giuseppe bianchi wireless cellular networks (basics) part 1 – propagation for dummies

Giuseppe Bianchi

Wireless Cellular NetworksWireless Cellular Networks(basics) (basics)

Part 1 – Propagation for dummies

Giuseppe Bianchi

The radio spectrumThe radio spectrum

ELF <3 KHz Remote control, Voice, analog phone

VLF 3-30 KHz Submarine, long-range

LF 30-300 KHz Long-range, marine beacon

MF 300 KHz –3 MHz AM radio, marine radio

HF 3-30 MHz Amateur radio, military, long-distance aircraft/ships

VHF 30-300 MHZ TV VHF, FM radio, AM x aircraft commun.

UHF 300 MHz - 3 GHz Cellular, TV UHF, radar

SHF 3-30 GHz Satellite, radar, terrestrial wireless links, WLL

EHF 30-300 GHz Experimental, WLL

IR 300 GHz – 400 THz

LAN infrared, consumer electronics

Light 400-900 THz Optical communications

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Spectrum AllocationSpectrum Allocation

Higher frequencies: more bandwidth less crowded spectrumbut greater attenuation through

wallsCurrent target: 60 GHz ultra high

throughput WLANs/WPANs Lower frequencies

bandwidth limitedlonger antennas requiredgreater antenna separation

requiredseveral sources of man-made

noise

Cellular Systems400-2200 MHz range (VHF-UHF)Simple, small antenna (few cm)With less than 1W transmit power,

can cover several floors within a building or several miles outside

wireless data systems2.4, 5 GHz zones (ISN band)Main interference from microwave

ovenslimitations due to absorption by

water and oxygen - weather dependent fading, signal loss due to by heavy rainfall etc.

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Antennas (ideal, free space)Antennas (ideal, free space)

Isotropic (omnidirectional) tx antenna in free spaceTransmitted power: Pt

Power attenuation Pa at distance d:down with sphere superficies

Power received by isotropic rx antennaPlanar waveAe = Effective Area

In two-way communication Same antenna may be used for tx and rx

24)(

d

PdP t

a

4

)()(2

e

ear

A

AdPdP

r

Idealization: Isotropic antennas cannot be practically built

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Antennas (real, free space)Antennas (real, free space)

Non isotropic tx antennaAntenna gain Gt

Gain = Power output, in a particular direction, compared to that produced in any direction by a perfect omni-directional (isotropic) antenna

Non isotropic rx antennaAntenna gain Gr

r

24)(

d

PGdP tt

a

44)()(

2

2 rtt

erar Gd

GPAGdPdP

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Friis Free-Space ModelFriis Free-Space Modelsummarizing all previous considerationssummarizing all previous considerations

Pt = transmitter power (W or mW)

Gt = transmitter antenna gain Gr = transmitter antenna gain

(dimensionless) = c/f = RF wavelength (m)

c = speed of light (3x108 m/s) f = RF frequency (Hz)

2

22

2

4)4()(

fd

c

L

GGP

Ld

GGPdP rt

trtt

r

0d

Pt Gt = Equivalent Isotropic Radiated Power (EIRP)

L = other system losses (hardware) L >=1 (dimensionless)

d = distance between transmitter and receiver (m)

2)( ddPrSummary: in free space,

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Power units – dB and dBmPower units – dB and dBm

Decibel (dB): log unit of intensity; indicates power lost or gained between two signals

Named after Alexander Graham Bell

dBm: absolute value (reference = 1 mW)Versus dB = relative value = ratio Power in dBm = 10 log(power/1mW)

21 /log10 PPPA = 1 WattPB = 50 milliWatt

PA = 13 dB greater than PB

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Decibels - dBmDecibels - dBm Examples

10 mW = 10 log10(0.01/0.001) = 10 dBm10 W = 10 log10(0.00001/0.001) = -20 dBm26 dBm = ___ 2W= ___ dBm?S/N ratio = -3dB S = ___ X N?

