1

3.9 Predictable Link Budget Design using Path Loss Models

Most RF propagation models are derived from combined

(i) analytical studies

(ii) experimental methods

Empirical Approach – measured data is fitted to a curve or an analytical expression

• uses field measurements• implicitly accounts for all factors (known and unknown)• model generally not valid for all frequencies or environments

Classical Models have evolved to predict large scale path loss• used to estimate receive signal strength as a function of distance• used along with noise analysis techniques used to predict SNR for RF mobile systems

2

Median Path Loss Determination• estimate receive power at distance d from transmitter

Ẽ = Ẽd

N

kkk jL

1exp

Ẽ = total received electrical field (V/m)

Ẽd = electric field of equivalent direct path

N = number of paths between T and R

Lk = relative loss of kth path

k = relative phase shift of kth path

if LOS exists L0 = 1 and 0 = 0

eAE

120

~ 2

Pr(d) =

3

n

t

r

d

d

dP

dPdPL

0)(

)()( (3.67)

00 log10)()(

d

dndPLdBPL (3.68)

d0 = close in reference distance, often determined emperically

d = transmitter - receiver separationn = path loss exponent - indicates rate of path loss increase with d0

3.9.1 Log Distance Path Loss Model

• average received power decreases logarithmically with distance • theory & measurements indicate validity for indoors & outdoors

• distance dependent mean path loss - over significant distances

(1) Average Large Scale Path Loss Model

4

Environment d0 large cellular 1km

microcell 1m-10m

Free Space Reference Distance, d0, • always in antenna’s far-field - eliminate near field effects for reference path• must be specified for different environments

Reference Path Loss, PL(d0) calculated using either

(i) free space path loss (eqn 3.5)

(ii) field measurements at d0

Path Loss Exponent, n

Environment n Environment n free space 2 In building LOS 1.6-1.8

Urban-cellular 2.7-3.5 Obstructed in Building 4-6Shadowed Urban Cellular 3-5 Obstructed in Factories 2-3

5

3.9.2 Log Normal Shadowing

(3.69b)Pr(d) (dB)= Pt(d) (dB) - PL(d) (dB)

(3.69a)PL(d) = )(dPL

σΧd

dndPL

00 log10)(PL(d) (dB) =

• antenna gains included in PL(d)• = zero-mean Gaussian distributed random variable (in dB) • = standard deviation of

• surrounding clutter isn’t considered by log distance model

• averaged received power (eqn 3.68) is inconsistent with measured data

• measured PL(d) at any location is random, with log normal distribution

about (normal distribution of log10(•) ))(dPL

6

Log Normal Distribution - describes random shadowing effects

• for specific Tx-Rx, measured signal levels have normal distribution about distance dependent mean (in dB)

• occurs over many measurements with same Tx-Rx & different clutter standard deviation, (also measured in dB)

Lognormal Model For Local Shadowing

• typically, dB ranges from 5-12

• let u = median path loss (dB) at distance d from transmitter

distribution xdB of observed path loss has pdf given by:

f(xdB) = 22/exp2

1dBdB

dB

ux

Pr[xdB = x] =

Pr(xdB > x) =

x

dBdB dxxf )(it follows that

x

dBdB

dB

ux 22/exp2

1 =

7

median 50% of samples expected to be > median & 50% expected to be < median

• all curves intersect at median

Log Normal Graph: Pr(xdB > x) vs Gain/Loss Relative to Median Path Loss

• shown for dB = 4,6,8, 12P

r (G

ain

< A

bsci

ssa)

Gain relative to Median Path Loss(dB)-12 -10 -8 -6 -4 -2 0 2 4 6

1

0.5

10-1

10-2

10-3

10-4

dB = 12 dB

8 dB

6 dB

4dB

dB loss relative to median path

% time

6dB > 10dB 1%12dB > 10dB 10%4dB > 7dB 1%

8

& n are derived from measurements using linear regression• minimizes difference between measured & estimated path loss • minimized in a mean-square sense over many measurements & d’s

