July, 2003©2003 by H.L.Bertoni1 IV. Propagation Characteristics Observed in Macro / Micro Cells Ray...

July, 2003 ©2003 by H.L.Bertoni1

IV. Propagation Characteristics Observed in Macro / Micro Cells

• Ray model of multipath propagation• Effects caused by multipath for narrowband

(CW) signals• Shadow fading • Range dependence in macrocells and

microcells


Direct Observation of Multipath at the 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


Angles of Arrival at a Street Level- CW Measurement at 900 MHz in Tokyo using 22º 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 stationRows ofbuildings Mobile locations

along street

Received signal versus azimuth for various elevations


Received Power Envelope P(t) forOmnidirectional 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-DDirection-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.


Delay Spread for Continuous Time Signals

Mean Excess Delay

T0 =

tP t( )dt0

∞

∫

P t( )dt0

∞

∫

RMS Delay Spread

τRMS2 =

t−T0( )2P t( )dt

0

∞

∫

P t( )dt0

∞

∫

T.S. Rappaport, Wireless Communications, Prentice Hall PTR, Upper Saddle River,NJ, p.163, 1996.


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 thanin 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.


Greenstein Model of Measured DS in Urban and Suburban Areas

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 system having 0.1 s time resolution

-Street runs North and South

-Many rays arrive alongthe street direction

J. Fuhl, J-P. Rossi and E. Bonek, "High-Resolution 3-DDirection-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 into clusters

-Time delay between clusters ~ 1 s, representing scatteringfrom more distant buildings

- Time delay within a cluster ~ 100 ns

K.I. Pedersen, et al., "Analysis of Time, Azimuth and Doppler Dispersionin 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) to direction from (measured station base at arrival of angle

delay time arrival

amplitude

=φ

=τ

=

jm

jm

jmA

DS( j ) =Am

(j )

m∑

2τm

(j ) −τm( j )

( )2

Am( j ) 2

m∑

where τm( j ) =

Am( j)

m∑

2τm

( j)

Am(j ) 2

m∑

AS( j) =Am

( j )

m∑

2φm

( j) −φm( j )

( )2

Am( j ) 2

m∑

where φm( j ) =

Am(j )

m∑

2φm

( j )

Am(j ) 2

m∑


Coordinate Invariant Method for Computing AS

€

Coordinate invariant method:

Ray arrival angle φn measured from any x-axis

Define the vector: un =(axcosφn +aysinφn)

AS=180π

⎛ ⎝

⎞ ⎠

un −U2An

2

n

∑ An2

n

∑ =180π

⎛ ⎝

⎞ ⎠

1−U2

( )

where U = (un)An2

n

∑ An2

n

∑


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 45º in the vertical direction

Ray paths shown for propagation from base station to subscriberReverse directions of arrows for propagation from subscriber to base station

Base StationL ~ 30 mt ~ 100 ns

L ~ 3 km t ~ 10 s


Ray Model of Received Voltage and Power

€

Complex received voltage envelope at position x along the street

V(x)e jψ(x) = Ane−jkLne jφn

n

∑where

An =amplitude of the ray contribution

Ln =path length of ray

φn =additional phase changes upon reflection, scattering

k=2π /λ =2πf /c

Received power

PR(x) =V(x)ejψ(x) 2= AnAm

m

∑n

∑ ej (φn−φm)e−jk(Ln−Lm)


Ray Fields Are Locally Like Plane Waves

n

x

Ln(x)

Narrow family of rays

Phase Front


Relation to Plane Wave Interference

€

Phase variation for small displacement s about a location x,

is approximately that of a plane wave

kLn(x+s) ≈kLn0 + kvn( ) ⋅ sax( ) =kLn0 +ksvn( )x

where vn( )x is the x component of the unit vector vn and

kLn0 is the phase of the central ray

Received voltage is then

V(x)e jψ(x) = Anej(φn−kLn0 )exp−jksvn( )x[ ]

n

∑This expression is like that found for plane waves having

complex amplitude Anej (φn−kLn0) and vn( )x =cosθn


Small Area Average Power

€

Received power PR(x) =V(x)ejψ(x) 2= AnAm

m

∑n

∑ ej (φn−φm)e−jk(Ln−Lm)

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

1

2WPR(x+s)ds

−W

W

∫ =

AnAmm

∑n

∑ e j(φn−φm)e−jk(Ln0−Lm0 ) 12W

exp−jksvn −vm( )x[ ]ds−W

W

∫

Provided 2W >1 k vn −vm( )x for n≠m, 1

2Wexp−jksvn −vm( )x[ ]ds

−W

W

∫ ≈0.