Transmit powerMeasured in dBm

Es. 33 dBm Receive Power

Measured in dBmEs. –10 dBm

Path LossReceive power / transmit powerMeasured in dBLoss (dB) = transmit (dBm) – receive (dBm)

Es. 43 dB = attenuation by factor 20.000

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Friis ExampleFriis Examplenormalized

frequency [MHz] 900 900000000speed of light [Km/s] 300000 300000000lambda (m) 0,333333333gain Tx 1Gain Rx 1Loss 1Ptx [W] 5distance (Km) Prx W Prx dBm

200 8,80E-08 -40,56400 2,20E-08 -46,58600 9,77E-09 -50,10800 5,50E-09 -52,60

1000 3,52E-09 -54,541200 2,44E-09 -56,121400 1,79E-09 -57,461600 1,37E-09 -58,621800 1,09E-09 -59,642000 8,80E-10 -60,562200 7,27E-10 -61,392400 6,11E-10 -62,142600 5,20E-10 -62,842800 4,49E-10 -63,483000 3,91E-10 -64,083200 3,44E-10 -64,643400 3,04E-10 -65,173600 2,71E-10 -65,663800 2,44E-10 -66,134000 2,20E-10 -66,584200 1,99E-10 -67,004400 1,82E-10 -67,414600 1,66E-10 -67,794800 1,53E-10 -68,165000 1,41E-10 -68,52

-70,00

-60,00

-50,00

-40,00

-30,00

0 1000 2000 3000 4000 5000

distance (m)

receiv

ed

po

wer

(dB

m)

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Reference distanceReference distance

If known received power at a reference distance do from tx can calculate Pr(d) for any d

Must be smaller than typical distances encountered in wireless communication systems;

Must fall in the far-field region of the antennaSo that losses beyond this point are purely distance-dependent

Typical d0 selection: 100-1000m

2

)()(

d

ddPdP o

orr

d

ddBmdP

d

ddPdBmdP o

oro

orr 101010 log20))((log20)(log10)()(

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More realistic propagation More realistic propagation modelsmodels

Inverse square power lawWay too optimistic (ideal case); valid only for very short

distancesReal world: -th power law

with ranging up to as much as If tough environment (e.g., lots of foliage),

typical values: for small distances (20 dB/decade)todB/decadefor mobile telephone distances

higher in cities and urban areas; lower in suburban or rural areas.

ddPr )(

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Formulae with ref. distanceFormulae with ref. distance

d

ddPdBmdP o

orr 1010 log10)(log10)()( d_ref 1 KmP_ref -51,5266 dBm (Ptx=10W; 900 MHz; 1000m)

distance prx (eta=2)prx (eta=3,5) prx (eta=4)1 -51,5266 -51,5266206 -51,5266

1,2 -53,1102 -54,2979642 -54,69391,4 -54,4492 -56,6411018 -57,37171,6 -55,609 -58,67082 -59,69141,8 -56,6321 -60,4611582 -61,7375

2 -57,5472 -62,0626704 -63,56782,2 -58,3751 -63,5114144 -65,22352,4 -59,1308 -64,834014 -66,73512,6 -59,8261 -66,0506877 -68,12562,8 -60,4698 -67,1771517 -69,4129

3 -61,069 -68,2258645 -70,61153,2 -61,6296 -69,2068698 -71,73263,4 -62,1562 -70,1283827 -72,78583,6 -62,6527 -70,9972081 -73,77873,8 -63,1223 -71,8190464 -74,718

4 -63,5678 -72,5987203 -75,6094,2 -63,9916 -73,3403457 -76,45664,4 -64,3957 -74,0474642 -77,26474,6 -64,7818 -74,7231447 -78,03694,8 -65,1514 -75,3700639 -78,7763

5 -65,506 -75,9905707 -79,4854

-85

-80

-75

-70

-65

-60

-55

-50

1 2 3 4 5distance (Km)

rec

eiv

ed

po

we

r (d

Bm

)

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Two-Ray Ground Two-Ray Ground Propagation ModelPropagation Model

