Propagation models.pdf

8/14/2019 Propagation models.pdf

1/21

Propagat ion in free space

The ability of EM wave to propagate depends on the environmentparameters. (Vacuum, free space, obstructions, area topology, etc)

According Maxwells equations EMW radiate in all direction in the

speed of light (3.3 sec to travel 1km)

So we need to calculate the free space losses, which follow thefollowing equation

( )24log10

dLfs = Where

d is the distance to travel

is the wavelength of the EMW

In logarithmic form

Lfs= 32.44 +20log(f) +20 log (d)

Then

Lfs= Lo + 10 log (d)

Where is the slope of attenuation as a function of distance to travel.

Now we have to calculate the Power at the end path of thetransmitted wave (Mobile). Considering a pure free spacepropagation us ing isotropic antenna as a reference antenna. Wecan find the following parameters

Pt: transmitting powerPr: receiving powerGt: transmitting antenna gain (linear)Gr: Receiving antenna gain (linear)D: Distance between transmitting and receiving antenna

: Frequency wave length


2/21

Then the receiving power will equal to the transmitting powermultiplied by the gain of the trans and receiving antenna multiplied bythe frequency divided by the distance between the transmit and thereceiving antenna

Taking the logarithmic for both sides

Pr(dbm)= Pt(dbm) + 10 log (Gt) + 10 log(Gr) 20 log (D) 20 logf(MHz) XWhere X : 32.45 db if distance in Km

36.58 db if distance in milesExampleCalculate the Pr whenPt: 4.3 wattGt is 14 dbiGr is 3 dbiD is 10 km

Freq is 850 MhzWave lengthRepweat when Freq is 6 Ghz

( )

=2

4Pr

D

GrGtPt


3/21

Propagation over flat earth

Now we have omni or directed antenna different heights oftransmitting and receiving antennaThen we have more factorsHt: transmitting antenna heightHr: Receiving antenna heightThen the receiving power will be

( ) 2

2Pr

=

D

HrHtGrGtPt

There are two radios waves are reaching the mobileThe earth is super conductor no losses

In log form

Pr(dbm) = Pt(dbm) + 10log(Gt) + 10 log(Gr) + 20 log(Ht) + 20 log(Hr) 40 log(D)

ExampleCalculate the previos example with

Ht is 150 ftHr is 6 ftGt is 12 dbiGr is 2 dbiD is 4 milesPt is 4.3 watt


4/21

Knife edge model

As practical exercise for the rf propagation in urban and dense urbanareas the rf wave propagates depending on a lot of diffractions; so

Knife edge model is created so that to include the factor of diffraction

We have new parametersD1: distance between the tx antenna and obstructionDf2: distance between the obstruction and the rx antennaH: difference between (the los between the top of the obstacle andthe tx antenna) and (the los between the tx antenna and the rxantenna)

Steps for calculating the knife model

Calculate the Fresnel-Kirchoff diffraction parameter

( )

+=

21

212

dd

ddh

h= Height of the obstacle height of the rx antenna

Example

Calculate the additional losses due to the presence of the Knife-edgeobstructionRepeat if freq is 6 Ghz


5/21

Multiple KED: Epstein Paterson model

Loss from each obstruction is calculated separatelyTotal loss is the summation of all the calculated losses

ExampleCalculate the total losses for the last figD1 Is 0.6 kmD2 is 0.75 kmD3 is 1.2 kmD4 is 1.3 kmTx height is 40 mRx height is 2 mH1 is 46 m

H2 is 48 mH3 is 25 m


6/21

Foose factor

The attenuation of the obstruction varies as a function of the actualheight and shape

Foose factor is a empirical correction for the conservative behavior ofthe Esptein Paterson model

fos FnRSL =

nos is number of obstaclesFf the foose factor correction (Db/obstruction)

ExampleAssume the foose factor is 3.9 db/obsFind the losses due to the last example


7/21

Classical propagation model

Propagation models are essentially curve fitting exercises.

