射频工程基础 Fundamentals of RF Engineering 学时 :60/20 学分 : 3.5 孙利国...

射频工程基础

Fundamentals of RF Engineering

学时 :60/20学分 : 3.5

孙利国中国科技大学信息学院电子工程与信息科学系

教材：以课堂讲义为主。主要参考书：[1]“Microwave and RF Design: A System Approach”, Michael Steer, SciTech Publishing, 2010其它参考书：[2] “ 射频电路设计 - 理论与应用”， Reinhold Ludwig 等著，王子宇等译，电子工业出版社， 2002[3] “ 射频微电子学”，拉扎维著，余志平等译，清华大学出版社， 2006[4] “RF and Microwave Circuit Design for Wireless Communications”, Lawrence Larson, Artech House, 1997[5]” 无线网络 RF 工程：硬件、天线和传播“， Daniel M.Dobkin 著，科学出版社， 2007[6] “Radio Propagation for Modern Wireless System”, Henry L. Bertoni, Prentice Hall PTR, 2000[7]”Microwave and millimeter wave propagation”, Xie Yixi, etal. International Academic Publishers, 1995[8]”Wireless Communications -Principle and Practice”, T.S. Rappaport, Prentice Hall PTR, 2002

第五讲射频电波传播（ Session 5 RF Radio-wave propagatio

n ）

“Microwave and RF Design: A System Approach”,

Chapter 2Antenna and RF linkReading: §2.6 to §2.8

Reference

Goal of This Lecture The goal here is to understand propagation in

wireless systems. You will be able to calculate loss in a radio link. You will also develop an understanding of fading and the schemes to overcome it.

Outline• Propagation• Fading

InformationSource

Channel InformationDestination

Three types of wave propagation

When dealing with radio signals, transmission-reception takes 3 types of wave propagation. Space wave: Line of sight (LOS) Ground wave Sky wave

Line of sight (LOS) propagation is very useful in RF frequencies, especially VHF and UHF.

Earth

Ionosphere

Sky-wave

Ground-wave

Space wave: Line of sight

6

Transmitter Receiver

Earth

Sky wave

Space wave

Ground waveTroposphere

(0 - 12 km)

Stratosphere (12 - 50 km)

Mesosphere (50 - 80 km)

Ionosphere (80 - 720 km)


7

Classification Band

Initials Frequency Range Characteristics

Extremely low ELF < 300 Hz

Ground waveInfra low ILF 300 Hz - 3 kHz

Very low VLF 3 kHz - 30 kHz

Low LF 30 kHz - 300 kHz

Medium MF 300 kHz - 3 MHz Ground/Sky wave

High HF 3 MHz - 30 MHz Sky wave

Very high VHF 30 MHz - 300 MHz

Space waveUltra high UHF 300 MHz - 3 GHz

Super high SHF 3 GHz - 30 GHz

Extremely high EHF 30 GHz - 300 GHz

Tremendously high THF 300 GHz - 3000 GHz


Line of Sight (LOS) Propagation

Free space - wave travels in a straight line atmospheric absorption (loss) refraction in the atmosphere reflections from the ground

reflected wave

direct (free space) wave

refracted waveTxRx

r

Free Space “Spreading” Loss energy intercepted by the red square is proportional to 1/r2

Free Space Path LossLine of Sight (LOS) Propagation

22

2D

T

in

22

2D

2D

4

)(4/)(

)/(PG

by defined is antennaer transmitt theofgain

antenna theinput topower P

antennaer transmitt theof efficiency the

where

antennalossy aFor

antenna thefrompower ed transmittthe

4

)(4/)(

)/(P)(

antennaer transmitt theofy directivit the,definition the toAccording

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mW

The

the

PP

P

d

DPP

mdWP

mWunitlessD

mW

TinDTT

in

T

inT

T

TTD

T

T

The antenna gain G is the factor by which the power density is increased compared with the isotropic case.

G is very large for antennas used in microwave point-to-point systems 100 (20 dB) to 10,000,000 (70 dB).

Tx Rxd

GR, DR, ηRGT, DT, ηT

Free Space Path Loss

4

20logLossPath

as defined is losspath space free The

)()()(log10log104

20log)P

10log(LLosson Transmissi

bygiven is lossion transmissThe

equation) (Friis 4

P

4P

44P

ispower receivedThen

antennareceiver theofgain theis 4

A

A area effectivean has antenna receiving theIf

,

,R

,

2

R

2

R

2

2DR

2

R

R

dL

dBGdBGdBLGGdP

dGG

PdGGP

Gd

GPAP

DG

GG

LOSPATH

RTLOSPATHRTin

TRLINK

RTin

RTin

RTin

R

RRR

RR

Tx Rxd



Free Space Path Loss

Typical path loss: 145 dB for a 50 km link at 10 GHz (high gain antennas help offset loss ~ 60 dB)

