05 outdoor observe

8/22/2019 05 Outdoor Observe

1/75

July, 2003 2003 by H.L.Bertoni1

IV.Propagation CharacteristicsObserved in Macro / Micro Cells

Ray model of multipath propagation Effects caused by multipath for narrowband

(CW) signals

Shadow fading

Range dependence in macrocells andmicrocells


2/75


Direct Observation of Multipath atthe Mobile and at the Base Station

Direction of arrival measurements at the mobile

Time delay measurements

Measurement of space-time rays

Ray model of propagation


3/75


Angles of Arrival at a Street Level- CW Measurement at 900 MHz in Tokyo using 22 spot beam antenna -

T. Taga, "Analysis for Mean Effective Gain of Mobile Antennas in Land Mobile Radio Environments", IEEE Trans., VT 39, May 1990, p. 117.

From base station

Rows ofbuildings Mobile locations

along street

Received signal versus azimuth for various elevations


4/75


Received Power EnvelopeP(t) for

Omnidirectional Subscriber Antennas

Paris, France Red Bank, NJ

Rays come in clusters that decay rapidly. Successive clusters have lower amplitudes.

J. Fuhl, J-P. Rossi and E. Bonek, High-Resolution 3-D

Direction-of-Arrival Determination for Urban Mobile Radio,

" IEEE Trans. Ant. and Prop., vol. 45, pp. 672- 682, 1997.

D.M.J. Devasirvatham, "Radio Propagation Studies in a Small

City for Universal Portable Communications, Proc. of the

IEEE VTC'88, pp. 100-104,1988.


5/75


Delay Spread for Continuous Time Signals

Mean Exc ess Delay

T0

tP t dt0

P t dt0

RMS Delay Spread

RMS

2

t T0 2P t dt

0

P t dt0

T.S. Rappaport, Wireless Communications, Prentice Hall PTR, Upper Saddle River,

NJ, p.163, 1996.


6/75


CDF of for Outdoor Links

- Measured at 1800 MHz for many subscriber location in Sweden

- Signals received at base station by horizontal and vertical antennas for

vertical subscriber antenna

RMS delay spread somewhat

larger in urban areas than

in suburban areas.

Co and cross Polarization

have nearly the same RMS

delay.

RMS delay of the average

power delay profile is

approximately the same as

the mean RMS delay spread.M. Nilsson, B. Lindmark, M. Ahlberg, M. Larsson and C. Beckmanm,

"Measurements of the Spatio-Temporal Polarization Characteristics of a Radio

Channel at 1800 MHz, Proc. IEEE Vehicular Technology Conference, 1999.


7/75July, 2003 2003 by H.L.Bertoni7

Greenstein Model of Measured DS in Urban and

Suburban Areas

DS T1km Rkm

where T1km is 0.3-1.0 s and

10logis a Gaussian random variabl

with standard deviation 2 - 6

Greenstein, et al., A New Path Gain/Delay Spread Propagation Model for Digital Cellular Channels, IEEE Trans. VT 46, May 1997.



Space-Time Rays Measured at Street Level- 890 MHz Measurement in Paris -

-Azimuth and time delay

of arriving rays

- Measured with systemhaving 0.1s time resolution

- Street runs North and South

- Many rays arrive along

the street direction

J. Fuhl, J-P. Rossi and E. Bonek, "High-Resolution 3-D

Direction-of-Arrival Determination for Urban Mobile Radio,

IEEE Trans. Ant. and Prop., vol. 45, pp. 672- 682, 1997.



Space-Time Rays at an Elevated Base Station- 1800 MHz measurements in Aalborg, Denmark -

-Rays arrive at base station

from a limited range of

angles

-Rays are grouped intoclusters

-Time delay between clusters

~ 1s, representing

scattering

from more distant buildings

- Time delay within a cluster

~ 100nsK.I. Pedersen, et al., "Analysis of Time, Azimuth and Doppler Dispersion

in Outdoor Radio Channels, Proc. ACTS, 1997.