Theoretical foundation for =4Two-ray model assumes one direct LOS path and one

reflection path reach receiver with significant powerEasy to solve

ht

hr

Line-Of-Sight ray

reflected ray

Transmit and receive antennas at different height (in general)

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Two-ray model – geometryTwo-ray model – geometry

hr

ht

( )

ddirect

dreflect

rt hhd ,

22/1222

22/1222

2

111

2

111

d

hhd

d

hhdhhdd

d

hhd

d

hhdhhdd

rtrtrtreflect

rtrtrtdirect

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Two ray model – path Two ray model – path analysisanalysis

EM waves travel for different distanceSum up with different phase!

A = attenuation along direct pathB = attenuation along reflected path (reflection not ideal, in general)

d

hh

d

hhd

d

hhddd rtrtrt

directreflect 22

11

2

11

22

c

dtfB

c

dtfA

reflect

direct

2cosrayreflect

2cosraydirect

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Two ray model – field Two ray model – field strengthstrengthPhase difference

Received field strength

Let Edirect be the field strength given by direct ray.Then

Assume ideal reflection (=-1)

d

hhd

c

df rt

42

2

jdirect eEE 1

2sin2

2

cos12

sincos2cos1

sincos112/122

directdirect

direct

directj

direct

EE

EE

jEeEE

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Two ray model – power Two ray model – power computationcomputation

Received power

Proportional to |E|2

d

hh

dL

GGPdP rtrtt

r

2

sin44

)( 22

2/sin4 2 directr EP

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Two ray model - conclusionTwo ray model - conclusion

Typical values:ht ~ few tens of m

hr ~ couple of meters ~ few tens of cmd ~ hundred meters – few km

22 22

sin2

d

hh

d

hhsmall

d

hh rtrtrt

4

22222

44

)(d

hh

L

GGP

d

hh

dL

GGPdP rtrttrtrtt

r

i.e. attenuation follows a 40 dB/decade rule! Versus 20 dB/decade of the free-space model

4)( ddPr

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Propagation impairmentsPropagation impairments

Line of sight

Reflection

Shadowing

BS

MS

Diffraction When the surface

encountered has sharp edges bending the wave

Scattering When the wave encounters

objects smaller than the wavelength (vegetation, clouds, street signs)BS

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Multipath CharacteristicsMultipath Characteristics(not just attenuation)(not just attenuation)

A signal may arrive at a receivermany different timesFrom many different directions

due to vector addition, signal mayReinforceCancel

signal strength differsfrom place to placefrom time to time!

(slow/fast fading)

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Attenuation + fadingAttenuation + fading

Signal power

Distance BS MS (km)

Distance BS MS (m)Slow fading

Fast fading

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Statistical nature of received Statistical nature of received powerpower

Sig

nal str

en

gth

(d

B)

Time (or movement)

Long term fading

Short term fading

Mean value predictedby attenuation model (constant at given d)

Different (statistical) mathematical models for slow and fast fading(details out of the goals of this lecture)

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Cell radiusCell radiusHow do we determine cell radius?

Seems very simple: givenPt = transmitted power (dBm)Pth = threshold power (dBm)

Sensitivity of the receiver, i.e. minimum amount of received power for acceptable performance

Path loss computed asLp = Pt - Pth

Radius computed from Lp

Via -law propagation formulaVia Okumura-Hata formula (or other empirical model)

But…

oop d

dddL 10log10

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Example (part 1)Example (part 1)

Received power at 10 mt: 0.1 WThreshold power: Pth = -50 dBm

= 3.7

mtR

RR

PR

mtPRP

mtP

thdBmrdBmr

dBmr

7801010

37

70

10log50

10log3720

10log10)10()(

20100log10)10(

37

70

1010

10

10

Result: because of statistical power fluctuation (fading) outage probability at cell border will be about 50%!!!