Propagation tests are conducted at different freqs, antenna heightsand locations over different periods and distancesThe received signal is analyzed using mathematical tools and is fittedto an appropriate curve. Formulae to match these curves are thengenerated and used as models.Frequently used Propagation models

Okumara

Okumara - Hata

Cost 231 Hata

Walfisch-Ikegame

Cost 231- Walfisch-Ikegame

Xlos (Motorola Proprietary model)


8/21

Okumara

In the early 1960s, a Japanese scientist by name Okumaraconducted extensive propagation test for mobile systems at different

frequencies. The tests were conducted at 200, 453,922,1310,140,1920 MHz. The tests were also conducted for different BTS andMobile antenna heights, at each freq, over varying distances betweenthe BTS and the mobile

The Okumara test are valid for

150-2000MHz

1-100Kms

BTS heights of 30-200m

MS antenna heights, typically 1.5m

These results of Okumara tests were graphically represented andwere not easy for computer-based analysis.

Fig 1 Okumara test results


9/21

Hata model

Hata took Okumara data and derived a set of empirical equations tocalculate the path loss in various environments. He also suggested

correction factors to be used in Quasi-open and suburban areas

The general path loss equation is given by:

( ) ( ) ( ) { } oBTSmBTSp

QdhhahfQQL +++= )log()log(55.69.44log82.13log21Where

=pL path loss

=f Freq in MHz=d Distance between BTS and the mobile (1-20Km)

=BTS

H Base station height in meters (30 to 100 m)

=mH Mobile height (1-10m)( ) =hma Correction required if mobile height is more than 1.5 meter

and is given by

( ) ( ){ } ( ){ }8.0log56.17.0log1.1 = fhfhma m For urban areas

( ) ( ){ } 97.475.11log2.3 2 = mm hha For dense urban areas55.691=Q For freq (150-1000 Mhz)

3.461=Q For freq (1500- 2000 MHz)

16.262=Q For freq (150-1000 Mhz)

9.332 =Q For freq (1500- 2000 MHz)

0=oQ For Urban area3=oQ For Dense urban area


10/21

Corrections to Okumara-Hata Model

The formulae we used for the Okumara model were the urbanenvironment. The model gets modified if the environment is semi

urban, suburban or open area.

Corrections

4.5)28/(log2 2)( = flL Basicpsub

94.40)log(33.18))(log(78.4 2)( += ffLL basicpopen

94.35)log(33.18)(log(78.4 2)( += ffLL BasicpQuasi

ExampleUse Okumara model to find the RSL at 2.3 miles from the BTSoperating ate 870 MHz using the following data

Radiation center line of the BTS = 40mHeight of the MS = 3mTerrain elevation at the location of the BTS = 340m

Average height of the terrain = 312mTransmitting power = 19.5 w

BTS gain = 10 dbMs gain = 0 dbArea = Urban area

SolutionThe free space loss is calculated by the following equationLfs= 32.45 +20log(2.3*1.609)+20log(870)-10=92.61db

The basic median attenuation is determined from figure

Amu = 24 db

The effective height of the BTS transmitting antenna

hte = 40+340-312= 68 m

Correction for the base station antenna height is determined fromfigure


11/21

Htu=-12 db

The total path loss is equal toPl= 92.61 +24+12=128.61

RSL=10log(19.5*1000) 128.61= -85.7dbm

ExampleUse the pervious data to get the RSl by the Hata equations

SolutionThe mobile antenna height gain can be obtained as:a(hm)= (1.1log(870)-0.7)*3 (1.56log(870)-0.8)=3.81 db

Qo=0 urban areaThe effective height of the BTS transmitter is given ashte= 68mRSL= 10log(19.5*1000) + 10 +69.55 26.16log(870) + 3.81 +13log(68) (44.9 6.55log(68)) log(2.3*1.609) = -84.61 dbm

If you make comparison between the two solutions there is anegligible amount.

ExampleCalculate the cell radius of the site has the following parametersFreq= 900 MHzBTS height= 30mMobile Height=3mBTS ERP=55dbmRSL at the mobile = -75 dbm

Attenuation slope= 3.5

RSL= ERP Lps

-75=55-LpsLps=130 dbm

Lps= Lo + 10log(d)Lo= 69.55 +26.16log(900) 13.82 log(30) a(hm)a(hm)= 1.1(log(900)-0.7)*3 (1.56log(900) 0.8)Lo=122.57 db


12/21

From RSL =ERP (Lo + 10log(d))

Then 130 122.57 = 10log(d)

Where = 3.5

Then d = 1.629 Km


13/21

Cost 231-Hata model

The cost 231-sub group on propagation models proposed animproved propagation model for urban areas to be applied above

1500 MHzHence this model can be used for planning DCS 1800 systems.Like Hata model, the cost 231 Hata model is also based on themeasurements of Okumara.The general path loss equation for Cost 231-hata model is identical tothe Hata model, excepting that the constants Q1 and Q2 havedifferent values.