Delay Spread (DS) and Angle Spread (AS) for

Discrete Arrivals

Delay Spread

Angle Spread(approximate expression for small spread)

From mth ray from the jth mobile

mobile)todirectionfrom(measuredstationbaseatarrivalofangle

delaytimearrival

amplitude

jm

jm

jmA

DS( j )

Am(j )

m

2m

(j ) m( j ) 2

Am( j ) 2

m

where m

( j ) Am

( j)

m

2m

( j)

Am(j ) 2

m

AS( j)

Am( j )

m

2m

( j) m( j ) 2

Am( j ) 2

m

where m

( j ) Am

(j )

m

2m

( j )

Am(j ) 2

m



Coordinate Invariant Method for

Computing AS

Coordinate invariant method:

Ray arrival anglen measured from any x- axis

Define the vector: un (ax cosn ay sinn )

AS180

un U2An

2

n

An2n

180

1 U2

whereU (un )An2

n

An2n



CDF of RMS Angle Spreads

- Measured at 1800 MHz for many subscriber locations in Sweden

- Signals received at base station by horizontal and vertical antennas for

vertical subscriber antenna

RMS angle spread is larger

in urban areas than in in

suburban areas.

Co- and cross polarization

have nearly the same RMS

angle spread.

M. Nilsson, et al., "Measurements of the

Spatio-Temporal Polarization Characteristics of

a Radio Channel at 1800 MHz, Proc. IEEE

Vehicular Technology Conference, 1999.



Ray Model for Street Level Mobiles

Rays arrive from all directions in the horizontal plane and up to 45 in thevertical direction

Ray paths shown for propagation from base station to subscriber

Reverse directions of arrows for propagation from subscriber to base station

Base Station DL ~ 30 mDt~ 100 ns

DL ~ 3 km

Dt~ 10s



Ray Model of Received Voltage and Power

Complex received voltage envelope at positionx along the streeV(x)e j(x ) Ane

jkL ne jn

n

where

An amplitude of the ray contributionLn path length of ray

n additional phase c hanges upon reflec tion,scattering

k 2/ 2f/c

Rec eived power

PR(x) V(x)ej(x ) 2 AnAm

m

n

ej (n m )ejk(Ln Lm )



Ray Fields Are Locally Like Plane Waves

n

x

Ln(x)

Narrow family

of rays

Phase Front

For narrow bundle of rays,An and n are approximately constantover a distance of several wave lengths.

Over a small region of space the phase front is approximately a

plane perpendicular to the direc tionv n of the central ray.



Relation to Plane Wave Interference

Phase variation for small displacements about a locationx,is approximately that of a plane wave

kLn (x s) kLn 0 kvn sax kLn0 ks vn x

where v n x is thex component of the unit vec torvn and

kLn 0 is the phase of the central ray

Received voltage is then

V(x)ej(x ) Ane

j(n kLn0 ) exp jks v n x n

This expression is like that found for plane waves having

complex amplitudeAnej (n k Ln0) and vn x cosn



Small Area Average Power

Rec eived powerPR(x) V(x)ej(x ) 2 AnAm

m

n e

j (n m )ejk(Ln Lm )

The spatial average PR(x) of the power overx is

1

2W

PR (x s)dsW

W

AnAmm

n

e j(n m )e jk(Ln0Lm0 ) 12W

exp jks vn vm x dsW

W

Provided 2W 1 k v n v m x forn m,1

2W

exp jks vn vm x dsW

W

0.

Hence1

2Wexp jks vn vm x ds

W

W

n ,m and PR (x) An2n

Thus the spatial average power is equal to the sum of the ray pow ers.