Hence 1

2Wexp−jksvn −vm( )x[ ]ds

−W

W

∫ ≈δn,m and PR(x) = An2

n

∑

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


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 at R = 1 km

• Rays arrive at the mobile from all directions in the horizontal plane, 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


Multipath Arrivals Set Up a Standing Wave Pattern in Space


Interference Effects of Multiple Rays

€

V(x) = Ane−jkLnejφn

n

∑ = AnAmej(φn−φm)e−jk(Ln−Lm)

m

∑n

∑⎧ ⎨ ⎩

⎫ ⎬ ⎭

12

Scattered rays coming from all directions result in:

1. Spatial fading - as subscriber moves a distance Δx ~λ,

the phases k(Ln -Lm) change by ~2π

2. Doppler spread - a subscriber moving with velocity u sees

an apparent frequency changes ν =12π

kddt

Ln =uλ

cosθ

3. Frequency fading - the phase k(Ln -Lm) = ω c( )(Ln - Lm)

changes with frequency

4. Slow time fading - moving scatterers change some Ln's


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) =1L

V(x+s)ds−L 2

L 2

∫


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

CD

F

r

Median value 0.939

K5

Rayleigh CDFRician 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


Complex Autocorrelation Function

€

Measures the degree to which the signal V(x)ejψ (x) received at one antenna

is predicted by the signal V(x−s)ejψ (x−s) received at a second antenna

separated by a distance s .

Ergodic assumption: Statistical dependence over different embodiements

is same as averaging over many locations x.

For complex signals

C(s)=1

2WV(x)ejψ (x)V(x−s)e−jψ(x−s)dx

−W

W

∫⎧ ⎨ ⎩

⎫ ⎬ ⎭

12W

V(x)[ ]2dx

−W

W

∫⎧ ⎨ ⎩

⎫ ⎬ ⎭

where 2W >>λ is the correlation window, assumed to be centered at x=0.


Autocorrelation Function for Ray Fields

€

If the voltage is the sum of ray fields V(x)ejψ (x) = Ane−jkLn (x)ejφn

n

∑Over distances of 10-20λ, we may approximate Ln(x) ≈Ln0 +x(vn)x. Then

1

2WV(x)e jψ(x)V(x−s)e−jψ (x−s)dx

−W

W

∫ =

= AnAmm

∑n

∑ e j(φn−φm)e−jk(Ln0−L m0 )e−jks(vm)x1

2Wexp−jkxvn −vm( )x[ ]dx

−W

W

∫⎧ ⎨ ⎩

⎫ ⎬ ⎭

≈ AnAmm

∑n

∑ ej(φn−φm)e−jk(Ln0−Lm0 )e−jks(vm)x δnm{ }= An2

n

∑ e−jks(vn)x

Similarly 1

2WV(x)[ ]

2dx

−W

W

∫ ≈ An2

n

∑

so that C(s)= An2

n

∑ e−jks(vn )x An2

n

∑


C(s) Measured Street Level

Measurements made at f = 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 Measurementsin the UHF Band," IEEE Trans. on Comm., vol. COM-22, pp. 1630-1636, 1974.

Sample Number

s (m)0.26 1 2 4


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 small θM :

C(s) ≈sinksθM sinα( )

ksθM sinα

For α → 0, C(s) → 1

For α =90o

C(s) ≈sinksθM( )

ksθM

has first zero at

s=λ 2θM

If θM =5o =π 36 rad

then s=6λ

Measured at 900 MHz in Liverpool, England

CR(s)


Summary of Fading at Both Ends of Link for an Elevated Base Station

xMxBS

Elevated Base Station Mobile in Clutter

xM

Sig

nal

/2xBS

Sig

nal

/2


Measured Doppler Spread

K.I. Pedersen, et al., "Analysis of Time, Azimuth and Doppler Dispersion in OutdoorRadio Channels,” Proc. ACTS, 1997.

f = 1800 MHz


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 for V(x) go

through 2π phase change

for frequency changes Δf

satisfying

2πΔf

cLi −L j( ) =2π

solving for Δf

Δf =c

Li −L j( )

For differences in path

length Li −L j( ) ≈1.2 km

Δf =0.25 MHz


Slow Time Fading Measured bya 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 2 phase change in time such that ut ~ .

At walking speed u = 1 m/s, and at 900 MHz, t ~ 0.33 sec.

N.H. Shepherd, et al., "Special Issue on Radio Propagation,” IEEE Trans. OnVeh.Tech., vol. VT-37, pp. 45, 1988.


