Statistical Tuning of Walfisch-Ikegami Model in Urban and Suburban Environments
Dayanand Ambawade #1
, Deepak Karia #2
, Tejas Potdar #3
, B.K.Lande #4, R.D.Daruwala #5,
Ankit Shah #6
# Sardar Patel Institute of Technology and Veermata Jijabai Technological Institute
# Electronics and Telecommunication Department, University of Mumbai, India
deepakckaria, tejasap87,,[email protected],[email protected],bklande,[email protected]
Abstract—Theoretical and experimental models have
been considered for the prediction of the path loss in
systems of mobile communications. This paper reviews
Cost231-Walfisch-Ikegami model for prediction of path loss
in mobile outdoor microcell environments. The proposed
statistical model aligns in accordance to the measured data,
considering roof height, road width as normal random
variables. The characterization used is a linear curve, fitting
the path loss to the variations. Five parameters are modelled
statistically, with the dependencies on height of base station,
distance from base station, road width and roof top height.
The model is validated by comparing the simulated results
with the measurement campaigns carried out in urban and
suburban regions.
Keywords— Cost231-Walfisch-Ikegami model, Microcell
environment, statistical models, random variables.
I. INTRODUCTION
In spite of the development of numerous empirical path
loss prediction models so far, the generalization of these
models to any environment is still questionable. They are
suitable for either particular areas (urban, suburbs rural,
etc.), or specific cell radius (Macrocell, Microcell,
Picocell). To overcome this drawback, the empirical
models’ parameters can be adjusted or tuned according to a
targeted environment. The propagation model tuning must
optimize the model parameters in order to achieve minimal
error between predicted and measured signal strength. This
will make the model more accurate for received wireless
signal predictions. COST 231 Walfisch–Ikegami non line-
of-sight form (CWI–NLOS) model’s [2, 3] superiority
over the other empirical models [6, 7, 8, 11, 12] has
provoked us to select and adjust this model to our target
environment. The model reports the relation between the
path losses measured in various areas and its parameters
such as frequency, distance, base station (BS), and mobile
station (MS) antenna heights. This model is applicable for
800-2000 MHz and within a distance below 1km which is
not the case in some models [9]. A typical application
involves taking measurements of the path loss in the target
environment and then tuning the Walfisch Ikegami model
parameters to fit it to the measured data. Unfortunately, the
Walfisch Ikegami model was developed based on
measurements conducted in propagation environments that
differ widely from the propagation environment in India.
In order to efficiently apply the Walfisch Ikegami model to
our region, a model tuning process is required. We have
used the LS algorithm in to tune the model's parameters to
fit the data (received signal strength) obtained for the
urban and suburbs areas of Panvel City, India. The LS
algorithm has been used to fit a linear model to measured
data [3]. This process can be achieved by minimizing the
summed square of residuals between measured data and
prediction model data. Further comparison of the
simulated results with the measured data shows that the
power calculated using the proposed model provides a
roadmap for an appropriate tie-up with that of the
measured received signal power. To make accurate
statistical comparison the Root Mean Squared Error of
Proposed model and Theoretical model with respect to
measured data are presented.
II. MEASUREMENT CAMPAIGNS
The measurement set up involves a transmission system,
comprising of a DBXLH-6565C-T0M, transmitting
antenna having double polarization (±45º) and operating
on 870– 960 MHz scale with gain of 15.4/17.5 (dBd/dBi).
The antenna is positioned at a height of 35m from the
ground, and is used by Mahanagar Telephone Nigam Ltd
(MTNL), a local network operator. The frequency of
transmission was set to 872 MHz for the measurement
campaigns carried out. On the other side, the reception
system used is, TEMS Investigation GSM 5.1. The
receiving antenna used in the measures is PIFA antenna
used in Samsung U600 model that operates in the interval of
870 –960 MHz with gain of 2 dBi with dimensions in mm:
30 x 6 x 5. The receiving module is assembled on a car and
the received signal is emitted by one laptop having an
PCMCIA card installed. The system of movement test uses
a GPS system to give the information of the geographic
position of all measures. The Figures below shows the
snapshots of the areas covered by the respective
transmitting base stations selected for collection of data,
the most of which were located in the neighbourhood of
Panvel.