Summary of the Ray Model of Propagation

Propagation to or from the mobile can take place along

multiple paths (rays)

Multiple rays give RMS delay spreads ~ 0.5 s atR = 1 km

Rays arrive at the mobile from all directions in the horizontalplane, and up to 45o in the vertical plane

Rays at the base station arrive in a wedge of width ~ 10o

Interference effects of multipath contributions over distances

~ 10 m are like those of plane waves



Effects Caused by Multipath

for CW Excitation

Fast fading at street level Correlation at mobile and base station

Other effects

Doppler spread

Slow time fading

Cross polarization coupling


20/75


Multipath Arrivals Set Up a Standing Wave

Pattern in Space


21/75


Interference Effects of Multiple Rays

V(x) Ane jkLn ejn

n

AnAmej(n m )e jk(LnLm )m

n

1

2

Scattered rays coming from all directions result in:

1. Spatial fading - as subscriber moves a dis tanceDx ~ ,

the phases k(Ln -Lm) change by ~ 2

2. Doppler spread - a subscriber moving with velocityu sees

an apparent frequency changes1

2

kd

dt

Ln u

cos

3. Frequencyfading - the phase k(Ln -Lm) c (Ln - Lm )changes with frequency

4. Slow time fading - moving scatterers change someLn 's


22/75


Received Signal as Omni Antenna Moves

Through Standing Wave Pattern

- Rapid Fluctuation of 20dB or more

- Separations between minima ~ 0.2 m

- Wavelength at 910 MHz is= 0.33 m

- Slow fluctuation of the small area average

M. Lecours, I.Y. Chouinard, G.Y. Delisle and J. Roy, Statistical Modeling of the Received Signal Envelope in a

Mobile Radio Channel, IEEE Trans. on Veh. Tech., Vol. VT-37, pp. 204-212, 1988.

Small area average

V(x) 1

LV(x s)ds

L 2

L 2


23/75


Rayleigh and Rician

Cumulative Distribution Function (CDF)

0 0.5 1.0 1.5 2.0 2.50

0.2

0.4

0.6

0.8

1.0

CDF

r

Median value

0.939

K5

Rayleigh CDF

Rician CDF

Define the random

varriable

r V(x) V(x)

For line - of - sight

(LOS) paths, r is

approximately Rician

For non- LOS

paths , r is

approximately Rayleigh


24/75


Complex Autocorrelation Function

Measures the degree to which the signalV(x)ej(x ) received at one antenna

is predic ted by the signal V(x s)ej(xs) received at a second antenna

separated by a distances .

Ergodic assumption: Statis tical dependenc e over different embodiementsis same as averaging over many locationsx.

For complex signals

C(s) 12WV(x)ej(x )V(x s)e j(xs)dx

W

W

12W V(x) 2 dx

W

W

where 2W is the correlation window,assumed to be centered atx 0.


25/75


Autocorrelation Function for Ray Fields

If the voltage is the sum of ray fields V(x)ej(x ) Ane jkLn (x )ejn

nOver distances of 10- 20, we may approximateLn (x) Ln 0 x(v n )x . Then

1

2WV(x)e

j(x )V(x s)e j(xs)dx

W

W

AnAmm

n

e j(nm )e jk(Ln0 L m0 )e jks(v m )x 12W

exp jkx v n v m x dxW

W

AnAmm

n

ej(n m )e jk(Ln0Lm0 )e jks(v m )x nm An2n

e jks(v n)x

Similarly1

2WV(x) 2 dx

W

W

An2n

so that C(s) An2

n

e jks(v n )x An2n


26/75


C(s) Measured Street Level

Measurements made atf = 821 MHz

= 0.365 m

Signal de-correlated

after s >/4

S-B. Rhee and G.I. ZYsman, "Results of Suburban Base Station Spatial Diversity Measurements

in the UHF Band," IEEE Trans. on Comm., vol. COM-22, pp. 1630-1636, 1974.

Sample Number

s (m)0.26 1 2 4


27/75


Correlation at Elevated Base Station

F. Adachi, et al., "Cross correlation between the envelopes of 900 MHz signals

received at a mobile radio base station site," IEE Proc., vol. 133, Pt. F, pp. 506-

512, 1980.

