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A New Generic Model for Signal Propagationin Wi-Fi and WiMAX Environments
Rana EzzinePRINCE Research Group
ISITCHammam Sousse, [email protected]
Ala Al-FuqahaComputer Networks’ Group
Engineering and Applied Sciences College, Western Michigan University
Michigan, USA
Rafik BrahamPRINCE Research Group
ISITCHammam Sousse, Tunisia
Abdelfettah BelghithResearch Pole RIM – CRISTAL Laboratory
ENSIMannouba, Tunisia
Abstract—The ability to accurately predict radio propagationbehavior for wireless communication systems, such as cellularmobile radio, is becoming crucial to system design. Since sitemeasurements are costly, propagation models have beendeveloped as suitable, low-cost, and convenient alternative. Inthis paper, we will propose a new generic signal propagationmodel for Wi-Fi and WiMAX environments. To develop thismodel we used existing models which are classified as: Free spacemodels and land propagation models. This includes differenttypes of loss: path loss, slow fading (shadowing) and fast fading.Our aim is to have a flexible model to be applicable in indoor andoutdoor environments. Experiments carried out for indoor Wi-Fiand outdoor WiMAX cases have shown excellent results for theproposed model.
Keywords-Curve fitting, fast fading, path loss, signalpropagation models, slow fading, parameters estimation, Wi-Fi,WiMAX
.
I. INTRODUCTION
The success of wireless technologies has led to animportant interest to predict radio propagation characteristics inurban, suburban and open areas. As the explosive growth ofusing wireless devices continues, it is essential to be able todetermine optimum base stations and antennas locations andtypes. It is therefore important to develop signal propagationmodels for Wi-Fi and WiMAX environments in the aim toestimate the received signal power by the user. Existing modelscan be classified into two classes: models for free spacepropagation and models for land propagation.
II. FREE SPACE PROPAGATION
First space is an ideal propagation medium. The Free spacemodel is the simplest one. It only assumes direct path betweentransmitter t and receiver r. The received power Pr depends ontransmitted power Pt, transmitter and receiver antennas gain(Gt, Gr), wavelength and distance d between the two nodes.All parameters, except distance d, are system constantparameters. The Free space model is also known as Friismodel. In this model received signal power, rP is expressed bythe following equation:
( ) trt
FSr Pd
GGP ×××
= 2
2
, 4π
λ (1)
III. LAND PROPAGATION
Propagation in free space and without obstacles is the idealcase. But when radio waves encounter an obstacle, severalpropagation effects occur: reflection, diffraction and scattering.The phenomenon of reflection occurs when obstacles are largerthan signal wavelength. Obstacles in this case can be earthsurface, tall buildings, and large walls. Diffraction takes placewhen the obstacle is a surface with sharp irregular edges.Scattering occurs when obstacles are smaller than thewavelength, for example foliage or street signs. In this case weuse land propagation equation and the received signal power isexpressed as:
978-1-4244-2829-8/08/$25.00 ©2008 IEEE
LPGGP ttr
LPr××
=, (2)
where L represents the propagation loss (clearly L >1).Wave propagation in wireless environments is characterized bythree aspects: path loss ( PL ), slow fading ( SL ), and fast
fading ( FL ). We can therefore express L as:
FSP LLLL ××= (3)
A. Path Loss
The path loss is the average propagation loss over a widearea. It depends on macroscopic parameters such astransmitter-receiver distance and land profile. We can expressit as follow:
αdALP ×= (4)
where A and α are propagation constants. Based onOkumura curves and to predict propagation constants, Hatapresented an empirical formula for PL in three cases: urbanarea, suburban area and open area.
• Urban area
In this case, the path loss PUL can be expressed as fellow:
[ ][ ] dh
hhfL
b
mbcPU
1010
1010
loglog55.69.44log82.13log16.2655.69
++−−+= α
(5)
where PUL is in dB, cf is carrier frequency in MHz, bh is
the effective base station antenna height, mh is the mobile
station antenna height and [ ]mhα is a correction factor for
the mobile antenna height. Values of [ ]mhα are calculateddifferently for large cities or for medium and small cities[1].• Suburban area
Suburban area path loss PSL is given in the following way:
4.528
log22
10 −
−= c
PUPSf
LL (6)
• Open area
Here, corresponding path loss POL is expressed byfollowing equation:
[ ] 94.40log33.18log78.4 102
10 −−−= ccPUPO ffLL (7)
B. Slow fading
Slow fading is caused by long term spatial and temporalvariations over distances large enough to produce big variationpath between base station and mobile station. Slow fading isalso called Log-normal fading or shadowing because itsamplitude has a log-normal pdf [1].
C. Fast fading
Fast fading is of short-scale nature due to fast spatialvariations. A number of fast fading models exist, for exampleRayleigh, Ricean, Nakagami and Weibull [2][9] [11].