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Fading MarginFading Margin Previous computation does

not account for long-termfadingNeed to keep it in count, as it does not

reduce when the MS makes small moves IDEA: reduce cell radius to account for

a “fading margin” M

Fading Margin definition:M = average received power at cell border

(dBm) – threshold power (dBm)M=0 means that the power received at

cell border is equal to the threshold M=6 (dB) power received at cell

border is 4 x the power threshold

Fading Margin computationThrough appropriate statistical model of

long-term fading (typically lognormal)

thtp PPL

MPPL thtp

Powerat cellborder

Mean pathloss

1% - 2%

M

prob

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Example (part 2)Example (part 2)Received power at 10 mt: 0.1 WThreshold power: Pth = -50 dBm

= 3.7If we use a fading margin M=6

mtRR

MPR

mtPRP thdBmrdBmr

537101065010

log3720

10log10)10()(

37

64

10

10

What is the experienced outage at cell border?If we assume lognormal slow fading, with dB=4 dB…

%68.642

6erfc

2

1

2erfc

2

1

dB

out

MbordercellP

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Empirical attenuation Empirical attenuation modelsmodels

Consider specific scenarios Urban area (large-medium-small city), rural area Models generated by combining most likely ray traces

(LOS, reflected, diffracted, scattered) Based on large amount of empirical measurements

Account for parameters Frequency; antenna heights; distance

Account for correction factors (diffraction due to mountains, lakes, road shapes, hills, etc)

Many models for distance ranges, frequency ranges, indoor vs outdoor Okumura-Hata ; Lee’, others cellular frequencies, large distances > 1km Walfish-Ikegami 800-2000 MHz , microcellular distances (20m – 5 km)

Adopted by European Cooperation in the field of Scientific and Technical (COST) research as reference model for 3G systems

Indoor propagation models

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Example: Okumura-Hata Example: Okumura-Hata modelmodel

Hata (1980): very simple model to fit Okumura results

Provide formulas to evaluate path loss versus distance for various scenariosLarge cities; Small and medium cities; Rural areasLimit: d>=1km

Parameters:f = carrier frequency (MHz)d = distance BS MS (Km)hbs = (effective) heigh of base

station antenna (m)hms = height of mobile antenna (m)

Effective BSAntenna height

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Okumura-Hata: urban areaOkumura-Hata: urban area

msbs

bs

path

hah

dh

fdBL

10

1010

10

log82.13

loglog55.69.44

log16.2655.69)(

a(hms) = correction factor to differentiate large from medium-small cities;

depends on MS antenna height

8.0log56.17.0log1.1:cities med-small

40097.475.11log2.3:cities large

1010

210

fhfha

MHzfhha

msms

msms

Very small correction difference between large and small cities (about 1 dB)

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Okumura-Hata: suburban & Okumura-Hata: suburban & rural areasrural areas

Start from path loss Lp computed for small and medium cities

94.40log33.18log78.4)(:rural

4.528

log2)(:suburban

102

10

2

10

ffLdBL

fLdBL

ppath

ppath

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Okumura-Hata: examplesOkumura-Hata: examples

80

90

100

110

120

130

140

150

0 1 2 3 4 5 6 7 8 9 10

distance (km)

pa

th lo

ss

(d

B)

large cities

small cities

suburbs

rural area

F=900MHz, hbs=80m, hms=3m

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Okumura-Hata and Okumura-Hata and

Coefficient of Log(d) depends only on hbs

10 = attenuation (dB) in a decade (d=1 d=10)

The higher the BS, the lower the coefficient

30

32

34

36

38

40

42

44

0 20 40 60 80 100 120 140

base station height (m)

1

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Wireless Cellular NetworksWireless Cellular Networks(basics) (basics)

Part 2 – Cellular Coverage Concepts

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Coverage for a terrestrial Coverage for a terrestrial zonezone

1 Base StationN=12 channels •(e.g. 1 channel = 1 frequency)

N=12 simultaneous calls

d

Signal OK if Prx > -X dBmPrx = c Ptx d-4

greater Ptx greater d

BS

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Cellular coverageCellular coveragetarget: cover the same area with a larger number target: cover the same area with a larger number

of BSsof BSs

19 Base Station12 frequencies 4 frequencies/cell

Worst case:4 calls (all users in same cell)Best case:76 calls (4 users per cell)Average case >> 12 Low transmit power

Key advantages:•Increased capacity (freq. reuse)•Decreased tx power

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Cellular coverage Cellular coverage (microcells)(microcells)

many BS

Very low power!!Unlimited capacity!!