Example:Calculate the path loss and Tr. loss for antennas 50 km apart, for a 10 GHz, system with antenna gains of 60 dB Path loss=20log(4x3.14x5x104/(3x10-2))=146 dBTr. Loss=146-60-60=26dB

Tx Rxd



C

fddL

dBGdBGdBL

GGdP

LOSPATH

RTLOSPATH

RTin

TRLINK

420log

420log

losspath space free The

)()()(

log10log104

20log)P

10log(L

Lossion transmissThe

,

,

R,

)(log20)(log205.32

)(log20)(log2098.121)(,

MHzfkmd

cmkmddBL LOSPATH

Example: Radio Link (Transmission Loss

Calculation)

+43 dBm TX output

−3 dB line efficiency= +40 dBm to antenna

+13 dB antenna gain= +53 dBm EIRP

−158 dB path attenuation

=−105 dBm if intercepted by dipole antenna

+13 dB antenna gain= −92 dBm into line

−3 dB line efficiency= −95 dBm to receiver

Receiver

Antenna

Antenna

Trans.Line

Transmitter

Trans.Line


Typical Cellular Link BudgetSource:

Cell TX PO Watts MS TX PO Watts

Cell TX PO dBM MS TX PO dBm

Cell Combiner Loss dB MS Combiner Loss db

Cell Cable Loss db MS Cable Loss db

Cell Antenna Gain dBd MS Antenna Gain dBd

EIRP Watts EIRP Watts

EIRP dBm EIRP dBm

MS Antenna Gain dBd Cell Antenna Gain dBd

MS RX Cable Loss dB Cell RX Cable Loss

MS Diversity Gain dB Cell Diversity Gain

MS RX Sensitivity dBM Cell RX Sensitivity dBM

FWD Link Budget, dB REV Link Budget, dB

Worst Case Link Budget

Input:

Calc:

Input:

Input:

Input:

Calc:

Calc:

Calc:

Input:

Input:

Input:

Calc:

Calc:

FWD Path

45.00

46.53

-3.00

-3.00

+10.00

113.03

50.53

0.00

0.00

0.00

-105.00

155.53

155.53

-2.00

REV Path

3.00

34.77

0.00

+5.00

5.99

37.77

10.00

-3.00

+4.00

-107.00

155.77

-0.24Imbalance, dB


Fresnel ZonesLine of Sight (LOS) Propagation

As radio waves propagate they spread out. The spreading out is understood from Huygens principle that every point of a propagating EM wave reradiates in every direction.One of the consequences of this is that an obstruction that is not in the LOS path can still interfere with signal propagation.The appropriate clearance is determined from the Fresnel zones.

Tx Rx1st Fresnel Zone

2nd Fresnel Zone

d=d1+d2

d / 2d

d1 d2

plane at right angles to path

Fresnel Zones

Note that path difference between rays at the edge of the 1st and 2nd Fresnel zones is /2

1st Fresnel Zone is the most important zone.


Tx Rx1st Fresnel Zone

2nd Fresnel Zone

d=d1+d2

d / 2d

d1 d2

plane at right angles to path

Fresnel Zones

Huygens principle: different Fresnel zones Z1,Z2,Z3,… Contribution from Fresnel zones Z1,Z2,Z3,…are B1,B2,B3,…



B1=Contribution from Fresnel zone1 (Z1) B1=2B0

B0=received for free-spaceContribution from Fresnel zone1 is double of the total field for free space.

)0(B 2

B

...2

B)

2

BB

2

B()

2

BB

2

B(

2

B

...2

B

2

BB

2

B

2

BB

2

B

2

B

...BBBBBB

zones. Fresnel all of )(B totalhe

n1

552

332

11

552

332

11

543210

0

SumspacefreeT


21

21nF

Ppoint at zone Fresnelth -n theof radius

dd

dd

The

Example: d1=d2=5kmF1=17.66m at 2.4 GHz

d1 d2

21

211

21

21

21

21

21

2

2

12

2

1

11

2/1

2

2

12

2/1

2

1

11

211

22

21

21

2111

F

2/)11

(2

)11

(2

)2

11()

2

11()1()1(

d,

2/dFdF2/

dd

dd

ddd

Fd

dd

Fdd

d

Fd

d

Fd

d

Fd

d

Fd

dF

ddr


Fresnel zones are a number of concentric ellipsoids with TX and RX in focus.Odd-numbered Fresnel zones have relatively intense field strengths, whereas even numbered Fresnel zones are nulls.


If the 1st Fresnel zone is clear, it can be thought as free-space propagation (LOS).If the 1st Fresnel zone is not clear, then free-space loss (LOS) does not apply and an adjustment term must be included. To avoid this :

Use an antenna with a narrower lobe pattern, usually a higher gain antenna will achieve this.Raise the antenna mounting point on TX and/or RX.


