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,,ankitsagar@gmail.com,dd_ambawade@rediffmail.com,bklande,rddaruwala@vjti.org.in

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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