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Path Loss Model in Mobile Cellular Network

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Okumura-Hata Model

Walfish-Ikegami Model

Lee’s Prediction Model

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• Microcellular areas span a few Kms.

• Okumura in 1968 drew some path-loss curve in the range of 100MHz to 1920 MHz

• Masaharu Hata developed empirical path-loss model based on measurement of Okumura known as Okumura-Hata model.

• Here separation between BS and MS is greater that 1Km.

Okumura-Hata Model

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Empirical formulation of data provided by the Okumura model and is valid for frequencies in the range 150MHz-1500MHz

dh

hahfdBUrbanL

BS

MSBScm

log)log55.69.44(

)()(log82.13)(log16.2655.69))((

For large city,

dBfhfha cMScMS )8.0log56.1()7.0log1.1()(

For small and medium city,

MHzffordBh

MHzffordBhha

cMS

cMSMS

300;9.4)75.11(log2.3

300;1.1)54.1(log29.8)(

2

2

5

dBfdBUrbanLdBSuburbanL cmm 4.5)]28/[(log(2))(())(( 2

dBffdBUrbanLdBruralL ccmm 94.40log33.18)}{log(78.4))(())(( 2

For suburban and open rural area,

The model is suitable for a distance above 1 Km. The model does not support path specific correction

CoverageFrequency: 150 MHz to 1500 MHzMobile Station Antenna Height: between 1 m and 10 mBase station Antenna Height: between 30 m and 200 mLink distance: between 1 km and 20 km.

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ExampleFrequency: 900MHzPropagation Environment: UrbanBS antenna height: 50mMS antenna height: 1.5mCell radius: 5KmAns. a(hm) =0.001dB ))(( dBUrbanLm

= 177.7077dB

LSuburban = 167.7651dB LRural =149.2012dB

fc=900;% Carrier frequency MHzhBS=50;%BS antenna height mhMS=1.5;%MS antenna height md=5;% Distance Kma_hMS=3.2*((log10(11.75*hMS))^2)-4.97;LUrban = 69.55+26.16*log10(fc)-13.82*(log10(hBS))+(44.9-6.55*log10(hBS))*log(d)-a_hMS;LSuburban= LUrban-2*(log10(fc/28))^2-5.4;LRural= LUrban-4.78*(log10(fc))^2+18.33*log10(fc)-40.94;

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%Code by Imdadfc=900;% Carrier frequency MHzhBS=100;%BS antenna height mhMS=2;%MS antenna height md=1.1:0.4:6;% Distance Kma_hMS=3.2*((log10(11.75*hMS))^2)-4.97;LUrban = 69.55+26.16*log10(fc)-13.82*(log10(hBS))+(44.9-6.55*log10(hBS))*log(d)-a_hMS;LSuburban= LUrban-2*(log10(fc/28))^2-5.4;LRural= LUrban-4.78*(log10(fc))^2+18.33*log10(fc)-40.94;plot(d,LUrban, 'r>:', d, LSuburban, 'ms:', d, LRural, 'bd:')legend('Urban', 'Suburban', 'Rural')xlabel('Distance in Km')ylabel('Path loss in dB')title('Okumura-Hata Model')grid on

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1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 690

100

110

120

130

140

150

160

170

180

Distance in Km

Pat

h lo

ss in

dB

Okumura-Hata Model

Urban

Suburban

Rural

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Walfish-Ikegami Model

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The Walfish–Ikegami model is an empirical propagation model for an urban area, which is especially applicable for micro cells but can also be used for macro cells.

Model Parameters:The mean value for street widths (w) is given in metres and the road orientation angle (θ or φ) in degrees. The mean value for building heights (hroof) is an average over the calculation area and is given in metres. The mean value for building separation (b) is calculated from the centre of one building to the centre of another building and is also given in metres.

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Walfish–Ikegami model is suitable for frequencies 800MHz to 2000 MHz where distance can be very small like 200m. Range of BS antenna height 4 to 50m and that of MS is 1 to 3m. Distance in the range of 20m to 5Km.

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For LOS case,

Lm(db) = 42.6 +26log(d) + 20log(fc); d ≥ 20m

For NLOS case, we have to consider,

Hroof = Height of roof-top

ΔhBS = hBS - hroof

ΔhMS = hroof - hMS

w: width of street in meter

b: Building separation in meter along the radio path

φ: Road orientation w.r.t. the direction of radio propagation in degrees incident angle relative to the street).

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NLOS path loss composed of three terms,

LP(DB) = L0 + Lrts + Lmsd

The model works best for the BS much taller than the surrounding buildings.

L0: Free space path loss = 32.4 + 20log(d) + 20log(fc)

Lrts: roof-street diffraction and scatter loss =

-16.9 -10log(w) + 10log(fc) + 20log(Δhm) + Lori

Lori is the street orientation loss:

00

00

0

9055;)55(114.00.4

5535;)35(075.05.2

350;354.010

)(

oriL

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Lmsd = multiscreen diffraction loss

= Lbsh+ Ka + Kdlog(d) + Kflog(fc) - 9log(b)

roofBTS

roofBTSroofBTS

bsh hh

hhhhL

;0

;)11log(18

roofBTSroofBTS

roofBTSroofBTS

roofBTS

a

hhandKmddhh

hhandKmdhh

hh

K

5.0;)(6.154

5.0);(8.054

;54

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roofBTS

MSroof

roofBTS

roofBTS

d hhhh

hh

hh

K;1518

;18

centersurban

f

centerssuburbanandcitymediumf

K f

;1925

5.1

;1925

7.0

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The parameter Ka increases the path loss in case the BTS is below the rooftop. The parameters Kd and Kf are for adjusting the correction between the distance and frequency with multiscreen diffraction.