Absorption by atmospheric gases Attenuation due to

molecular absorption, for example, water vapour and O2

Important bands at frequencies >10 GHz, especially at 22 GHz (water vapor) and 60GHz (O2)

Atmospheric Absorption (clear air)


Attenuation due to precipitationsRain: usually at frequency >10GHzSnow, cloud, fog, sand

Atmospheric Attenuation (not clear air)

Atmospheric Absorption

- rainfall (snow/fog)- water vapour (molecular res. at 22 GHz)

- oxygen (molecular res. at 60 GHz)

Typical path loss:140 dB for a 50 km link at 10 GHz(high gain antennas help offset loss ~ 60 dB)

Atmospheric AttenuationLine of Sight (LOS) Propagation

Refraction in the Atmosphere

Refraction effect- ray bending Refractive index n of

atmosphere changes with height and temperature

This leads to beam bending . Normally n decreases with

increasing height. n1

n2

n3

n4

n n n n1 2 3 4

beam bending


θ2

θ1

n1

n2

y

x 122

1

1

2

2211220110

x2x1

1sin

sin

law) Snell sinsinsinksink

kk

0)(y

zone2 and zone1between interface At the

n

n

nnnn （



Radio waves get “bent” downwards.

Be able to propagate beyond the geometric horizon, which extends range.



sinn

cos0cosnsin

cosnsinnsinnsin

cosnsinnsin

coscosnsinnsin

)cos)(sinn(

)sin( and 1)cos( that so small very is

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))sin(n(nsin

law Snell the toAccording

dndddn

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dndddn

ddnright

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dddnright

ddn

cos

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curvature of adius

dh

ddh

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kmunitsN

kmunitsN

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Earth curvature Radio wave go behind the

geometrical horizon due to refraction ：the air refractivity changes with height, temperature, water vapor contents, etc.

In standard conditions the radio wave travels along arc bent slightly downward 。

An equivalent Earth radius Re=K Rearth

is introduced to “makes “the path straight.




1111

eRR

Except zero refraction, the ray is curve. We can “make” it a straight line by pretending the Earth has a larger radius which we call the equivalent Earth radius Re.



RR

RR

RR

e

e

1)

11/(1

1111

dhn11

dn

dhdn

nR

K

RK

dhdn

nRR

R

e

ee

1

1

1 An equivalent Earth radius K Rearth “makes “the path straight. K-factor is a scaling factor of the ray path curvature. K=1 means a straight line. For standard atomsphere K=4/3.



equationlinear a isequation Above

line.straight a isray

cos)r

1(cos

cos)r

1(cosr

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atmosphere uniform-non is atmosphere theIf

2

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36

Other Propagation Mechanisms Reflection

Propagation wave impinges on an object which is large as compared to wavelength

- e.g., the surface of the Earth, buildings, walls, etc.

Diffraction Radio path between transmitter and receiver obstructed by surface

with sharp irregular edges Waves bend around the obstacle, even when LOS (line of sight) does

not exist Scattering

Objects smaller than the wavelength of the propagation wave

- e.g. foliage, street signs, lamp posts


37

Transmitterd

Receiver

hb

hm

Diffracted Signal

Reflected Signal

Direct Signal

Building

Line of Sight (LOS) PropagationOther Propagation Mechanisms

Any object which is half a wavelength ( /2) long can interfere with signal.

/2 = 7.0 in., cellular radio (860 MHz) /2 = 3.2 in., PCS (1.9 GHz)

d

h

r

d

hth

MULTIPATH

ht

d

hrh

MULTIPATH

d

hthr

h

KNIFE-EDGEDIFFRACTION

hthr

h

TREE

SCATTERING


Other Propagation Mechanisms

Ground Reflections - Path Clearances and Antenna Heights

If the ground is in the 1st Fresnel zone, the ground reflection needs to be considered.

There are two kinds of reflections Smoth surface- specular reflection Rough surface -diffuse reflection

Tx Rxdirect


Ground Reflections - Path Clearances and Antenna Heights Smoth surface- specular reflection


d

HH

dHHdHHd

dHHdHHd

dHHdHHrrr

eEEEE rjk

21

212

212

2/1212

2/1212

2212

221212

121

2

]})/)((2

11[])/)((

2

11{[

}])/)((1[])/)((1{[

)()(

)1(

2

2

2

2

cos)60(sin)60(

cos)60(sin)60(on polarizati vertical

cos)60(sin

cos)60(sinon polarizati horizontalfor

cy.coefficien reflection is

jj

jjfor

j

j

rr

rrH

r

rH

Ground Reflections - Path Clearances and Antenna Heights Smoth surface- specular reflection


According to image theory, the ground reflection can be thought as field radiated from image point A’.

The 1st Fresnel zone due to image point A’ is shown in the figure. It is called efficient reflection zone.