Path Loss Model Parameters for arbitrary location & specified Tx-Rx • d0 – close in reference distance

• - clutter standard deviation• n – path loss exponent

Used for system design & analysis simulations to provide estimated Pr(d) at random locations

9

Q(z) =

Q-function is used to determine probability that PR(d) threshold

z

x

dxe 2

2

2

1

3.70a

3.70b where Q(-z) = 1- Q(z)

3.71Pr [Pr(d) > ] =

)(dPQ r

(ii) Pr(d) > or Pr(d) < is determined from CDF

3.72Pr [Pr(d) < ] =

)(dPQ r

(i) PL(d) is RV with a normal distribution in dB about

• as a result, Pr(d) inherits these characteristics

)(dPL

10

3.9.3 Determination of % Coverage Area • in a given coverage area, let = desired receive signal level – could be determined by receiver sensitivity (or visa versa)

• random shadowing effects cause some locations at d to have received power, Pr(d) <

Determine boundary coverage vs % area covered within a boundary, assuming

• a circular coverage area with radius R from base station• likelihood of coverage at cell boundary is known (given)• d = r represents radial distance from transmitter

U() =

ddrrrPR

R

r ])(Pr[2

1 2

0 02

dArPR r ])(Pr[

2

12

U() =

(3.73)

useful service area (coverage area): U() = % area with Pr(d) >

11

Left Axis = % area with Pr(r) > (coverage area-use 3.73)

Right Axis = Pr[Pr(r) > ] (boundary coverage-use 3.68)

/n = std deviation of path loss exponent

Pr[Pr(r) > ] /n U()

0.95 2 0.990.70 2 0.90.60 2 0.82

0.950.900.850.800.750.70

0.65

0.60

0.55

0.50

Pr[Pr(r) > ]1

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

U() %

0 1 2 3 4 5 6 7 8 /n

12

3.10 Outdoor Propagation Model

estimating PL(d) requires terrain profile for propagation over irregular terrain such as

• simple curved earth profile• highly mountainous• obstacles: trees, building,

all models predict Pr(d) at given point or small area (sector)• wide variations in approach, complexity, accuracy• most based on systematic interpretation of empirical data

- Longely Rice- Durkins Model- Okumura Model- Hata Model- Wideband PCS Microcell- PCS Extension to Hata Model- Walfisch – Bertoni Model

13

3.10.1 Longely Rice Model (ITS irregular terrain model)• used for point-point systems under different types of terrain• frequency ranges from 40MHz-100GHz

(ii) Signal Strengths within radio horizon predicted using Geometric Optics Techniques (primarily 2-ray ground reflection)

(iii) Diffraction Loss over isolated obstacles predicted using Fresnel-Kirchoff knife edge models

(iv) Troposcatter over long distances predicted using Forward Scatter Theory

(v) Far-Field Diffraction losses in double horizon paths predicted usingModified Van der Pol-Bremner Method

(i) Median Transmission Loss predicted using path geometry of terrain profile & refractivity of troposphere

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Longely Rice Model: available as a computer program

calculates large scale median transmission loss over irregular terrain for frequencies between 20MHz-10GHz

input parameters include: • transmission frequency, • path length & antenna heights, • polarization, • surface refractivity • earth radius & climate • ground conductivity & ground dielectric constant• path specific parameters: antennas’ horizon distance, horizon elevation angle, trans-horizon distance, terrain irregularity

Prediction Modes for Longely Rice

1. point-point mode: used when detailed terrain profile or path specific parameters are known

2. area mode prediction: uses estimated path specific parameters

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3.10.2 Durkins Model: similar to Longly-Rice• predicts field strength contours over irregular terrain• adopted by UK joint radio committee• consists of two parts

(1) ground profile • reconstructed from topographic data of proposed surface along radial joining transmitter and receiver• models LOS & diffraction derived from obstacles & local scatters• assume all signal received along radial (no multipath)

(2) expected path loss calculated along the radial• move receiver location to deduce signal strength contour• pessimistic in narrow valleys• identifies weak reception areas well