IV.EXAMPLES OF SIGNAL PROPGATION MODELS
In this section we present two frequently used landpropagation models.
A. Okumura and al. model
This is one of the most widely used models forpropagation in urban areas. The model can he expressed byfollowing expression:
(8)
where 50L is the median value of the propagation path loss,
FL is the free-space propagation loss, muA is the medianattenuation in the medium relative to free space atfrequency f , and d corresponds to the distance between the
base station and the mobile station. )( tehG and )( rehG are thegain factors for the base-station antenna and the mobileantenna respectively. teh and reh are the effective heights ofthe base-station and the mobile antennas (in meters),respectively. AREAG is the gain generated by the environment
in which the system is operating. Both ( )dfAmu , and
AREAG can be found from empirical curves.
The major disadvantage of Okumura et al.’s model is its slowresponse to rapid changes in terrain profile.
B. Two-ray ground model
The Two-ray Ground model is an improved version of thefree space model. It considers the direct ray between senderand receiver, but also ground reflection. As with the free spacemodel, both nodes are assumed to be in Line Of Sight (LOS).
AREAretemuF GhGhGdfALdBL −−−+= )()(),()(50
Up to a crossover distanceλ
π rtTh
hhd ××=
4, the Two-ray
Ground model is equal to the free space model. Suppose thatthe transmitter and receiver antenna heights, th and
rh respectively, are constants. Beyond the distance, theground reflection destructively interferes with the direct rayand further reduces the field strength. The received signalstrength grows then proportionally to 4−d .
Just like the free space model, the distance betweentransmitter and receiver is the only parameter in Two-rayGround model. Equation 9 represents the Two-ray Groundmodel:
If d < Thd : FSrtrt
TRr Pd
PGGP ,2
2
, )4(=
×××=
πλ
If Thdd ≥ : 4
22
, dPhhGG
P trtrtTRr
××××= (9)
C. Shadowing model
For both free space model and two-ray ground model, thesender-receiver distance is the only variable parameter. Thisforms a circular coverage around a sending node and a sharprange limit. Beyond this range, no further reception is possible.To introduce random events, the shadowing model utilizes arandom variable X. The shadowing model requires a referencedistance 0d to calculate the average received free space signal
strength )( 0, dP FSr . In equation 10, X is normally distributedwith an average of zero and a standard deviation (calledshadow deviation).
XFSrSHr d
ddPP 10)(0
0,, ×
×=
−β
(10)
where the exponent β depends on the propagationenvironment. For open-space area, like in the free spacemodel, we have =2. For urban areas with obstacles, isbetween 2.5 and 3.5.
The shadowing model introduces some kind ofunpredictability for data transmissions. Correct receptions areguaranteed for close proximities and impossible over longdistances, whereas correct receptions are unpredictable formedium distances. Nevertheless, the correct reception areastill forms a disc when considering many transmissions [10].The unpredictability is a severe disadvantage of this model.Signal strength variations are not direction-dependent andpossible errors can occur during every transmission. It varies
significantly between consecutive transmissions and evendiffers for the reception of the same transmission at differentreceiver.
D. COST-231-Walfisch-lkegami model
This model utilizes the theoretical Walfisch-Bertoni modeland is composed of three terms :
If 0fmsdrts LL + : msdrtsb LLLL ++= 0
If 0≤+ msdrts LL : 0LLb = (11)
Where :- 0L represents the free space loss,
- rtsL is the “roof top to street diffraction and scattering loss”,
- msdL is the “multi screen diffraction loss”.
The free space loss is given by:
fdL log20log204.320 =+= (12)
where d is the radio path length (in km) and f is the radiofrequency (in MHz).
rtsL is function of the street width (in m) and the differencebetween the height of the building on which the base stationantenna is located, and the height of the mobile antenna.
More detailed discussions can be found in [2] and [11]. Inthe following section we present our model.
V. A GENERIC RADIO SIGNAL PROPAGATION MODEL
The models presented above are valid for specificenvironment and working conditions. So for a given situationwe are not sure that we are using the appropriate model.Therefore, our idea is then to design a generic model whichtakes in to consideration most types of signal attenuation. Inthe model we propose, the signal power at the receiver GRrP ,
takes on the following expression:
DdCdBPAP t
GRr +×+××
=βα )(log10
, (13)
As can be seen from (13), GRrP , (in mw) depends as usual
on distance d (in m) between base station and mobile station.The transmitted signal power (in mw) at given base station is
assumed fixed. A , B , C , D ,α and β are propagationconstants that have to be estimated. This way, the modelingproblem has become a parameters estimation problem. Anumber of parameter estimation techniques exist. We havechosen to use Levenberg-Marquardt algorithm (LMA), whichis a well known and popular curve-fitting algorithm [3].