Usage of same spectrum(12 frequencies)(4 freq/cell)

Disadvantage: Location mobility management

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Cellular system architecture: Cellular system architecture: the GSM Network examplethe GSM Network example

high-level viewhigh-level view

Base Station

MSC

PSTNPublic switched

telephone network

PSTNPublic switched

telephone network

Base Station

MSC

PLMNPublic Land

Mobile Network

MSC = Mobile Switching Center = administrative region

MSC role: telephone switching central with special mobility management capabilities

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GSM system hierarchyGSM system hierarchy

BTS

BSCLOCATION AREA

MSC MSC region

Hierarchy: MSC region n x Location Areas m x BSC k x BTS

MSC: Mobile Switching CenterLA: Location AreaBSC: Base Station ControllerBTS: Base Transceiver Station

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GSM essential componentsGSM essential components

BTS

BTSBTS

BTS

BTS

BSC

BSC

MSC

VLRHLRAUCEIRGMSC

To fixed network (PSTN, ISDN, PDN)

OMC

MS Mobile StationBTS Base Transceiver StationBSC Base Station ControllerMSC Mobile Switching Center GMSC Gateway MSCOMC Operation and Maintenance CenterEIR Equipment Identity RegisterAUC Authentication CenterHLR Home Location RegisterVLR Visitor Location Register

MS

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Cellular capacityCellular capacity

Increased via frequency reuseFrequency reuse depends on interferenceneed to sufficiently separate cells

reuse pattern = cluster size (7 4 3): discussed later

Cellular system capacity: depends onoverall number of frequencies

Larger spectrum occupation frequency reuse patternCell size

Smaller cell (cell microcell picocell femtocell) = greater capacity

Smaller cell = lower transmission powerSmaller cell = increased handover management burden

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AB

CD

AB

CD

hexagonal cellshexagonal cells Hexagon:

Good approximation for circle

Ideal coverage patternno “holes” no cell superposition

AB

CD

AB

CD

AB

CA

AB

CD

AC

D

D

DB

Example case:Reuse pattern = 4

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Cells in real worldCells in real world

Shaped by terrain, shadowing, etcCell border: local threshold, beyond which neighboring BS signal

is received stronger than current one

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Reuse patternsReuse patternsReuse distance:

Key conceptIn the real world depends on

Territorial patterns (hills, etc)Transmitted power

» and other propagation issues such as antenna directivity, height of transmission antenna, etc

Simplified hexagonal cells model:reuse distance depends on reuse

pattern (cluster size)Possible clusters:

3,4,7,9,12,13,16,19,…

13

4

5

6

7

21

3

4

5

6

7

2

D R

Cluster: K = 7

12

3

4

12

3

4

12

3

4

D

K = 4

12

3

4

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Reuse distanceReuse distance

General formula Valid for hexagonal geometry K = cluster size D = reuse distance R = cell radius q = D/R =frequency reuse factor

3KRD

K q=D/R3 3,004 3,467 4,589 5,2012 6,0013 6,24

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ProofProof Distance between two cell

centers: (u1,v1) (u2,v2)

Simplifies to:

Distance of cell (i,j) from (0,0):

Cluster: easy to see that

hence:

21212

2

12 30sin)()(30cos)( oo uuvvuuD

30°

v

u

(1,1)

(3,2)

))(()()( 12122

122

12 vvuuvvuuD

RijjiD 322

ijjiDK R 222

KRD 3

ijjiDR 22

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K=7(i=2,j=1) K=4 (i=2,j=0)