Ground Reflections - Path Clearances and Antenna Heights

Rough surface -diffuse reflection


hsin2

hsin2sin2sin

h )2cos1(kCC

)2cosCCk(CC)k(CCrk

bygiven is b and aray between difference

2'

''1

'

k

kk

CC

Phase

decreases. field on total reflection ofeffect that theso

occurs reflection diffuse therough, is surface when the

rough as thought is surface the, 8sin

hor 2

smooth as thought is surface the, 8sin

hor 2

hsin2

criterion

when

when

k

Rayleigh

Direct propagation –curvature of the Earth

Propagation: curvature of the Earth is considered.


))()((12.4)(

refraction catomspheri standard

))()((57.3)(

km 6370R radius

)(2

2 and 2

,R

2)(

2)(

212010

212010

212010

220110

21

222

22220

211

22110

mHmHrrkmr

For

mHmHrrkmr

Earth

HHRrrr

RHrRHr

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HRHRHRr

HRHRHRr

zone. shadow-halfin isreceiver the,2.1d75.0when

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00

0

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2100

0

rr

r

r

and

d

Knife-Edge Diffraction

Sometimes a single well-defined obstruction blocks the path. This case is fairly easy to analyze and can be used as a manual tool to estimate the effects of individual obstructions.

First calculate the parameter from the geometry of the path

Next consult the table to obtain the obstruction loss in db Add this loss to the otherwise-determined path loss to

obtain the total path loss. Other losses such as reflection cancellation still apply,

but computed independently for the path sections before and after the obstruction.

21

112

ddHv

Tx Rxd1 d2

H

Atten.(dB)

0

+5

+10

+15

+20

+25

-4 -3 -2 -1 0 1 2 3-5


Knife Edge Diffraction Example 1/3

What is the total path loss at 1 GHz?

Tx Rxd1 d2

H5 m

100 m 150 m

AB

• Loss = (Path Loss, no diffraction) + (Diffraction Loss)

• Path Loss (dB) (no diffraction)

= 20 log10 (4d/)

= 20 log10 (4250/

dB

• Diffraction Loss

Atten.(dB)

0

+5

+10

+15

+20

+25

-4 -3 -2 -1 0 1 2 3-5

Use

= -5 sqrt[2/0.3 * (1/100 + 1/150)]= -1.667

Loss = 80.4 + 17.5 = 97.9 dBAdd atmospheric absorption loss to this.


Diff. Loss = 17.5 dB

Atten.(dB)

0

+5

+10

+15

+20

+25

-4 -3 -2 -1 0 1 2 3-5

-1.68

17.5 dB

Diffraction Loss = 17.5 dB

Knife Edge Diffraction Example 2/2Line of Sight (LOS) Propagation

Radio Propagation in Mobil Communication


Effect of mobilityChannel varies with user location and timeRadio propagation is very complex

Multipath scattering from nearby objects Shadowing from dominant objectsAttenuations effects

Results in rapid fluctuations of received power



Large scale modelPath lossnSlow fading(long term fade)

Small scale model fast fading(short term fade)

49

Signal Strength

(dB)

Distance

Path Loss

Slow Fading (Long-term fading)

Fast Fading (Short-term fading)



50

The received signal power:

where Gr is the receiver antenna gain,

L is the propagation loss in the channel, i.e.,

L = LP LS LF

L

PGGP trt

r

Fast fading

Slow fading

Path loss

Line of Sight (LOS) PropagationRadio Propagation in Mobil Communication

51

Definition of path loss LP

,r

tP P

PL


)](log[20)](log[20])/(

4log[20

)]()()/(

4log[20

420log(dB) L

as defined is losspath space free The

PF

kmdMHzfuskmC

kmdMHzfuskmC

d

Path Loss in Free-space:

52

dBdBI

dBdBF

kmdMHzfdBLPF

45.32)(L 1kmd and 1MHzf f

45.32)(L 1kmd and 1MHzfor

)(log20)(log2045.32)(

PF

PF

1010


)](log[20)](log[2045.32

)](log[20)](log[20]3.0

4log[20)(

skm/ 3.0/103

)](log[20)](log[20])/(

4log[20)(

8

kmdMHzf

kmdMHzfdBL

smC

kmdMHzfskmC

dBL

PF

PF

Path Loss in Free-

space:


d

d

mW

Wddbmd

or

d

ddd

dGGPd

d

dGGPd

RTin

RTin

00RR

2

00RR

2

00R

0

2

R

log201

))((Plog10 )(P

)(P)(P

4)(P

point referencepower receivedknown a as

used is d distancein -close a modelsn propagatio scale-largeIn zero. benot can

4)(P

space freeIn



er. transmitt the tocloset measuremen from determined is which distance referencein -close theisd

distance, with increase losspath heat which t rate theindicatehich exponent w losspath theis

log10)()(

)()(

:losspath scale-large average The

0

00

00

n

d

dndBPLdBPL

or

d

ddPLdPL

n


Most radio propagation models are derived using a combination of analytical and empirical methods. Both theoretical and measurement-based propagation models indicate that average received signal power decreases logarithmically with distance, whether in outdoor or indoor radio channelLong distance path loss model is as following

