediction is thus needed. These characteristics 
can be used to determine the optimum location of the base 
station antenna for a desired coverage within a building. They 
can also be used to determine signal to interference ratio for 
frequency planning. 
The paper is organized as follows: section 2 provides the 
formulation and the definition of all the coefficients which 
will be used in our statistical study, section 3 describes the 
results of a statistical study undertaken on simulations. 
Section 4 presents the validation of conclusions obtained at 
paragraph 3 by applying the results to a series of 
measurements 
2 Description of the problem 
Thanks to its performance (fast computation time and 
relatively good accuracy), the Multi-Wall model [3,4] is 
applied for WLAN indoor coverage predictions. lt proved 
better performance with optimised parameters. This is a semi-
empirical approach based on fixing empirical parameters for 
the attenuation produced by the obstacles in the building. 
This path loss model is given by the following analytical 
formula: 
L 
Where: 
/J + L k;Att; + a log 10 (d) (1) 
d is the distance between the transmitter and the 
receiver [m]. 
ki is the number of penetrated walls of type i 
Atti is the loss of wall of type i [dB] 
� is a constant loss [dB]
A multiple regression analysis method [2,5] is used to predict 
a, � and the different attenuation parameters (from 
measurement data). 
Such estimation requires the undertaking of an extensive 
series of measurements. However, this is not always possible 
because of the high cost of required experiments. lt is 
therefore necessary to perform the tuning of the model 
parameters choosing a limited number of measurement 
points. We thus present in this work, the impact of the 
measurement points choice on the model robustness and 
accuracy. 
An important issue in regression analysis is assessing its 
overall quality. An analysis of residuals or errors is a useful 
way of evaluating how good the regression is. 
The goodness of the regression analysis can be assessed 
using the coefficient of determination R2 which measures the 
proportion of variation in L explained by a regression model. 
Indeed for n measurements of the path loss L and for p 
variables thought to affect all the measured values of L, the 
multiple regression model (1) that relates an individual value 
Li of L to the p variables can be expressed by: 
p 
L i = /JO + I /J j X if + & i (2)
j�l 
Xi i are the elements of the data matrix X (made up in our 
case by log(d) and ki). The parameters �i, are the regression 
coefficients corresponding to the p variables; and Ei is the 
error or residual. �o is a constant which can account for all 
other unconsidered variables. The predicted value of the 
dependent variable Li, can be expressed by: 
p 
L i = j3 o + L /J 1 X !i (3) 
j�l 
The coefficient of determination is then defined as follows: 
n 
I (L; L) 2 
R 2 i�l 
n 
(4) 
I (L; - L) 2 
i�l 
Where L is the mean value of L, and n the number of 
points used for tuning. The ratio R2 must lie between zero and 
unity. When R2=1, all variation has been explained but if it is 
equal to zero, the regression model does not explain anything. 
However R2 is a statistic which we calculate for a sample of 
points. We can also define another coefficient which gives a 
statistic for the whole population. lt is named the adjusted 
coefficient of determination Ra and given by: 
n 
I (L; i;) 2 n - I 
R 1 - i�l X (5) a n n - pI (L; - L) 2 
i�l 
Another statistical test dealing with residuals is the F-test, 
which is (for p independent variables and n observations) 
expressed by: 
n 
I 
F i�l n 
I 
i�l 
(L; - L) 2 
A 
2 (L; - L;) 
X 
n - p (6)
p - I
The tabulated value of F p.n-p.a for a given level of significance 
a is compared to the calculated F. If the computed F is greater 
than the tabulated value it can then be concluded that the 
regression results are significant. 
Furthermore, for evaluating the robustness of the regression 
model it is also necessary to check the significance of the 
partial regression coefficients �i- This is done by means of the 
t-test. The appropriate statistic of this test for the jth variables,
is
(7) 
Where eij are the diagonal elements of the matrix (X'TX'r1 . 
X'= [ l ,X] is deduced from the matrix of measurement data X. 
a is a root mean square estimation of the error. This error is 
defined as the difference between the reference path loss 
values (given by measurements or by an accurate ray tracing 
model [l]) and those estimated by multiple regression using 
(1). The diagonal elements of the matrix a2(X'rX'y1 represent 
also the regression parameters variance. 
As in the F-test, the computed ti should be greater than the 
tabulated În-p,a for a level of significance a. More details for all 
this statistical coefficients are given in [5]. 
In the following paragraph we will use the statistical 
coefficients defined above, to study the influence of the 
choice of the calibration points on the stability and accuracy 
of the regression model. 
3 Statistical analysis and simulation results 
As it is difficult to perform a measurement campaign with 
several thousand points we have chosen to use an accurate 
ray tracing model to have a very large number of data to 
analyze. The ray tracing model [l] includes transmission and 
reflection. These simulated path loss values are then used as 
"measurements" data for a regression analysis. 
The simulation was conducted within a typical office 
building in Belfort city. lt was performed in the 2.4GHz 
frequency band. The simulation was taken with the 
transmitter at one location. The reception locations were 
taken in different rooms of building. 