LMA provides a numerical solution to the problem ofminimizing a function, generally nonlinear, over a space ofparameters of the function. These minimization problems ariseespecially in least squares curve fitting and nonlinearprogramming. The LMA is more robust than the Gauss-Newton algorithm (GNA), which means that in many cases itfinds a solution even if it starts far off the final minimum. Onthe other hand, for well-behaved functions and reasonablestarting parameters, the LMA tends to be a bit slower than theGNA [3].
A. Measurement environments and scenarios
We have taken measurements at the Engineering andApplied Sciences College in Western Michigan University,USA. The building where measurements were taken iscomposed of two floors and contains a dozen of access points.We have considered four scenarios: Wi-Fi measurementsinside and outside the building and WiMAX measurementsinside and outside the building. Actually we realised the twoscenarios: Wi-Fi indoor the building and WiMAX outdoor thebuilding.
In this zone we considered some measurement points so thatwe had an empirical data base. Each measurement point isdefined by two sets. The first set is the set of distancesbetween the measurement point and all access points whichare in the building. The second set is the set of received signalpowers by the measurement point from each access point. Forthe transmitted power we consider that tP = mw100 .
B. Results and Discussion
To achieve our work and to reach our aim we implementthe parameter estimation program for each access point. So wehave (A, B, C, D, α , β ) for each access point and wecalculate received power by each measurement point from thisaccess point.
Figure 1.a and Figure 1.b show the experimental data basecurve and the curve obtained from calculated values ofreceived power considering the new model.
AP1 : EXP vs LMA
00.000020.000040.000060.000080.0001
0.000120.000140.00016
0 50 100 150
distance (m)
Pow
er (m
W)
Exp results (mW)LMA results (mW)
Figure 1.a
AP2 : EXP vs LMA
-0.000050
0.000050.0001
0.00015
0.00020.00025
0.00030.00035
0 20 40 60 80
distance (m)
pow
er (m
W)
Exp resultsLMA results
Figure 1.b
Figure 1. Experimental curves VS curves from the model
In two figures we remark that two curves are very close.We conclude that the estimate received power by the model isvery close to the measured received power.
VI. CONCLUSION AND FUTURE WORK
In this paper, we proposed a new generic model for signalpropagation in Wi-Fi and WiMAX environments. The modelwas validated for indoor Wi-Fi and outdoor WiMAX cases.Future work would be in a first step to validate this model forthe two other cases which are outdoor Wi-Fi and indoorWiMAX cases. Then, as a second step, we will develop asimulator to have a random data base similar to the empiricaldata base and which will be used as input for the implementedprogram using LMA. Comparison between the two resultsshould provide more validation for the new model.
ACKNOWLEDGMENT
Support for this work was provided by PRINCE researchunit, ISITC-HS, University of Sousse, Tunisia. Part of thiswork was carried out during a stay of the first author (R.Ezzine) within the Computer Networks’ Group, Engineeringand Applied Sciences College, Western Michigan University,USA.
REFERENCES
[1] D. P. Argrawal and Q.-A. Zeng, “Introduction to wireless and mobilesystems”, second edition, Brooks/ Cole (Thomson Learning), August2002.
[2] T. K. Sarkar, Z. Ji, K. Kim, A. Medouri, and M. Salazar-Palma, “ASurvey of Various Propagation Models for Mobile Communication”,IEEE Antennas and Propagation Magazine, Vol. 45, No. 3, June 2003,pp. 51 – 82.
[3] M. I. A. Lourakis, “A Brief Description of the Levenberg-MarquardtAlgorithm Implemened by levmar”, February 11, 2005. Available:http://www.ics.forth.gr/~lourakis/levmar/levmar.pdf
[4] http://www.curvefit.com/
[5] “NLOS Optimization Outfits WiMax for Wide Coverage”, RTCMagazine, March 2005.
[6] IEEE 802.16-2004, IEEE Standard for local and metropolitan areanetworks, Air Interface for Fixed Broadband Wireless Access Systems,Oct 2004.
[7] H. Yaghoobi, “Scalable OFDMA Physical Layer in IEEE 802.16WirelessMAN”, Intel Technology Journal, August 2004, vol.8, no.3,pp.201–212.
[8] E. Grenier, “Signal propagation modeling in urban environment”, whitepaper, ATDI, June 2005.
[9] F. Belloni, “Physical Layer Methods in Wireless CommunicationSystems”, Fading models course, Helsinki University of Technology,November 2004. Available:
http://www.comlab.hut.fi/opetus/333/2004_2005_slides/Fading_models.pdf
[10] I. Stepanov, D. Herrscher and K. Rothermel, “On the Impact of RadioPropagation Models on MANET Simulation Results”, Institute ofParallel and Distributed Systems (IPVS), Universität StuttgartUniversitätsstr. 38, 70569 Stuttgart, Germany.
[11] T. S. Rappaport, “Wireless Communications, Principles and Practice”,second edition, Prentice Hall, March 2008.