55

In general a simplest Formula is given:

where

d : distance between transmitter and receiver

α and β : propagation constants which are determined experimentally for different environments

β : value of 2 for free space

value of 3 ~ 4 in typical urban area


dLp

17 March 1999 Radio Propagation56

Value of characterizes different environments

Environment Exponent

Free Space 2Urban area 2.7-3.5Shadowed urban area 3-5Indoor LOS 1.6-1.8Indoor no LOS 4-6

Rappaport, Table 3.2, pp. 104



Reflection with Partial Cancellation

Analysis: physics of the reflection cancellation

predicts signal decay approx. 40 db per decade of distance

twice as rapid as in free-space! observed values in real systems

range from 30 to 40 db/decade

TX EIRPDBM

HTFT HTFT

DMILES

Comparison of Free-Space and Reflection Propagation ModesAssumptions: Flat earth, TX EIRP = 50 dBm, @ 870 MHz. Base Ht = 200 ft, Mobile Ht = 5 ft.

FS Link Loss Free-SpaceDBMFS Link Loss using ReflectionDBM

DistanceMIL

ES -45.3-69.0

1-51.4-79.2

2-55.3-89.5

4

-57.4

-95.4

6

-63.4

-99.7

8

-65.4-103.0

10

-68.9-109.0

15

-71.4-113.2

20


Pass Loss in a Mobile System

Power of a signal drops off as 1/Dn

n ranges from 2 to 4 n = 4 dense urban area n = 3 suburban area n = 2 rural area

(dBm)

StrengthSignalReceived

0 4 16 20 24 28 32128

-50

-60

-70

-80

-90

-100

-110

-120

Distance from cell site (km)

SignalMeasured

Free-Space 20 dB per decade of distance

Reflection Cancellation 40 dB per decade of distance

Real-life cellular propagation decay rates are typically somewhere between 30 and 40 dB per decade of distance.

F = 1900 MHz TowerHeight

(meters)

EIRP(watts)

Range(km)

Dense Urban 30 200 1.05Urban 30 200 2.35Suburban 30 200 4.03Rural 50 200 10.3

Example:




Outdoor propagation modelsThere are lots of out-door models to predict signal strength at a particular receiving point or in a specific local area. The methods vary widely in their approach, complexity, and accuracy.Okumura’s model is one of the most widely used models for signal prediction in urban areas. The more common form is a curve fitting of Okumura’s original results, which is called Okumura-Hata model.

61

Urban area:

where

Suburban area:

Open area:

)(log)(log55.69.44

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

1010

1010

kmdmh

mhmhMHzfdBL

b

mbcPU

citymediumsmallfor

MHzfformh

MHzfformh

cityelforMHzfmhMHzf

mh

cm

cm

cmc

m &,400,97.4)(75.11log2.3

200,1.1)(54.1log29.8

arg,8.0)(log56.1)(7.0)(log1.1

)(2

10

210

1010

4.528

)(log2)()(

2

10

MHzfdBLdBL c

PUPS

94.40)(log33.18)(log78.4)()( 102

10 MHzfMHzfdBLdBL ccPUPO



Okumura-Hata Model



Okumura-Hata Model

Path loss in decreasing order: Urban area (large city) Urban area (medium and small

city) Suburban area Open area



indoor propagation models

Indoor models are less generalized Environment

comparatively more dynamic Significant

features are physically smaller

Shorter distances are closer to near-field

More clutter, scattering, less LOS



Indoor propagation modelsPhysical effects:

Signal decays much fasterCoverage contained by walls, etc.Walls, floors, furniture attenuate/scatter radio signalsPeople moving around:

Path loss formula:

onModificatid

dndBPLdBPL

0

0 log10)()(

Fading The result of variation (with time)

of the amplitude or relative phase, or both, or one or more of the frequency components of the signal.

Cause: changes in the characteristics of the propagation path with time.

There are slow fading and fast fading


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Signal Strength

(dB)Distance

Path Loss

Slow Fading (Long-term fading)

Fast Fading (Short-term fading)


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Area-mean power (pass loss) is determined by path loss is an average over 100 m - 5 km

Local-mean power (slow fading) is caused by local 'shadowing' effects has slow variations is an average over 40 λ (few meters)

Instantaneous power (fast fading) fluctuations are caused by multipath reception depends on location and frequency depends on time if antenna is in motion has fast variations (fades occur about every half a wave length)


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Slow Fading The long-term variation in the mean level is known as slow

fading(shadowing or log-normal fading). This fading caused by shadowing. Example of Shadow: Local obstacles cause random shadow attenuation


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Slow Fading The long-term variation in the mean level is known as slow fading