The general path loss equation is given by:

{ } 0

2

21

)log()log(55.69.44)()log(82.13)log( QdhhahfQQLBTSmBTSp

+++=

3.461=Q For freq from 1500 to 2000 MHz

9.332=Q For 1500 to 2000 MHz

00=Q For urban

30=Q For dense Urban


14/21

Walfisch-Ikegami Model

Line of sight propagation:This is useful for dense urban environment. The model is essentially

based on Okumara studies but takes into account several factors likebuilding density, average height of buildings, street widths and so on.

The simplest model is to assume that the antenna height for the BTSis generally below rooftop so that the signals are guided through astreet canyon. It is assumed the there a LOS between the MS andthe BTS.


15/21

The path loss is given by:

)log(26)log(206.42 dfLLOS ++=

This can be written as LOS equation as:

)log(10 dLL oLOS +=

Where, Lo=42.6 + 20 log (f) and is 2.6

The value of attenuation slope is 2.0 in free space. In dense urbanenvironment, under LOS conditions, signals are actually guidedbetween, thereby causing a wave-guide effect. (Which is similar tofree space propagation).


16/21

COST 231 Walfisch-Ikegami ModelNON LOS modelHere, we assume that the BTS antenna is above roof level for anybuilding within the cell and that there is no LOS between the BTS and

the MS

We define the following parameters

WIs the distance between street MS and Building

mh MS height

Bh BTS antenna height

rh Roof height

Bh Difference between rooftop and the BTS antenna height

mh Difference between MS and rooftop

For the sake of simplicity, we assume that the environment hasbuildings of uniform height. For MS on the street, the signalundergoes diffraction from rooftop and also multiple diffraction due tothe surrounding buildings.


17/21

The general form is

LMDRFTFSp LLLL ++=

Where

=FsL Free space loss= 32.44 + 20log(f) + 20log(d)=RFTL Roof top diffraction loss=MDBL Additional loss due to multiple diffraction due to

surrounding buildings

)()log(20)log(10)(109.16 LhfWlofL mRFT +++=where

mrm hhh =

L()= Losses due to elevation angle

357.010)( +=L For 0


18/21

)(1518r

bd h

hK

=

+= 1925

7.04 f

Kf For suburban areas

+= 1

9255.14 f

Kf For urban areas

Bh BTS antenna height

rBB hhh =

For simplified calculations, we can assume Ka=54 and Kd=18.

Fresnel Zone

In Multipath environment, the signal suffers from unpredictable deepfades. To facilitate an estimation of the Multipath effects, we havestudied various propagation models

In all cases we have seen that the path loss can be characterized bythe straight-line equation

)log(10 dLL oP +=

From the above equation we can find that there is a certaincombination of parameters for which the path loss is not sensitive to

. But it is not possible to achieve this in reality

However, there exists a Fresnel zone point within which LOSconditions are met and beyond which Multipath effects come into play

Such a point is called Break Point.


19/21

To explain the concept of break point we use a 2 ray model.We are going to define the following parameters

hbBTS antenna heighthmMS heightd distance between the BTS and MSd1 reflected pathd2 direct path

21 ddd =

( ){ } ( ){ } 21

2221

22

dhhdhhdmBmB

+++=

Using binomial series we can simplify the above equation as

dhhdmB /2=

When dhh mB /)( is


20/21

apart from each other. The diffraction is maximum when the

difference between the direct ray and the diffracted is /2.

Then we can write

2//2 == dhhd mB Or

/4 mBo hhD =

Now Do is the break pointThe path loss slope is similar to LOS path loss within the break point.Diffractions and Multipath phenomena usually happen beyond thispoint.


21/21

Date post:	04-Jun-2018
Category:	Documents
Upload:	larissa-lissina
View:	229 times
Download:	0 times

Propagation models.pdf

Documents