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3.10.3 Okumura Model – wholly based on measured data - no analytical explanation

• among the simplest & best for in terms of path loss accuracy in cluttered mobile environment

• disadvantage: slow response to rapid terrain changes

• common std deviations between predicted & measured path loss 10dB - 14dB

• widely used for urban areas

• useful for- frequencies ranging from 150MHz-1920MHz - frequencies can be extrapolated to 3GHz- distances from 1km to 100km- base station antenna heights from 30m-1000m

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Okumura developed a set of curves in urban areas with quasi-smooth terrain

• effective antenna height:- base station hte = 200m- mobile: hre = 3m

• gives median attenuation relative to free space (Amu)

• developed from extensive measurements using vertical omni- directional antennas at base and mobile

• measurements plotted against frequency

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Estimating path loss using Okumura Model

1. determine free space loss, Amu(f,d), between points of interest

2. add Amu(f,d) and correction factors to account for terrain

L50(dB)= LF + Amu(f,d) – G(hte) – G(hre) – GAREA (3.80)

L50 = 50% value of propagation path loss (median)

LF = free space propagation loss

Amu(f,d) = median attenuation relative to free space

G(hte) = base station antenna height gain factor

G(hre) = mobile antenna height gain factor

GAREA = gain due to environment

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G(hte) = 200log20 teh

10m < hte < 1000m (3.81a)

G(hre) = 3log10 reh

hre 3m (3.81b)

G(hre) = 3log20 reh

3m < hre <10m (3.81b)

model corrected for• h = terrain undulation height• isolated ridge height• average terrain slope• mixed land/sea parameter

Amu(f,d) & GAREA have been plotted for wide range of frequencies antenna gain varies at rate of 20dB per decade or 10dB per decade

20

70

60

50

40

30

20

10

Am

u(f,d

) (d

B)

70 100 200 300 500 700 1000 2000 3000 f (MHz)

100

8070605040

302010521

d(km)

Urban Areaht = 200mhr = 3m

Median Attenuation Relative to Free Space = Amu(f,d) (dB)

21

35

30

25

20

15

10

5

0

GA

RE

A(d

B)

100 200 300 500 700 103 2103 3 103 frequency (MHz)

suburban areaquasi open areaopen area

Correction Factor = GAREA(dB)

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3.10.4 Hata Model: empirical model of graphical path loss data from Okumura

- predicts median path loss for different channels

- valid over UHF/VHF band from 150MHz-1.5GHz

- charts used to characterize factors affecting mobile land propagation

- standard formulas for approximating urban propagation loss

- correction factors for some situations

- compares closely with Okumura model as d > 1km large mobile systems

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(3.82)L50 (urban)(dB) = A + B log10d

Parameter CommentL50 50th % value (median) propagation path loss (urban)fc frequency from 150MHz-1.5GHz

hte, hre Base Station and Mobile antenna height (hre) correction factor for hre , affected by coverage area

d Tx-Rx separation

A= 69.55 + 26.16 log10(fc) – 13.82 log10(hte) – (hre)

• represents fixed loss – approximately 2.6 power law dependence on fc

• dependence on antenna heights is proportional to hre1.382

B= 44.9 - 6.55 log10(hte)• represents path loss exponent, worst case ≈ 4.5

L50 (urban)(dB) = 69.55 + 26.16log10 fc – 13.82 log10 hte – (hre)

+ (44.9-6.55hte)log10 d

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Mobile Antenna Height Correction Factor for Hata Model

(hre) Comment(1.1log10 fc - 0.7)hre – (1.56log10 fc - 0.8)dB Medium City 3.83

8.29(log10 1.54hre)2 – 1.1 dB Large City (fc 300MHz) 3.84a

3.2(log10 11.75hre)2 – 4.97 dB Large City (fc > 300MHz) 3.84b

L50 (dB) Comment

L50 (urban) - 2[log10 (fc/28)]2 – 5.4 Suburban Area 3.85

L50 (urban) - 4.78(log10 fc)2 - 18.33log10 fc - 40.98 Rural Area 3.86

Hata Model for Rural and Suburban Regions• represent reductions in fixed losses for less demanding environments