Both transmitter and receiver used an omnidirectional 
antenna. Three different materials are present: concrete, 
concrete with windows and plaster. 
The simulation points realized will be used as a reference 
sample for our study. 
From these reference points, 6 different samples of points 
( designated "by configuration") were selected for testing 
calibration strategies. The resulting path loss is then used to 
estimate (by multiple regression) the parameters of the model 
(1). 
From the parameters estimated in each configuration we have 
calculated using (1) the path loss on the entire environment 
and compare deviation RMSE (the error is defined as the 
difference between reference values losses and those 
estimated by multiple regression using (1)). We have also 
calculated the adjusted coefficient of determination for the 
entire environment. 
For the six configurations the criteria in the choice of the 
measurement points is different. That results in a different 
number of combinations for each configuration. 
The points belonging to the same combination undergo the 
same number of transmission per material (in our 
environment there are three materials). In other words it is 
the set of the identical (k1 , k2, k3) lines of measurements data 
matrix X, with k1 (resp. k2, k3) is the number of penetrated 
walls of type 1 (resp. 2, 3). 
Both the overall and partial quality tests have been applied to 
the regression model calibrated with each sample of 
simulation points. 
Table 1 summarizes the number of different combinations, 
and the number of simulation points used to compute the 
statistics for each configuration. lt shows also the different 
regression parameters ti values, the RMSE and the adjusted 
coefficient of determination values, for the six studied 
configurations. 
From table 1, it can be seen the great influence of the choice 
of calibration points on the accuracy and the robustness of 
the model, even if the number of measurement points is the 
same. 
Indeed it can be seen that for the first configuration the 
RMSE was found to be 10.96 dB, and the adjusted 
coefficient of determination Ra was 0.4 (i.e. only 40% of the 
path loss is explained by model). In this case the t1 value 
corresponding to the Att1 variable is equal to 0.74 (for a level 
of significance a= l % the tabulated value of t100• l% is 2.326) 
Although the number of points in the first configuration is the 
larger, the t1 value becomes higher than t1 oo.1% only starting 
from the 3rd configuration for which the number of points is 
448 and the number of different combinations becomes equal 
to 8. lt can also be seen that the RMSE decreased from 10.96 
dB to 2.37dB, and the coefficient of determination increased 
from 0.4 to 0.98 when the number of different combinations 
increased from 4 to 21. 
Although the number of points is the same, the choice of the 
points has a great influence on the accuracy and the 
robustness statistics of the model. With a reduced number of 
points but a large number of different combinations, a sample 
can be as representative as a sample with all the points. lt 
makes possible to have a better conditioned matrix (less 
identical lines k1 , k2, k3). 
Now we make the same study for four other configurations 
but for these cases with a different number of points for each 
configuration. 
The simulation points for each configuration are selected in 
the reference sample in order to take a number of 
combinations by configuration equal to that of the reference 
configuration. 
The number of points by combinations increases from 2 to 5 
for the four configurations which increases the number of 
points from 46 to 105. The reference configuration counts 
452 simulation points. Table 2 shows the evolution of the 
different regression parameters ti values, the RMSE, the 
Fisher factors "F" and the adjusted coefficient of 
determination values, for the four studied and the reference 
configurations. 
From table 2 we can observe the stability of the RMSE and 
the adjusted coefficient of determination (respectively 
-3.27dB and - 0.96) for the forth configuration. The results
obtained for the F values, considering the level of
significance a= 1 %, are all significant (i.e. F is greater than
2.53 which is the tabulated value of F4•4o,1% =2.53, it
decreases when the number of points increases). The F value
increases statistically (proportionally with n) from 212 to 451
when the number of points (n) increases from 46 to 102.
The ti values for all variables and for the fourth configuration
are also all significant ti>2.465 (when 2.465 is the tabulated
value of t1%,3o , it decreases when number of points
increases).
W e can note nevertheless a small decrease in the ti value
corresponding to the variables Att2 and Att3 between the third
and the forth configurations even if the number of points
increases from 86 to 102. That can be due to the increase of
the number of points by combinations which implies an
increase of data matrix X lines correlated between them.
W e can thus conclude that it is not an increase in the number
of points in a calibration sample which increases the
precision and the robustness of the model but good selected
measurement points. With a sufficient number of
combinations and representative sample of the varions
reception locations in an environment, we can carry out a
good calibration of the model with few points. Indeed, we
can note in table 2 that with 46 points we carry out a
comparable RMSE to that with 450 (resp. 3.27 dB and 3.04
dB). With only 46 points we explain 96% of path loss by
regression model.
In the next paragraph we will try to validate the conclusions
of this paragraph by applying them to a propagation
measurements campaign in an office building.