(shadowing or log-normal fading). Received power in dB follows normal distribution. Log-normal distribution:

- The pdf of the received signal level is given in decibels by

where M is the true received signal level m in decibels, i.e., 10log10m, M is the area average signal level, i.e., the mean of M,

is the standard deviation in decibels

,2

1 2

2

2

MM

eMp


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Log-normal Distribution

MM

2

p(M)

The pdf of the received signal level


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Fast Fading The signal from the transmitter may be reflected from objects such

as hills, buildings, or vehicles. When MS far from BS, the envelope distribution of received signal is

Rayleigh distribution. The pdf is

where is the standard deviation. Middle value rm of envelope signal within sample range to be satisfied by

We have rm = 1.777

0,2

2

22

rer

rpr

.5.0)( mrrP



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The pdf of the envelope variation

r

2 4 6 8 10

P(r)

0

0.2

0.4

0.6

0.8

1.0

=1

=2

=3

Rayleigh Distribution


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Proof of Rayleigh Distribution


There are many objects in the environment that scatter the radio signal.

If the electric field is divided into Ex and Ey, the total fields as superposition of scattering field are given by

N

iyiy

N

ixix

EE

EE

1

1

If there are sufficiently much scatters, the Ex and Ey obey Gauss distribution respectively according to the central limit theorem.


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PDF of Ex and Ey are given by

)2

exp(2

1)(

)2

exp(2

1)(

2

2

2

2

y

yg

xxg

y

x

E

E

Because Ex and Ey are independent with each other, the joint PDF is

)2

exp(2

1),(

2

22

2 , yx

yxgyx EE


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PDF of E is given by

22yx EEE

The magnitude ( envelop) of the field is defined as

)2

exp(1)2

exp()2

exp(2

1

)2

exp(2

1)()(

2

2

0

2

2

0

2

02

2

2

2

22

222

Rrdrrd

r

dxdyyx

REPRF

RR

Ryx

E

The probability of E<R is

x

y

Rφ

)2

exp()(

)(2

2

2 xx

x

xdFxg E

E

It is Rayleigh distribution


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Fast Fading (Continued) When there is a dominant stationary(no fading) signal

component (direct signal), the envelope distribution of received signal is Ricean distribution. The pdf is

where is the standard deviation,

I0(x) is the zero-order Bessel function of the first kind, is the amplitude of the direct signal

0,02

2

2

22

rr

Ier

rpr


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Ricean Distribution

r

Pdf

p(r)

r86420

0.6

0.5

0.4

0.3

0.2

0.1

0

= 2

= 1

= 0 (Rayleigh)

= 1

= 3

The pdf of the envelope variation



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Characteristics of Instantaneous Amplitude Level Crossing Rate:

Average number of times per second that the signal envelope crosses the level (some threshold) in positive going direction.

Fading Rate: Number of times signal envelope crosses middle

value in positive going direction per unit time. Depth of Fading:

Ratio of mean square value and minimum value of fading signal.

Fading Duration: Time for which signal is below given threshold.


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Doppler Effect: When a wave source and a receiver are moving towards each other, the frequency of the received signal will not be the same as the source. When they are moving toward each other, the frequency of the received signal is higher

than the source. When they are opposing each other, the frequency decreases.

Thus, the frequency of the received signal is

where fC is the frequency of source carrier,

fD is the Doppler frequency. Doppler Shift in frequency:

where v is the moving speed, is the wavelength of carrier.

C

vf

vf CD

coscos

DCR fff

MS

Signal

Moving speed v

Doppler Shift



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Moving Speed Effect

Time

V1 V2 V3 V4

Sig

nal s

tren

gth



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Delay Spread When a signal propagates from a transmitter to a

receiver, signal suffers one or more reflections. This forces signal to follow different paths. Each path has different path length, so the time of

arrival for each path is different. This effect which spreads out the signal is called

“Delay Spread”.


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Delay Spread

Delay

Sig

nal S

tren

gth

The signals from close by reflectors

The signals from intermediate reflectors

The signals from far away reflectors



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Intersymbol Interference (ISI) Caused by time delayed multipath signals Has impact on burst error rate of channel Second multipath is delayed and is received

during next symbol For low bit-error-rate (BER)

R (digital transmission rate) limited by delay spread d.

dR

21



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Intersymbol Interference (ISI)

Time

Time

Time

Transmission signal

Received signal (short delay)

Received signal (long delay)

1

0

1

Propagation timeDelayed signals



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Coherence Bandwidth

Coherence bandwidth Bc: Represents correlation between 2 fading signal

envelopes at frequencies f1 and f2. Is a function of delay spread. Two frequencies that are larger than coherence

bandwidth fade independently. Concept useful in diversity reception

Multiple copies of same message are sent using different frequencies.