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Valid Range for Parameters• 150MHz < fc < 1GHz

• 30m < hb < 200m

• 1m < hm < 10m

• 1km < r < 20km

Propagation losses increase• with frequency• in built up areas

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Pat

h L

oss

(dB

)

hte (m)

160155150145140135130125120

20 60 100 140 180

20km

10km

5km

fc = 700MHz

Pat

h L

oss

(dB

)

Range (km)0 4 8 12 16 20

180170160150140130120110100

900 MHz700 MHz

• hte = 30m• hre = 1m

Example Tables for Okumura-Hata Model

Terrain Legend• Urban• Suburban• Open

27

3.10.5 PCS Extension to Hata Model• European Co-operative Scientific & Technical (EUROCOST) formed COST-231• extend Hatas model to 2GHz

L50 (urban)(dB) = 46.3 + 33.9logfc – 13.82 loghte – (hre) +

(44.9-6.55hte)logd + CM

• (hre) defined in 3.83, 3.84a, 3.84b

CM = 0dB• for medium sized cities

CM = 3dB• metropolitan centers

fc = frequency from 1500MHz - 2 GHz

hte = 30m-200m

hre = 1m-10m

d = 1km-20km

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3.10.6 Walfisch & Bertoni Model

path loss: S = P0Q2P1 (3.89)

P0 = (3.90)2

4

R

P0 = free space path loss between isotropic antennas

Q2 = reduction in rooftop signal due to row of buildings that immediately shadow hill

P1 = based on diffraction determines signal loss from roof top to street

S (dB) = L0 + Lrts + Lms (3.91)

L0 = free space loss

Lrts = roof-to-street diffraction & scatter loss

Lms = multi-screen diffraction loss from rows of building

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3.10.7 Wideband PCS Microcell Model

Feuerstien Measured cellular systems in Bay Area- 20MHz pulsed transmitter at 1900 MHz- base station antenna heights 3.7m, 8.5m, 13.3m- mobile antenna heights 1.7m

• assume flat ground reflection model

• let df = 1st Fresnel zone clearance

df = (3.92a) 16

161 4

22222

rtrt hhhh

Model for Average Path Loss - LOS channel• double regression model with regression breakpoint at 1st Fresnel zone clearance• fits measured data well • model assumes omni-directional vertical antennas

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f112

f11

d dfor )log(10)/log(10

d d 1for )log(10)(

pdnddn

pdndPL

fr

(3.92b)

p1 = = path loss in dB at reference distance d0 = 1m)( 0dPL

d = T-R separation distancen1, n2 = path loss exponents relates to antenna heights

e.g. at 1900MHz p1 = 38.0dB

Average Path Loss – PCS Microcell

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Transmit Antenna Height 1900 MHz LOS

n1 n2 (dB)

1900 MHz OBS n (dB)

low (3.7m) 2.18 3.29 8.76 2.58 9.31 med (8.5m) 2.17 3.36 7.88 2.56 7.67 high(13.3m) 2.07 4.16 8.77 2.69 7.94

(dB) )(dPL = 10nlog(d) + p1 (3.92c)

n = OBS path loss exponent – related to transmitter height

= log normal shadowing component from distance dependent mean (3.10.2)

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• Dominated by same mechanisms as outdoor propagation (reflection, refraction, scattering)• Classified as either LOS or OBS • Surveyed by [Mol91], [Has93]

- Partition Losses – Same Floor- Partition Losses – Different Floor- Log-distance path loss model- Ericsson Multiple Breakpoint Model- Attenuation Factor Model

3.11 Indoor Propagation Model• smaller Tx-Rx separation distances than outdoors• higher environmental variability for much small Tx-Rx separation

- conditions vary from: doors open/closed, antenna position, - variable far field radiation for receiver locations & antenna types

• strongly influenced by building features, layout, materials

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Partition Losses – Same Floor• hard partitions: immovable, part of building• soft partitions: movable, lower than the ceiling