Ray theory for smallM :

C(s) sin ksM sin ksM sin

For 0, C(s) 1

For 90o

C(s) sin ksM ksM

has first zero at

s 2M

IfM 5o 36 rad

thens 6

Measured at 900 MHz in Liverpool, England

CR(s)


28/75


Summary of Fading at Both Ends of Link for an

Elevated Base Station

xM

xB

S

Elevated Base Station Mobile in Clutter

xM

Signal

/2

xB

S

Signal

/2


29/75


Measured Doppler Spread

K.I. Pedersen, et al., "Analysis of Time, Azimuth and Doppler Dispersion in Outdoor

Radio Channels, Proc. ACTS, 1997.

f= 1800 MHz


30/75


Frequency Fading Due to Multipath(910 MHz in Toronto)

E.S. Sousa, et al, Delay Spread Measurements for the Digital Cellular

Channel in Toronto,IEEE Trans. on VT, VT-43, pp. 837-847, 1994.

Individual terms in the

expression forV(x) go

through 2 phase chang

for frequency changesDf

satisfying

2Dfc

Li Lj 2solving forDf

Dfc

Li Lj For differences in path

length Li Lj 1.2 km Df 0.25 MHz


31/75


Slow Time Fading Measured by

a Stationary Subscriber (900 MHz)

For a wave incident on a

moving scatterer at angle

relative to the velocity u of

the scatterer, the scattered

wave will undergo 2phasechange in time such that

uDt~ .

At walking speedu= 1

m/s, and at 900 MHz,Dt~ 0.33 sec.

N.H. Shepherd, et al., "Special Issue on Radio

Propagation, IEEE Trans. On

Veh.Tech., vol. VT-37, pp. 45, 1988.


32/75


Local Scattering Produces

Cross-Polarization

EV

EVEV

EVEV

EHEH


33/75


Cross Polarization Coupling Measured at Base

Stations in Sweden

Measured ratios of the

sector average power

received in the horizontal

and vertical polarized

fields (H/V) at 1800 MHz.

The error limits represent

one standard deviation

Lotse, et al., "Base Station Polarization

Diversity Reception in Macrocellular

Systems at 1800 MHz", Proc. VTC 96,

pp. 1643 - 1646

EnvironmentMobile

configuration

Horizontal-to-vertical power

ratio (dB)

Roof-mounted -7 2Portable, outdoors -4 2Portable, inside van -3 2

Kungsholmen,urban

Portable, indoors -1 4Roof-mounted -8 2Portable, outdoors -2 1Portable, inside van -1 1

Kista,suburban

Portable, indoors -3 1

Roof-mounted -13 1Portable, outdoors -6 1Portable, inside van -7 1

Veddesta,suburban

Portable, indoors -7 1


34/75


Cross Correlation of Complex and Real Signals

Cross correlation of two complex functions with zero me

CR E U(x)V(x)

E U(x)2

E V(x)

2

Cross correlation of two real functions with non- zero mean

CR

E U(x) U(x) V(x) V(x) E U(x) U(x)

2

E V(x) V(x) 2

E is the expectation value or average.


35/75


Fast Fading Patterns of Horizontal and Vertical

Polarization Are Uncorrelated

Cross correlations of

the signals received by

horizontally and

vertically polarized base

station antennas for aroof mounted mobile

antenna. Integration

taken as the mobile

travels over a travel

distance 2W= 10

Lempiainen, et al.,"Experimental Results of

Cross Polarization Discrimination and Signal

Correlation Values for a Polarization Diversity

Scheme", Proc. VTC 97, pp.1498-1502.


36/75


Summary of Multipath Effects

Multipath arrivals set up a standing wave pattern in space

that is perceived as fast fading by a moving mobile

Fast fading approximates Rayleigh statistics on Non-LOS

links

Interference patterns have correlation length of/4 at the

mobile, and 6or greater at an elevated base station

Multipath causes frequency fading, Doppler spread and slow

time fading

The scattering processes that create multipath also cause

depolarization of the waves


37/75


Statistical Properties of the

Shadow Fading

Separating the shadow fading from fast fading and range

dependence

Statistical distribution of shadow fading

Correlation distance of shadow fading

Correlation of shadow fading for signals from different basestations


38/75


RnARULS log10log10)(

).()( RURU LSk

)()( RURUP LSk

How to Find Shadow Fading From

Drive Test Measurements

Drive tests conducted over many small areas of

length >20at different distances R from base station

Find Uk(R) = 10log V(x)2 for each small area k= 1, 2, ...