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Cochannel Interference Cells having the same frequency interfere with each other. rd is the desired signal

ru is the interfering undesired signal is the protection ratio for which

rd ru (so that the signals interfere the least)

If P(rd ru ) is the probability that rd ru ,

Cochannel probability Pco = P(rd ru )



Fixed Wireless System: Due to rapidly changing atmosphere

with small regions of different values of refractive index.

Varies over a few seconds.

Mobile Wireless System:• Principally due to movement of mobile

terminal unit or moving reflect objects.• Slow variations come from blockage

and shadowing by large objects such as hills and buildings as for fixed wireless systems.

• Time interval between fades depends on speed.

Rayleigh Fading• Named after the statistical model

that describes it.• Due to cancellation resulting from

individual paths drifting in and out of phase.

• Varies over distances of roughly /2 apart. Amplitude

Time

10-15 dB


Diversity Techniques Multipath fading is minimised by using

Diversity Techniques Many different methods for diversity. Major diversity methods:

Frequency signal transmitted at 2 or more frequencies.

Space 2 spaced Rx antennas used.

Polarization two antenna polarizations (not very effective because

the paths are still similar).



Space DiversityMethod for Combating Rayleigh Fading

Fortunately, Rayleigh fades are very short and last a small % of the time Two antennas separated by several wavelengths generally will not fade

concurrently. Switch instant-by-instant to whichever is best. Required separation D for good decorrelation is 10-20 12-24 ft. @ 800 MHz, 5-10 ft. @ 1900 MHz. Space Diversity can be applied only on the receiving end of a link. On the downlink the only way to overcome fading (in TDMA and narrow

band CDMA) is to boost the transmit power by 10–15 dB.

Signal received by Antenna 1

Signal received by Antenna 2

Combined Signal

D



Coding Technologies that Overcome Multipath Fades

OFDM (Orthogonal Frequency Division Multiple Access)In OFDM a channel is subdivided in frequency and independent bit streams transmitted in each subchannel. Rapid fading tends to affect only a portion of the channel and so only a fraction of the symbols are affected by multipath. In commercial wireless OFDM investigations the total spectrum utilized is a small fraction of the operating frequency.

Wideband CDMA (WCDMA)Fades tend to have an instantaneous bandwidth of ½ MHz independent of the carrier frequency. In CDMA the information is spread out of the operating bandwidth. The bandwidth of WCDMA is around 5 MHz and with error correcting codes the bit errors due to the 10% loss due to fading can be recovered.



Space-Time Coding (for combating fading)

Space-time coding techniques exploit the presence of multiple transmit antennas to improve performance on multipath radio channels. Commercial space-time modulation methods use accurate channel estimates at the receiver.The information is transmitted by two or more antennas using different codes but at the same frequency. The terminal unit has one but preferably two or more receive antennas. The antenna sets (Tx and Rx) can be as little as λ/2 apart and yet we can overcome fading.

D



Radio Link: Reciprocity in Cellular?

Between two antennas, on the same exact frequency, path loss is the same in both directions

But things aren’t exactly the same in cellular -- Different transmit and receive frequencies. antenna: gain/frequency slope different Rayleigh fades up/downlink often, different TX & RX antennas RX diversity

Notice also the noise/interference environment may be substantially different at the two ends.

-148.21 db@ 870.03 MHz

-148.21 db@ 870.03 MHz

-151.86 db@ 835.03 MHz



Propagation AnalysisWhat is needed, and when?

Initial System Planning how many cells required?

statistical models for average propagation, along with traffic and link budget requirements

actual measurement data for example sites to fine-tune models number of cells is whatever needed for coverage & capacity

Cell Planning, Frequency Planning, Interference Planning where should the site(s) be placed?

propagation software tool: coverage, interference analysis possible test measurements for specific

problem sites Ongoing Growth Planning, Interference Control

example: what can I do to solve the interference along the highway?

test measurements propagation software tool iterative interactive changes to frequency plan, cell configuration



Statistical Propagation Model

Power of a signal drops off as 1/Dn

n ranges from 2 to 4 n = 4 dense urban area n = 3 suburban area n = 2 rural area

SignalMeasured

(dBm)

StrengthSignalReceived

dB V/mStrengthField

0 4 16 20 24 28 32128

-50

-60

-70

-80

-90

-100

-110

-120

90

80

70

60

50

40

30

20

Distance from cell site (km)Okumura-HataPropagation Model

Deterministic Propagation Prediction Models:Use of terrain data for construction of path profilePath analysis (ray tracing) for obstruction, reflection analysis.Commonly-required Inputs:Frequency ， Station Height ， Distance ， Obstacle Height ， Geometry ， Separation ，Radius of first Fresnel zone ， Forest/Roof Height ， Loss allowances based on: land use; building/vehicle penetration



Statistical Propagation Models ： Okumura-Hata Model

A (dB) = 69.55 + 26.16 log (F) – 13.82 log(H) + (44. 9 – 6.55 log(H) )*log (D) + C

Where:AFDHC

C

=====

=

Path lossFrequency in MHz Distance between base station and terminal in kmEffective height of base station antenna in mEnvironment correction factor

0 dB- 5 dB

- 10 dB- 17 dB

====

Dense UrbanUrbanSuburbanRural



Statistical Propagation Models

Walfisch-Ikegami Model

Useful in dense urban environments, but often superior to other methods in this environment.