2010 Fourth Asia International Conference on Mathematical/Analytical Modelling and Computer Simulation
978-0-7695-4062-7/10 $26.00 © 2010 IEEE
DOI 10.1109/AMS.2010.109
538
Figure 1. TEMS Investigation GSM 5.1.Snapshot of ONGC Township
and MTNL Panvel south site
Figure 2. TEMS Investigation GSM 5.1.Snapshot of Milan Co-operative Housing Society
Figure 3. TEMS Investigation GSM 5.1.Snapshot of Old Panvel area and
Vrindavan
A. Cost231- Walfish – Ikegami Model
The COST231- Walfish – Ikegami model [4]
distinguishes between LoS and NLoS propagation. The
model is accurate for carrier frequencies in the range 800 ≤
fc ≤ 2000 (MHz), & path distances in the range 0.02 ≤
d ≤ 5 (km).LoS propagation: For LoS propagation in a
street canyon, the path loss is,
pL )(dB = 42.6+26 )(log10 d +20 )(log10 cf , d ≥ 20 m
(1)
where, the first constant is chosen, so that pL is equal to
the free space path loss at a distance more than 20 m. The
model parameters are the distance d (km) and carrier
frequency cf (MHz).
Non Line of Sight Propagation: As defined in figure 4, the
path loss for non-of-sight (NLoS) propagation in terms of
the following parameters:
bh = BS antenna height, 4 ≤ bh ≤ 50 (m)
mh = MS antenna height, 1 ≤ mh ≤ 3 (m)
roofh = roof heights of buildings (m)
bh∆ = bh – roofh = heights of BS relative to rooftops (m)
`
Figure 4. Typical propagation situation in urban and suburban areas and
definition
of the parameters used in the COST-WI model and other
Walfisch-type models
Here ,
mh∆ = mroof hh − = height of MS relative to rooftops
(m)
w = width of streets (m)
s = building separation (m)
φ = road orientation with respect to the direct radio path
If no data on the structure of the building and roads are
available, the following default values are recommended, s =
20. . 50 (m), 2sw = , φ = 900, roofh = 3 × floors + roof (m),
where roof= 3(m) and 0(m).
The NLoS path loss is composed of three terms, viz.,
msdrtso LLL ++ , 0≥+ msdrts LL
pL )(dB = oL , 0<+ msdrts LL
(2)
d
∆hm
hroof
Direction of travel Ф
Incident wave
BS
ω
s
MS
hm
∆hroof
539
Where
oL = free space loss = 4.32 + 10log20 ( d ) + 10log20 )( cf
rtsL = roof-to-street diffraction and scatter loss
msdL = multi-screen diffraction loss
The roof-top-to-street diffraction loss is
orimcsrt LhfL +∆+++−= )(log20)(log10)(log109.16 101010 ω
(3)
where
-10 + 0.354 (φ ), 0 ≤ φ ≤ 350
oriL = 2.5 + 0.075 (φ – 350), 350 ≤ φ ≤ 55
0
4.0 – 0.114 (φ – 550), 55
0 ≤ φ ≤ 90
0
(4)
The multi-screen diffraction loss is
)(log9)(log)(log 101010 bfKdKKLL cfdabshmsd −+++=
(5)
where
)1(log18 10 bh∆+− , roofb hh >
bshL = 0, roofb hh ≤
(6)
is the shadowing gain (negative loss) for cases when the
BS antenna is above the roof tops. Here aK and dK
depends on the path length, d, and the base station with
respect to the rooftops bh∆ . The term aK accounts for the
increase in the path loss when the BS antennas are
situated below the rooftops of adjacent and are given by
54, roofb hh >
aK = 54 – 0.8 ∆ bh , 5.0≥d km & roofb hh ≤
54 – 0.8 ∆ bh 5.0d∗ , 5.0<d km & roofb hh ≤
(7)
The terms dK and fK control the dependency of the
multi screen diffraction loss on the distance and the
frequency, respectively and are given by
18, roofb hh >
dK =
18 – 15 roofb hh∆ , roofb hh ≤
(8)
−1925*7.0 fc , medium city & Suburban
fK = -4 +
−1925*5.1 fc , metropolitan area
(9)
This model works best for, roofb hh >> . Large
prediction errors can be expected for roofb hh > .The
theoretical model in terms of the above factors shown
below
))(log*9)(log*
)(log*))(1(log*18
)(log*20)(log*10
9.16)(log*30)(log*204.32(
1010
1010
1010
1010
sfK
xKKhh
Lhhw
fxpp
f
daroofb
orimroof
tltheoritica
+
−−−−+
+−−−
++−−−=
(10)
where,
roofbd
f
roofba
hhK
fcK
hhK
>=
−+−=
>=
,18
1925*7.04
,54
(11)
s = distance between the base station and the mobile
station.