Plot Uk(R) versus logR and fit data with a least squares line

having dependence of the form

For each sector compute For the resultingset of numbers form the distribution function

The distribution function is typically found to be Gaussian


39/75


Separating Shadow Fading from Range

Dependence

Least Squares Fit

Small Area Average

ULS 10log PT 10log A n10log R

corresponds to power law

P PTA / Rn

Small area average power plotted versus logR

Uk ULS


40/75


CDF of Shadow Fading Measured Simultaneously

at Two Frequencies (955 MHz and 1845 MHz)

Straight line plots for distorted sc ale

indicate that Uk ULS is Gaussia

Fading distributions of smallarea averages normalized to

Standard deviation for:

Uk(955) 8.0dB

Uk(1845) 8.1dB

Difference Mean

Uk(955) 10.5 3.3dB

- Uk(1845)

Small area averages

Morgensen, et al., Urban Area Radio Propagation Measurements at 955

and 1845 MHz for Small and Micro Cells, Proc. Of Globecom, 1991

CDFUkULS

UkULS


41/75


Interpreting the Shadow Fading Statistics

8 dB

3.3 dB

x

Uk(955) U(955)Uk(1845) U(1845)

Uk

U

dB

At each frequency the shadow loss fluctuates by 8 dB about its average

Shadow loss at the two frequencies are highly correlated, differing from each

other by only 3.3 dB (correlation coefficient C= 0.92)

Shadow loss has weak frequency dependence.


42/75


Multiple Distance Scales of Signal Variation

Travel distances ~/2 -- Fast fading

Travel distances ~ 10 m ~20-- Shadow fading

Entire cell out to ~ 20 km -- Range dependenceA/R n

Distance

Signa

lStrength

(dB)

/2

Small Area Average UAverageOverall

UUk FadingShadow


43/75


U

p U U 12SF

exp U U 2 /2SF2

V(x)2

4

V(x) 2

Shadow Fading Statistics

For many small areas (sectors) k= 1, 2, ... at the same

distanceR from the base station

Treat V(x)2 over each small area as a random variable

Define new random variable Uk= 10log V(x)2

Probability distribution ofUkabout its mean valueis typically found to be the Gaussian distribution

In citiesSF

8 -10 dB

Note: ifV(x) is Rayleigh distributed, then

2SF


44/75


Autocorrelation of the Shadow Fading at

900MHz

Suburban Environment Urban Environment

250 m 5 mDecorrelation Distance

M.Gudmundson, Correlation Model for Shadow Fading in Mobile Radio Systems, Electronics Letts., vol. 27 pp. 2145-2146, 1991.


45/75


Cross Correlation of the Shadow Loss for Links

to Two Different Base Stations

C()

A. Mawira, Models for the Spatial

Correlation Functions of the (Log)-

Normal Component of the Variable-

ity of VHF/UHF Field Strength in

Urban Environment,

IEEE 0-7803-0841-7/92, 1992.


46/75


Propagation Model for Shadow Fading

As the subscriber moves along street, the received signal passes overbuildings of different height, or misses the last row of buildings

S

treetand

s

idewalks

Subscriber

From base station

Full width of Fresnel

zone near one end of link:

2wF 2 s

For 90 0 MHz at mid street

s = 20 m, = 1 3 m

2wF

5.2 m

about the w idth of a house.

Shadow loss is not sensitiv

to f requency.


47/75


Summary of Shadow Fading Statistics

Shadow fading has lognormal distribution (power in dB has a

normal distribution)

Shadow fading has weak frequency dependence

Correlation length of the shadow fading is on the order of

building dimensions in cities and on street length in suburban

areas

There is correlation of the fading to different base stations

when they are located in the same direction from the mobile


48/75


Range Dependence of the Received Signal

High base station antenna measurements for macrocells( forR out to 20 km )

Low base station antenna measurements for microcells

( forR out to 2 km )

Line of sight(LOS) paths Obstructed paths


49/75


Range Dependence of Macrocells & Microcells

Early system using macrocells (R < 20 km)