Local Scattering Produces Cross-Polarization

EV

EVEV

EVEV

EHEH


Cross Polarization Coupling Measured at Base Stations in Sweden

Measured ratios of thesector average powerreceived in the horizontaland vertical polarizedfields (H/V) at 1800 MHz.

The error limits representone standard deviation

Lotse, et al., "Base Station PolarizationDiversity Reception in MacrocellularSystems at 1800 MHz", Proc. VTC 96,pp. 1643 - 1646

EnvironmentMobile

configuration

Horizontal-to-vertical power

ratio (dB)Roof-mounted -7 ±2Portable,outdoors -4±2Portable,insidevan -3±2

Kungsholmen,urban

Portable,indoors -1±4Roof-mounted -8±2Portable,outdoors -2±1Portable,insidevan -1±1

Kista,suburban

Portable,indoors -3±1Roof-mounted -13±1Portable,outdoors -6±1Portable,insidevan -7±1

Veddesta,suburban

Portable,indoors -7±1


Cross Correlation of Complex and Real Signals

€

Cross correlation of two complex functions with zero mean

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.


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 a roof mounted mobile antenna. Integration taken as the mobile travels over a traveldistance 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.


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 6 or 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


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 base stations


RnARU LS log10log10)( −=

).()( RURU LSk −

( ))()( RURUP LSk −

How to Find Shadow Fading FromDrive Test Measurements

• Drive tests conducted over many small areas of length > 20 at different distances R from base station

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

• Plot Uk(R) versus log R and fit data with a least squares line having dependence of the form

• For each sector compute For the resulting set of numbers form the distribution function

• The distribution function is typically found to be Gaussian


Separating Shadow Fading from Range Dependence

Least Squares Fit

Small Area Average

U LS =10logPT +10logA−n10logR

corresponds to power law

P =PT A/ Rn

Small area average power plotted versus logR

U k −U LS


CDF of Shadow Fading Measured Simultaneously at Two Frequencies (955 MHz and 1845 MHz)

€

Straight line plots for distorted scale

indicate that Uk −U LS( ) σ is Gaussian

Fading distributions of smallarea averages normalized toStandard 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

€

CDFU k −U LS

σ

⎧ ⎨ ⎩

⎫ ⎬ ⎭

€

U k −U LS( ) σ


Interpreting the Shadow Fading Statistics

±8 dB

±3.3 dB

x

€

Uk(955)−U(955)

Uk(1845)−U(1845)

€

U k −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.


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 dependence A/R n

Distance

Sig

nal S

tren

gth

(dB

)

/2

Small Area AverageU AverageOverall

UU k − FadingShadow


€

U

€

V(x)2 =4π

V (x)[ ]2

Shadow Fading Statistics

• For many small areas (sectors) k = 1, 2, ... at the same distance R 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 of Uk about its mean value

is typically found to be the Gaussian distribution

• In cities SF 8 -10 dB

• Note: if V(x) is Rayleigh distributed, then

2SF


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.


Cross Correlation of the Shadow Loss for Links to Two Different Base Stations

C()

A. Mawira, ”Models for the SpatialCorrelation Functions of the (Log)-Normal Component of the Variable-ity of VHF/UHF Field Strength inUrban Environment,”IEEE 0-7803-0841-7/92, 1992.


Propagation Model for Shadow Fading

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

Stre

et a

ndsi

de w

alks

Subscriber

From base station

€

Full width of Fresnel

zone near one end of link:

2wF =2 λs

For 900 MHz at mid street

s=20 m, λ =1 3 m

2wF =5.2 m

about the width of a house.

Shadow loss is not sensitive

to frequency.


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


Range Dependence of the Received Signal

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

• Low base station antenna measurements for microcells( for R out to 2 km )– Line of sight(LOS) paths

– Obstructed paths


Range Dependence of Macrocells & Microcells

• Early system using macrocells (R < 20 km)– Base station antennas well above buildings– Isotropic propagation with range variation A/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


Scale of City Blocks Compare to Cell Size

0km 1 2 3 4

ELMHURST

FLUSHING

JACKSON HEIGHTS

CORONA

FLUSHING

MEADOWS

REGO PARK HILLCRESTUTOPIA

EASTELMHURST


Measurements of Propagation Characteristics in Different Cities for High Base Station Antennas

• Field Strength and Its Variability in VHF and UHFLand-Mobil Radio Service


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.


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 rise Building environment

Base station in a residentialenvironment


Range Dependence for Composite of Five Base Station Sites in Philadelphia at 820 MHz

G.D. Ott and A. Plitkins, “Urban Path-Loss Characteristicsat 820 MHz,” IEEE Trans. Veh. Tech., vol. VT-27, pp. 189-197, 1978.