x = distance between buildings
w = width of road
B. Proposed Statistical Model
This work proposes a method that consists in modelling
through the multiple linear regressions [5] of difference
from received power among the propagation loss obtained
by the COST 231Walfisch-Ikegami model (1) in relation to
the involved environment and the received power
measured in each environment. After the calculation of the
regression equation of each one of the areas covered by the
four base stations, an average among the partial
coefficients of regression was made to find out that one
which would be the generic equation of adjustment to be
added for the representative equation of Walfisch-Ikegami
model for the studied environment. To generalize still the
model, parameters roofh , oriL and s , were modelled as
random variables with Gaussian distribution functions (17)
(18) with mean specified in Table I. This distribution
function was chosen by the criterion chi-square, because it
was the distribution that presented the best adjustment. The
Gaussian distribution function is given by:
( ) )2^*2/(2)^(^**2*1)( σµσ −Π= xexf
(12)
where, µ is the average, σ is the standard deviation and
x is a random variable of a standard normal distribution.
Here simple Linear Regression explains the values of a
variable y using the values of another variable x , these
two variables being assumed to entertain a linear relation:
540
( )xbaxy ε++= (13)
where, ε is a random "noise" that depends a priori on x .
Multiple Linear Regression (MLR) addresses just about
the same problem except that here, the response
variable y is supposed to be explained not by just one
variable x , but by several variables { }jx . If we slightly
change the foregoing notations, we assume that the
linear relation between y and { }jx is:
( )xXxy pp εβββ ++++= .....110 (14)
where, p is the number of “independent" variables, ( )xε
is a random noise (e.g. measurement errors) whose
properties depend a priori on the point of the data space
defined by the values of the jx . The data is made of
n measurements iy , where ni ..,2,1= ,taken for n sets
of values { }ijX of the independent variables:
( )xXxy ijpi εβββ ++++= .....110
(15)
where, values of iβ are fixed but unknown numbers and
( )ixε are n realizations of the ( )xε .
The proposed Model is shown below:
))5()(log*9*)3()(log*
)(log**)1())(1(log*18*)2(
*)4()(log*20*)2()(log*10*)3(
9.16)(log*30)(log*20*)1(4.32(
1010
1010
1010
1010
pspfk
xKpKhhp
Lphhpwp
fxppp
f
daroofb
orimroof
tproposed
++
−−−−+
+−−−
++−−−=
(16)
randnhrh roof += (17)
randnss mean += (18)
where,
randn = normal random variable
2sw = (width of street)
roofba hhK >= ,54 ,
−+−= 1925*7.04 fcKf for suburban.
means : mean values of the distance between buildings.
TABLE I. MEAN VALUE S OF DISTANCE BETWEEN BUILDING
AND ROOFTOP HEIGHT OBTAIN FROM DATA OBTAIN FROM PANVEL
MUNICIPALITY IN THE AREA OF OPERATION
Base Station means hr
ONGC Township 10 12.07
OLD Panvel 11 13.92
Vrindavan 9 12.52
MTNL South 10 13.07
Milan CHS 10 12.01
The significance of Lori is that it contributes
significantly to the output power values obtained through
the model. In [1], this metric was not taken into account
during the measurements campaigns. Hence we have made
a point to approximately calculate it. In the method of
calculation, we have considered the shortest distance from
the base station as perpendicular side of a right angle
triangle, the distance of the base station from other points
along the path as hypotenuse. Geometrically, we estimated
the angle made by this hypotenuse and the road along
which measurements were taken. In order to consider the
angle made in the direction of the travel, the following
correction formula is used
φφ −= 180corrected (19)
III. PRESENTATION OF RESULTS
To verify the tuned Walfisch Ikegami path loss model,
comparison between path loss predicted and measured data
have been performed over the suburbs areas of the Panvel
city. The network operates in the 872 MHz band. The
values of Walfisch Ikegami path loss model parameters
p(1),p(2),p(3),p(4) and p(5) are calculated [10] and
presented in Table II . The performance of the tuned model
is then compared to measured data. The values of the
performance measures, RMSE, are tabulated in Tables III
for the adjusted and the theoretical model. The obtain
results are presented in Figs. 4 To 7, correspondent to the
experiments carried through in four areas of the
measurement campaign. The figures present the variation
of the received signal (dBm) (simulated and measured) in
function of the distance in relation to the radio base station
(Km), along the travelled Avenues and Streets. A
statistical analysis of the measures was accomplished for
the areas covered by base station located at Old Panvel,
ONGC Township, Vrindavan avenue and MTNL Panvel
south, to compare among the power values of the measures
and simulated signal for the proposed model, in order to
verify the model validity for each area covered by the base
station of the measurement campaign used for calculating
the parameters of the proposed model. To make a more
perceptive study of the proposed model, an analysis was
accomplished through the collected data in one area more
from the measurement campaign (Milan Co-operation
Housing Society) which were not part of the processing of
the data for obtaining of the regression parameters inserted
541
in (16). Figures 4 to 7 show the comparative graphics
power from the received signal versus distance to the radio
base station, simulated (theoretical model of COST
231Walfisch-Ikegami and proposed model) and measured
for the Milan CHS (Figure 8) was not part of the data
processing for acquisition of the correction parameters of
the considered model.