Based on “urban canyon” assumption a “carpet” of buildings divided into

blocks by street canyons Uses diffraction and reflection

mechanics and statistics for prediction Input variables relate mainly to the

geometry of the buildings and streets

Useful for two distinct situations: macro-cell - antennas above building

rooftops micro-cell - antennas lower than most

buildings© 2009 by Remcom, Inc. Used with permission.



Practical Application of Distribution Statistics Technique:

use a model to predict RSSI (Received Signal Strength Indication)

compare measurements with model

obtain median signal strength obtain standard deviation now apply correction factor to obtain

field strength required for desired probability of service

Applications: Given a desired signal level the standard deviation of signal

strength measurements a desired percentage of locations

which must receive that signal level

We can compute a “cushion” in dB which will give us that % coverage

RSSI, dBm

Distance

10% of locations exceed this RSSI

50%90%

Percentage of Locations where Observed RSSI exceeds Predicted RSSI

Median Signal Strength ,

dB

Occurrences

RSSI

Normal Distribution



Statistical TechniquesExample of Application of Distribution Statistics

Suppose you want to design a cell site to deliver at least -95 dBm to at least 90% of the locations in an area

Measurements you’ve made have a 10 db. standard deviation above and below the average signal strength

On the chart: to serve 90% of possible

locations, we must deliver an average signal strength 1.29 standard deviations stronger than -95 dbm

-95 + ( 1.29 x 10 ) = -82 dbm

Design for an average signal strength of -82 dbm!

Cumulative Normal Distribution

Standard Deviations from Median (Average) Signal Strength

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

-3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3



Deterministic Propagation Prediction Models

Based on deterministic methods use of terrain data for construction of path profile path analysis (ray tracing) for obstruction, reflection analysis appropriate algorithms applied for best compliance with radio physics.

Commonly-required Inputs: Frequency, Distance from transmitter to receiver, Effective Base Station

Height Obstacle Height & Geometry, Radius of the first Fresnel zone, Forest

Height / Roof Height , Distance between buildings, Arbitrary loss allowances based on land use (forest, water, etc.), Arbitrary loss allowance for penetration of buildings/vehicles

© 2009 by Remcom, Inc. Used with permission.



Propagation in an Urban Area



Propagation: Indoor



Propagation: Diffraction



Free Space Communications

3–30 kHz VLF Long distance, low fading, military& Navigation.

Earth-ionosphere waveguide (sky wave).

30–300 kHz LF LW band, small fadinghigh atmospheric noise.

Ground Wave, some sky wave. 300 kHz–3 MHz MF MW band, more fading , less a

atmospheric noise. Ground wave & sky wave. 3–30 MHz HF Fading severe, less noise, 3-6 MHz

continental, 6-30 intercontinental mobile land comms. Sky wave

30–300 MHz VHF Line-of-sight VHF links, fading problems. Space Wave.

300 MHz–3 GHzUHF Line-of-sight, fading a problem. Space wave + scatter wave.

3–30 GHz SHF Line-of-sight, satellite links, radio relay, atmospheric absorption at higher

frequencies. Space wave. 30–300 GHz EHF Line-of-sight. Satellite links, local

distribution networks.Atmospheric absorption is a problem.

RF Link and Calculations

Diversity Techniques for overcoming fading.

Propagation Fading, Diffraction, Refraction, Scattering

Summary

1. A transmitter and receiver operating at 2 GHz are at the same level, but the direct path between them is blocked by a building and the signal must diffract over the building for a communication link to be established. This is a classic knife-edge diffraction situation. The transmit and receive antennas are separated from the building by 4 km and the building is 20 m higher than the antennas (which are at the same height). Consider that the building is very thin. It has been found that the path loss can be determined by considering loss due to free-space propagation and loss due to diffraction over the knife edge.(a) What is the additional attenuation (in decibels) due to diffraction?(b) If the operating frequency is 100 MHz, what is the attenuation (in decibels) dueto diffraction?(c) If the operating frequency is 10 GHz, what is the attenuation (in decibels) dueto diffraction?

2. A transmit antenna and a receive antenna are separated by 10 km.(a) What is the radius of the first Fresnel zone?(b) What is the radius of the second Fresnel zone?(c) To ensure LOS propagation, what should the clearance be from the direct linebetween the antennas and obstructions such as hills and vegetation?

Exercises

射频工程基础 Fundamentals of RF Engineering 学时 :60/20 学分 : 3.5 孙利国...

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