€

Power law variation

PdBm= PT( )dBm+10logA−n10logR

or

P =PT A Rn( )

Path loss index

n=3.68


Definition of Path Loss and Path Gain

€

PG≡ Path Gain =Power Received

Power Transmitted( PG is always less than 1 )

PL ≡ Path Loss =Power TransmittedPower Received

=1

PG( PL is always greater than 1 )

When expressed in dB, PGdB =10logPG =−L where

L ≡10logPL

If P =PT A/Rn, then PGdB =10logA−10nlogR and

L =−10logA+10nlogR


Hata-Okumura Model for Median Path Loss

• Urban area:

L50 = 69.55 + 26.16 log fc - 13.82 log hb- a(hm) + (44.9-6.55 log hb) log R

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 Hata’s model is valid is

150 fc 1500 MHz

30 hb 200 m

1 hm 10 m

1 R 20 km


Hata-Okumura Model (cont.)

• Urban area (cont.):

– For a small or medium-sized city:

a(hm)=(1.1 log fc - 0.7) hm - (1.56 log fc - 0.8 ) dB

– For a large city:

a(hm)=8.29(log 1.54 hm)2 - 1.1 dB, fc 200 MHz

or

a(hm)=3.2(log 11.75 hm)2 - 4.97 dB, fc 400 MHz

• Suburban area:

• Open Area:

L50 = L50(urban) - 4.78 (log fc)2+18.33 (log fc) -40.94

€

L50 = L50 urban( ) - 2 logfc

28⎛ ⎝

⎞ ⎠

⎡

⎣ ⎢ ⎤

⎦ ⎥

2

+5.4⎧ ⎨ ⎩

⎫ ⎬ ⎭ dB


Range index of Hata-Okumura Model

n = ( 44.9 - 6.55 loghb ) / 10

20 200hb (m)

3.84

2.98


Measurement of Path Loss forLow Base Station Antennas of Microcells


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


Mission District of San Francisco


Drive Routes In the Mission District


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 inthe Sunset District vs. Distance Traveled

f = 1937 MHz, hBS= 8.7 m, hm = 1.6 m


Regression Fit to Received Signal Versus R on Staircase Route in Sunset District



Received Signal on Zig-Zag Route inthe Sunset District vs. Distance Traveled

f = 1937 MHz, hBS= 8.7 m, hm = 1.6 m



Regression Fit to Received Signal Versus R on the Transverse Portions of the Zig-Zag Route



Regression Fit to Received Signal Versus R on the Lateral Portions of the Zig-Zag Route



Comparison of Regression Fits onDifferent 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.


Har-Xia-Bertoni Model forLow 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


Har-Xia-Bertoni Model for LOS Paths

( )

( ) ( )

( ) [ ] ( )( ) kb

bbkGbkk

bkk

kbbGk

bkk

mmb

bk

k

G

Rh

hRfRRL

RR

RhhfRL

RR

hhh

R

R

f

loglog90.1310.32

loglog90.1334.25log70.45log10.3238.48

)(

loglog73.580.15log09.0log40.3914.81

)(

6.11000

4

++

−++−=

>

−+−+=

<

=≅

=

=

segment out-Far

segment in-Near

m

km in distance

GHz infrequency

λ


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

Δ+Δ−+

Δ+Δ+−+=

Δ+Δ−+

Δ+Δ+−+=

=Δ

=

=

:Paths Lateral

:paths transverse and staircase Combined

m in buildings (below) above station base of height

km in distance

GHz infrequency


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+29.74logfG −0.99loghb + 47.23+3.72loghb( )logRk

Lateral paths

L Rk( ) =135.41+12.49logfG −4.99loghb + 46.84+2.34loghb( )logRk


Comparison of Hata and Har Models

€

For base station antenna heights outside measurement

limits of both models

For f =1GHz

Hata urban area

L =69.55+26.16log1000−13.82log20+ 44.9−6.55log20( )logRk

=130.0+36.4logRk

Har combined staircase and transverse (residential)

L =138.31−13.74log(1+9)+ 40.06−4.35log(1+9)[ ]logRk

=124.6+35.7logRk

Two models go into each other for middle height base station antennas

hm = 1.6 mhBS = 20 m

h = 9 m


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 station antennas 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 match continuously with measurements made with low antennas

July, 2003©2003 by H.L.Bertoni1 IV. Propagation Characteristics Observed in Macro / Micro Cells Ray...

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Transcript of July, 2003©2003 by H.L.Bertoni1 IV. Propagation Characteristics Observed in Macro / Micro Cells Ray...