Base station antennas well above buildings

Isotropic propagation with range variationA/Rn

Hexagonal tessellation of plane

Frequency reuse independent of antenna height

Modern systems using microcells (R < 2 km)

Base station antenna near (or below) rooftops

Anisotropic propagation-A, n depend on: Direction of propagation relative to street grid

Base station antenna height, location relative to buildings

Cell shape is open issue


50/75


Scale of City Blocks Compare to Cell Size

0km 1 2 3 4

ELMHURST

FLUSHING

JACKSON HEIGHTS

CORONA

FLUSHING

MEADOWS

REGO PARK HILLCREST

UTOPIA

EAST

ELMHURST


51/75


Measurements of Propagation Characteristics in

Different Cities for High Base Station Antennas

Field Strength and Its Variability in VHF and UHF

Land-Mobil Radio Service


52/75


Range Dependence Measured in Tokyo

Y. Okumura, E. Ohmori, T. Kawano and K. Fukuda, Field Strength and Its Variability in VHF and UHF Land-Mobile

Radio Service, Re. Elec. Com. Lab., vol. 16, pp. 825-873, 1968.

d i


53/75


Range Dependence Measurements in

Philadelphia at 820 MHz

G.D. Ott and A. Plitkins, Urban Path-Loss Characteristics at 820 MHz, IEEE Trans. Veh. Tech., vol. VT-27, pp.

189-197, 1978.

Base station in a high riseBuilding environment

Base station in a residentialenvironment


54/75


Range Dependence for Composite of Five Base

Station Sites in Philadelphia at 820 MHz

G.D. Ott and A. Plitkins, Urban Path-Loss Characteristics

at 820 MHz, IEEE Trans. Veh. Tech., vol. VT-27, pp. 189-

197, 1978.

Power law variation

PdBm PT dBm 10logA n10logRor

P PT A Rn

Path loss index

n 3.68


55/75


Definition of Path Loss and Path Gain

PG Path Gain Power Received

Power Transmitted

(PG is always less than 1 )

PL Path Loss Power Transmitted

Power Received

1

PG(PL is always greater than 1 )

When expressed in dB,PGdB 10logPG L wher

L 10logPLIfP PTA /R

n, then PGdB 10logA 10nlogR and

L 10logA 10n logR


56/75


Hata-Okumura Model for Median Path Loss

Urban area:L50 = 69.55 + 26.16logfc - 13.82loghb- a(hm) + (44.9-6.55 loghb) logR

where

fc frequency (MHz)

L50 mean path loss (dB)

Hb base station antenna height

a(hm) correction factor for mobile antenna height (dB)

R distance from base station (km)

The range of the parameters for which Hatas model is valid is

150 fc 1500 MHz

30 hb 200 m

1 hm 10 m

1 R 20 km


57/75


Hata-Okumura Model (cont.)

Urban area (cont.):

For a small or medium-sized city:

a(hm)=(1.1 logfc - 0.7) hm - (1.56 logfc - 0.8 ) dB

For a large city:

a(hm)=8.29(log

1.54 h

m)2- 1.1 dB, f

c 200 MHz

or

a(hm)=3.2(log11.75 hm)2- 4.97 dB, fc 400 MHz

Suburban area:

Open Area:

L50 =L50(urban) - 4.78 (logfc)2+18.33 (logfc) -40.94

L50 L50 urban - 2 log fc

28

2

5.4

dB


58/75


Range index of Hata-Okumura Model

n = ( 44.9 - 6.55 loghb ) / 10

20 200hb (m)

3.84

2.98


59/75


Measurement of Path Loss for

Low Base Station Antennas of Microcells


60/75


Drive Routes for Microcell Measurements

in San Francisco

LOS drive route

Staircase drive route

Zig-Zag drive route

Transverse paths - directly over buildings

Lateral paths - to side streets perpendicular to the LOS street


61/75


Mission District of San Francisco


62/75


Drive Routes In the Mission District

Received Signal on LOS Route in Mission


63/75


Received Signal on LOS Route in Missionf= 1937 MHz, hBS= 3.2 m, hm = 1.6 m

Telesis Technology Laboratories, Experimental License Progress Report to the FCC, August, 1991.