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Example:1

Find cell radius for the following parameters.

fc =1800MHz

Street width (w) = 20m

Spacing between buildings (b) = 40m

Average roof height (hroof) = 40m

Mobile antenna height (hm) = 2m

BS antenna height (hb) = 40m

Street orientation φ = 900

Allowable path loss =140dB

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ΔhBS = hBS – hroof = 40 – 40 = 0

ΔhMS = hroof – hMS = 40 – 2 = 38m

Orientation loss,

Lori = 4 - 0.114(φ - 55) = 0.001

Lbsh = -18log(11) + (hBS - hroof) = -18.75dB

Ka = 54

Kf = 4 + 1.5(fc/925 -1) = 5.42

The roof street diffraction and scatter loss,

Lrts = -16.9 -10log(w) + 10log(fc) + 20log(ΔhMS) + Lori

= -16.9 -10log(20) + 10log(1800) + 20log(38) + 0.001

=34.25dB

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Free space path loss,

L0 = 32.4 + 20log(r) + 20log(fc) = 97.5 + 20log(r) dB

Multi screen diffraction loss,

Lmsd = Lbsh+ Ka+ Kflog(fc) - 9log(b) = 38.47 + 18log(r) dB

Allowable path loss,

140 = L0 + Lmsd + Lrts= 97.5 + 20log(r) + 38.47 +18log(r) + 34.25

Or, 38log(r) = -30.23

Or, r = 0.16Km = 160m

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Lee’s Path Loss Model

Lee’s model can be used to predict area-to-area path loss. The

model consists of two parts,

a) Path loss prediction for a specified set of conditions

b) Adjustment factors for a set of conditions different from the specified one

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ro = 1mil = 1,6 km

rPro

Pr

P Pr

r

f

fr roo o

n

o

. . .

o

ooror f

fn

r

rPP

log10.log10. o

ooror f

fn

r

rPP

log10.log10.

Received power, In (dB),

Lee’s Prediction Model

The model requires two parameters:

a) Power at 1mile interception Pro in dB.

b) Path loss exponent γ

n is a constant between 2 and 3 depend on geographical location and operating frequency

0 is an adjustment factor for different set of conditions

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Carrier frequency, fc = 900MHz

BS antenna height = 30.48 m (100ft)

MS power at the antenna =10W

BS antenna gain = 6dB above dipole gain

MS antenna gain = 0dB above dipole gain

MS antenna height = 3 m (10ft)

Specified conditions

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o = 1 . 2 . 3 . 4 . 5

Lee’s Prediction Model

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1 (m) 48.30

(m)height antennastation base New

2

))(100

(ft)height antennastation base New

ft

v

3

(m)height antenna MS New2

v

01

(ft)height antenna MS New

5

10

ii α0 in dB,

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(watts) 10

(watts)power transmittNew3

4

2antena dipole gain w.r.t antenastation base New4

1

MSat factor correctiongain antena 5

There is a 3dB gain received from an actual 4-dB gain antenna at the mobile unit in a suburban area and less than 1-dB gain received from the same antenna in an urban area fro adjusting α5

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Lee’s Prediction Model

Correction factor to determine v in a2 v = 2, for new mobile-unit antenna height > 10 m

v = 1,for new mobile-unit antenna height < 3 m

Terrain P0γ(dBm) γ

Free space -45 2

Open area -49 4.35

Suburban area -61.7 3.84

Urban area(New York) -64 4.31

Urban area(Tokyo) -84 3.05

Parameters in Lee’s path loss model

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For suburban area,

Pr = -61.7-38.4log(r) - nlog(f/900) + α0

α0 = 20log(hBS) +10log(Pt) + gBS + gMS +10log(hMS) - 64

Here transmit power in Watt, height of antenna in feet and gain of antenna in dB

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%Lee's path loss modelv=3;Pt=55;% in wattsn=2;gBS=12;hBS=200;hMS=12;f0=900; %in MHzf=1200;alpha1= (hBS/30.48)^2;alpha2= (hMS/10)^v; alpha3= (Pt/10);alpha4= (gBS/4);alpha5= (1/1);d=1:0.4:6;

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gama=3.84;%Suburban arear0=1.609; % in KmPr0= -61.7; %in dB for Suburban areaPr1=Pr0-gama*10*log10(d/r0)-n*10*log10(f/f0)+(10*log10(alpha1)+10*log10(alpha2)+ 10*log10(alpha3)+ 10*log10(alpha4)+ 10*log10(alpha5));Loss1=10*log10(Pt)-Pr1;gama=3.05;%urban area ToKyoPr0= -84; %in dB for urban area ToKyoPr2=Pr0-gama*10*log10(d/r0)-n*10*log10(f/f0)+(10*log10(alpha1)+10*log10(alpha2)+ 10*log10(alpha3)+ 10*log10(alpha4)+ 10*log10(alpha5));Loss2=10*log10(Pt)-Pr2;gama=4.35;%for open areaPr0= -49; %in dB for open areaPr3=Pr0-gama*10*log10(d/r0)-n*10*log10(f/f0)+(10*log10(alpha1)+10*log10(alpha2)+ 10*log10(alpha3)+ 10*log10(alpha4)+ 10*log10(alpha5));Loss3=10*log10(Pt)-Pr3;plot(d,Loss1, 'r>:', d, Loss2, 'ms:', d, Loss3, 'bd:')legend('Suburban', 'Urban', 'Rural or Open area')xlabel('Distance in Km')ylabel('Path loss in dB')title('Lee’s Model')grid on

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1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 620

30

40

50

60

70

80

90

Distance in Km

Pat

h lo

ss in

dB

Lee’s Model

Suburban

UrbanRural or Open area