Configuration description tj value of the model parameters dB] Analysis 
configuration number of combinations number of  points cte Attl Att2 Att3 log(d) RMSEfdB Ra 
1 4 486 4.89 0.74 3.75 4.6 4.21 10.96 0.4 
2 6 462 6.81 2.2 7.04 5.84 5.02 5.83 0.8 
3 8 448 17.36 3.27 7.54 7.14 12.6 4.27 0.89 
4 11 448 20.33 4.9 16.6 9.9 8.59 4.19 0.94 
5 18 455 24.64 6.17 21.68 12.66 9.02 3.99 0.95 
6 21 452 25.91 5.04 21.99 13.57 10.29 2.37 0.985 
Table 1: Influence of the number of combinations on the overall and partial multiple regression qualities (statistical regression 
analysis for six simulated configurations having the same number of points). 
Confü?uration descriotion ti value of the model oarameters [dB] Analvsis 
confi!!Uration number of combinations number of points cte Attl Att2 Att3 loe(d) RMSE [dB] Ra F 
1 21 46 9.65 2.4 9.2 5.01 3.32 3.27 0.96 212 
2 21 67 12.3 2.7 11. 7 7.26 4.0 3.27 0.96 369 
3 21 86 12.13 3.3 12.21 7.4 3.79 3.29 0.96 422 
4 21 102 12.23 3.8 12.12 7.3 4.01 3.29 0.96 451 
ail points 21 450 34.0 6.3 29.0 16.0 12.69 3.04 0.97 
Table 2: Influence of the number of points on the overall and partial multiple regression qualities (statistical regression 
analysis for four simulated configurations having the same number of combinations). 
4 Application to the measurements results 
Field strength measurements were carried out in an office 
building in Belfort city. Measurements have been realized 
in the 2.4GHz frequency band using 802- l lb/g equipments 
and a software developed by France Telecom for data 
acquisition. 
The transmitters were placed at four locations within the 
building. Figl shows the locations of the transmitters in 
the environment where the measurements were carried out. 
Figure 1: Location of the transmitter antenna in the 
measurements environment - ( lOOmx 18.5m). 
Both transmitters and receiver use an omnidrectionnal 
antenna. The transmitters are placed at a height of 2.5m 
near the ceiling (ceiling height was about of 2.88 m). The 
locations of reception points were at a height of 1.2m. The 
measurements were processed in line of sight (LOS) and 
non line of sight (NLOS). 
Internai walls were made of 7 cm thick plasterboard with 
3 cm thick wooden doors. The outer walls are made of 44 
cm thick concrete with double-glazing. Floor is made of 
concrete. Most of the furniture is made of agglomerated 
wood and metallic cupboards. The building had a 
rectangular shape, with a S-shaped corridor separating the 
different rooms. 
In order to remove fast fading effect, several field strength 
measurements, around the considered reception point, are 
performed and averaged. For averaging the measurements 
period at each point is equal to 20s. From the 350 measured 
values four configurations are selected with the same number 
of combinations and different number of points. 
The number of points par combinations increases from 2 to 5 
which increase the number of points from 77 to 148. 
Table 3 shows a stability of the adjusted coefficient of 
determination (-0.62) and the RMSE (-5.3). 
The F value is always greater than the tabulated value (for a 
level of significance a= 1 %, 6 variables and 60 points F 1 %. 6• 60 
is equal to 2.37). The F value increases statistically from 34.6 
to 80 when the number of points increases from 77 to 148. 
The ti corresponding to the regression variables are greater 
than the tabulated value except for Att3 which falls bellow the 
acceptable 11 %,60 =2.37 and consequently could not be 
considered as influent in the regression model. 
As we said in the last paragraph we can note that with only 
77 points we carry out a comparable RMSE to that with 350 
points (resp. 5.3 dB and 4.96 dB). With 77 points we explain 
69% of path loss by regression model while we explain the 
same quantity with 145 points. 
5 Conclusion 
The calibration of propagation models is presented in many 
articles, but none interested in the impact of the measurement 
points selection on the robustness of the final result. 
In this paper, statistical study of the multiple regression 
analysis was presented. Numerical results show that it is not 
an increase in the number of calibration points which 
increases the performances of the model. With a reduced 
number of points, a representative calibration points sample 
of the environment which provides a data matrix with better 
properties for parameters estimation allows a good model 
robustness and accuracy. 
Confieuration description tj value of the model parameters [dB] Analysis 
confieuration number of combination number of points loe(d) Attl Att2 Att3 Att4 cte RMSE[dB] F Ra 
1 38 77 7.16 4.05 4.7 0.5 2.4 26 5.3 34.6 0.69 
2 38 104 7.49 4.91 5.04 0.32 2.33 29 5.4 45.6 0.7 
3 38 128 7.7 6.3 5.5 0.51 2.69 32 5.35 60 0.72 
4 38 148 8.5 6.6 5.9 1.00 2.8 34 5.22 80 0.73 
ail measurements 350 350 1.3 12.29 12.2 1.3 6.9 44 4.96 225 0.79 
Table 3: Statistical regression analysis for four measured configurations in France telecom building (validation of the 
conclusion established with simulated configurations) 
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Measurements and calibration method for WLAN indoor path loss modelling

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Measurements and calibration method for WLAN indoor path loss modelling

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