Received Signal on Staircase Route in


64/75



Received Signal on Staircase Route in

the Sunset District vs. Distance Traveledf= 1937 MHz, hBS= 8.7 m, hm = 1.6 m


65/75


Regression Fit to Received Signal VersusR

on Staircase Route in Sunset District


R i d Si l Zi Z R t i


66/75


Received Signal on Zig-Zag Route in

the Sunset District vs. Distance Traveledf= 1937 MHz, h

BS= 8.7 m, h

m= 1.6 m


Regression Fit to Received Signal Versus R on the


67/75


Regression Fit to Received Signal VersusR on the

Transverse Portions of the Zig-Zag Route


Regression Fit to Received Signal Versus R


68/75


Regression Fit to Received Signal VersusR

on the Lateral Portions of the Zig-Zag Route


C i f R i Fit


69/75


Comparison of Regression Fits on

Different Paths in Sunset

H.H. Xia, et al., Microcellular Propagation Characteristics for Personal Communications in Urban and

Suburban Environments, IEEE Trans. Veh. Tech., vol. 43, no. 3, pp. 743 -752, 1994.


70/75


Har-Xia-Bertoni Model for

Low Base Station Antennas

Expressions fit to regression lines for:

900 MHz and 1900 MHz

hBS= 3.2, 8.7 and 13.4 m

hm = 1.6 m

Separate expressions for:

LOS paths

Obscured paths in residential environment

Obscured paths in high rise environment


71/75


Har-Xia-Bertoni Model for LOS Paths

kb

bbkGbkk

bkk

kbbGk

bkk

mmb

bk

k

G

Rh

hRfRRL

RR

RhhfRL

RR

hhh

R

Rf

loglog90.1310.32

loglog90.1334.25log70.45log10.3238.48

)(

loglog73.580.15log09.0log40.3914.81

)(

6.11000

4

segmentout-Far

segmentin-Near

m

kmindistanceGHzinfrequency


72/75


Har-Xia-Bertoni Model for Obscured Paths in

Residential Environments

k

GGk

k

GGk

k

G

Rhh

hhffRL

Rhh

hhffRL

h

R

f

log1logsgn70.618.29

1logsgnlog35.405.13log63.3139.127

log1logsgn35.406.40

1logsgnlog58.474.13log88.3831.138

DD

DD

DD

DD

D

:PathsLateral

:pathstransverseandstaircaseCombined

minbuildings(below)abovestationbaseofheight

kmindistance

GHzinfrequency

H Xi B i M d l f Ob d P h


73/75


Har-Xia-Bertoni Model for Obscured Paths

in High Rise Environments

fG frequency in GHz

Rk distance in km

hb height of base station above ground in m

Combined staircase paths and transverse paths

L Rk 143.21 29.74log fG 0.99loghb 47.23 3.72log hb logRk

Lateral pathsL Rk 135.4112.49log fG 4.99loghb 46.84 2.34 log hb logRk

Comparison of Hata and Har Models


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Comparison of Hata and Har Models

For base station antenna heights outside measurement

limits of both models

Forf 1GHz

Hata urban area

L 69.55 26.16log1000 13.82log20 44.9 6.55log20 logRk 130.0 36.4logRk

Har co mbined staircase and transverse (residential)

L 138.31 13.74log(1 9) 40.06 4.35log(1 9) logRk 124.6 35.7logRk

Tw o models go into each other for middle height base station anten

hm = 1.6 m

hBS= 20 m

Dh= 9 m


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Summary of Range Dependence

Range dependence over large distances takes the form

(PR/PTr)=A/Rn in watts or

10log (PR/PTr)= 10logA + 10nlogR in dB

The slope index n ranges between 3 and 4 for base stationantennas above the rooftops, and is the same for all cities

Simple formulas fit to measurements give the path gain or

path loss as a function of antenna height and frequency

Measurements made with high base station antennas matchcontinuously with measurements made with low antennas

05 outdoor observe

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