Partition Losses – Different Floor: dependent on external building dimensions, structural characteristics & materials

Log-distance path loss model: accurate for many indoor paths

PL(dB) =

00 log10)(

d

dndPL (3.93)

• n depends on surroundings and building type• = normal random variable in dB having std deviation • identical to log normal shadowing mode (3.69)

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(1) Ericsson Multiple Breakpoint Model: measurements in multi-floor office building

• uses uniform distribution to generate path loss values between minimum &maximum range, relative to distance

• 4 breakpoints consider upper and lower bound on path loss• assumes 30dB attenutation at d0 = 1m

- accurate for f = 900MHz & unity gain anntenae • provides deterministic limit on range of path loss at given distance

20dB

30

50

70

90

110

atte

nuat

ion

(dB

)

1 3 10 20 40 100 meters

35

(2) Attenuation Factor Model (Seidel92b)• includes effect of building type & variations caused by obstacles • reduces std deviation for path loss to 4dB• std deviation for path loss with log distance model 13dB

nSF = exponent value for same floor measurement – must be accurate

FAF = floor attenuation factor for different floor

PAF = partition attenuation factor for obstruction encountered by primary ray tracing

)()(log10)( )( )( )(

00 dBPAFdBFAF

d

dndBdPLdBdPL SF 3.94

primary ray tracing = single ray drawn between Tx & Rxyields good accuracy with good computational efficiency

FAF

PAF(1)

PAF(2)

Rx

Tx

36

)(log10)()()()(

00 dBPAF

d

dndBdPLdBdPL MF 3.95

decreases as average region becomes smaller-more specific

Building Path Loss obeys free space + loss factor () (Dev90b)

• loss factor increases exponentially with d

(dB/m) = attenuation constant for channel

Replace FAF with nMF = exponent for multiple floor loss

3.96

)()(log20)()()()(

00 dBPAFdBFAFd

d

ddBdPLdBdPL

f 850MHz 0.621.7GHz 0.57

4-story bldgf

850MHz 0.481.7GHz 0.35

2-story bldg

37

Location n σ (dB) number of pointssame floor 2.76 12.9 501

through 1 floor 4.19 5.1 73through 2 floor 5.04 6.5 30through 3 floor 5.22 6.7 30

Path Loss Exponent & Standard Deviation for Typical Building

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(3) Simple Indoor Path Loss Model

Lp (dB) = (dB) +

Q

q

P

p

n

qFAFpWAFr

r

11010 )()(log10 2.47

• r = distance between transmitter & receiver• r0 = nominal reference distance (typically 1m)

• WAF(p) is wall attenuation factor, for P floors• FAF(q) is floor attenuation factor, for Q floors• n 2 for close distances, larger for greater distances

• more accurate when P and Q are small• model neglects angle of incidence & effect of distance on n

material loss at 900MHz loss at 1700MHzplaster wall 5dB 11dBconcrete wall 10dB 17dB

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3.12 Signal Penetration into Buildings

• no exact models

• signal strength increases with height

• lower levels are affected by ground clutter (attenuation &

penetration)

• higher floors may have LOS channel stronger incident signal on walls

RF Penetration affected by - frequency- height within building- antenna pattern in elevation plain

40

penetration loss • decreases with increased frequency • loss in front of windows is 6dB greater than without windows• penetration loss decreases 1.9dB with each floor when < 15th floor• increased attenuation at >15 floors – shadowing affects from taller buildings

• metallic tints result in 3dB to 30dB attenuation• penetration impacted by angle of incidence

41

Frequency

(MHz)

Attenuation

(dB)441 16.4

896.5 11.61400 7.6

Ray Tracing & Site Specific Models• rapid acceleration of computer & visualization capabilities• SISP – site specific propagation models• GIS – graphical information systems

- support ray tracing

- augmented with aerial photos & architectural drawings

Penetration Loss vs Frequency for two different building

Frequency

(MHz)

Attenuation

(dB)900 14.2

1800 13.42300 12.8

(1) (2)