TABLE II. REGRESSION PARAMETERS FOR THE PROPOSED MODEL
Parameters Average Values
P [1] -0.7680
P [2] -0.4520
P [3] -0.2006
P [4] -0.3730
P[5] 42.3241
TABLE III. STANDARD DEVIATION FOR THE BEST FIT AND
THEORETICAL MODEL
Name of Base
Station
Root Mean Squared
Error(RMSE) of
Proposed model
with respect to
Measured data
Root Mean Squared
Error(RMSE) of
Theoretical model
with respect to
Measured data
ONGC 7.6334 10.7185
OLD Panvel 3.1354 17.5261
Vrindavan 3.5808 16.9955
MTNL South 8.1373 19.4218
Milan CHS 5.1134 9.0457
IV. ANALYSIS OF RESULTS
The proposed model presents variations in relation to
each area analysed. The Old Panvel, ONGC Township,
MTNL Panvel south site and Vrindavan all of them
involved in the measurement campaign to analyse the
regression models obtained for the five areas from the
involved environment in the study, we referred to the
regression equation and the test of significance of its
coefficients. The results verified through the simulation of
the Walfisch-Ikegami model (10) had presented significant
errors when compared with the results obtained for the
model adjusted (proposed model)(16) and with the values
measured in field. From figs. 4 to 7, it is observed that the
root mean square errors of the tuned model in relation to
the value measured in the field are of 7.6334, 3.1354,
3.5808, 8.1373 and 5.1134, respectively which are
comparatively lower than theoretical model. Thus it can be
said that the proposed model can be used in the prediction
of propagation in urban and suburban centres with a
smaller deviations as compared to the theoretical model
from the measured data. To prove the validity of the
coefficients we verified that the assessed value of
coefficients in the regression equations are significant at
the level of 5%, proved by the p-value obtained for the
coefficients p(1),p(2),p(3),p(4) and p(5) ,which are less
than 0.005.
0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3-85
-80
-75
-70
-65
-60
-55
-50
-45
Radius
Pow
er
in d
Bm
Measured value
Best fit model
Theoretical model
Figure 4. Power estimated versus Distance from the Base
station (ONGC Township)
1.5 1.6 1.7 1.8 1.9 2 2.1 2.2 2.3 2.4-105
-100
-95
-90
-85
-80
-75
-70
Radius
Pow
er
in d
Bm
Measured value
Best fit model
Theoretical model
Figure 5. Power estimated versus Distance from the Base station
(OLD Panvel)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
-45
Radius
Pow
er
in d
Bm
Measured value
Best fit model
Theoretical model
Figure 6. Power estimated versus Distance from the Base station
( MTNL Panvel South)
542
0.8 0.9 1 1.1 1.2 1.3 1.4 1.5-100
-95
-90
-85
-80
-75
-70
-65
-60
-55
-50
Radius
Pow
er
in d
Bm
Measured value
Best fit model
Theoretical model
Figure 7. Power estimated versus Distance from the Base station
(Vrindavan)
0.2 0.4 0.6 0.8 1 1.2-85
-80
-75
-70
-65
-60
Radius
Pow
er
in d
Bm
Measured value
Best fit model
Theoretical model
Figure 8. Power estimated versus Distance from the Base station
( Milan CHS)
V. CONCLUSIONS
The proposed statistical model consists of a fine-tuning
of COST 231 Walfisch-Ikegami Model in environment of
propagation for signals of mobile communications cellular
in the suburban centre of the city of Panvel. The
methodology used for analysis provides, a roadmap for
establishing the modelling statistics of the signal made
through the parameters, viz., distance of mobile station
with respect to the base station, height and distance
between buildings which varies randomly with respect to
the specified mean depending upon the terrain structure
around the base station. The results obtained shows a good
average fit of the proposed model with respect to the
measured data collected from different urban and suburban
areas compared to the classic Walfisch-Ikegami Model.
With this, we propose the necessity of providing a
statistical management in the standard propagation models,
so as to mitigate the prediction error involved in the power
measurement of the urban and suburban centres.
ACKNOWLEDGMENT
The authors wish to thank the MTNL GSM cell,
especially MR. Wasane, Mr. Palkar and Mr. Jaiswal for
providing the required help. The authors also thank Ms.
Amruta Borse and Mrs. Sukanya Kulkarni for their support
at various measurement campaigns carried out.
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