K=13(i=3,j=1)

ClustersClustersClusters:• Number of BSs comprised in

a circle of diameter D• Number of BSs whose inter-

distance is lower than D

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Clusters (dim)Clusters (dim)

AB

CD

AB

CD

AB

CD

AB

CD

AB

CD

AB

C

AB

C

AB

CD

B

CD

AB

CD

AB

CD

B

CD

AB

CD

AB

CD

BD

BD

B

AB

AB

ABC

D

ABC

D

ABC

DABC

D

ABC

D

ABC

D

ABC

D2

2

2

2

2

2

3

2

323

23

2

3

32

3

RCK

K

C

DR

DKAKA

DH

HH

Aclusterarea

RAcellaarea

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Possible clustersPossible clustersall integer i,j valuesall integer i,j values

i j K=ii+jj+ij q=D/R1 0 1 1,731 1 3 3,002 0 4 3,462 1 7 4,582 2 12 6,003 0 9 5,203 1 13 6,243 2 19 7,553 3 27 9,004 0 16 6,934 1 21 7,944 2 28 9,174 3 37 10,544 4 48 12,005 0 25 8,665 1 31 9,64

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Co-Channel InterferenceCo-Channel Interference

Frequency reuse implies that remote cells interfere with tagged one

Co-Channel Interference (CCI) sum of interference from

remote cellsCB

AD

E

CB

AD

EF

G

C

AD

EF

AE

FG A

EF

G

CB

A

FG

CB

AD

small N as

(I)power signal ginterferin

(S)power signal

(I)power signal ginterferin )(Npower noise

(S)power signal

S

S

I

S

N

S

I

S

N

S

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CCI Computation - CCI Computation - assumptionsassumptions

Assumptions

NI=6 interfering cells NI=6: first ring interferers

onlywe neglect second-ring

interferers

Negligible Noise NS

S/N ~ S/I

d propagation law=4 (in general)

Same parameters for all BSsSame Ptx, antenna gains, etc

Key simplificationSignal for MS at distance RSignal from BS interferers at

distance D

RR

D

PowerPo

PowerPo

Dint

Dint ~ D

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CCI computationCCI computation

qNR

D

ND

R

N

D

R

I

S

N

S

III

N

k

I

111

cost

cost

1

Results depend on ratio q=D/R

(q=frequency reuse factor)

KRD 3

By using the assumptions of same cost and same D:

Alternative expression: recalling that

III N

KK

NKR

R

NI

S

N

S 22

33

1

3

1

USAGE: Given an S/I target, cluster size K is obtained

NI=6,=4 2

2

2

3

6

3K

K

I

S

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ExamplesExamples

target conditions: S/I=9 dB=4

Solution:

target conditions: S= 18dB=4.2

Solution:

33.2

3

2

6

3

894.710

4

2

9.0

KK

I

SK

K

I

S

I

S

763.53

10

23.121

78.7183log

6log103log5

23.1

KK

K

KdBI

S

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S/I computationS/I computationassuming assuming ηη=4 & 6 interferers only (first =4 & 6 interferers only (first

ring)ring)

K q=D/R S/I S/I dB3 3,00 13,5 11,34 3,46 24,0 13,87 4,58 73,5 18,79 5,20 121,5 20,812 6,00 216,0 23,313 6,24 253,5 24,016 6,93 384,0 25,819 7,55 541,5 27,321 7,94 661,5 28,225 8,66 937,5 29,7

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Additional interferersAdditional interferers

case K=4note that for each

cluster there are always NI=6 first-ring interferers

AB

CD

AB

CD

AB

CD

AB

CD

AB

CD

AB

C

AB

C

AB

CD

B

CD

AB

CD

AB

CD

B

CD

AB

CD

AB

CD

BD

BD

B

AB

AB

In CCI computation, contribute of additional interferers is marginal

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sectorizationsectorization

Directional antennas

Cell divided into sectors

Each sector uses different frequenciesTo avoid interference at sector

borders

PROS:CCI reduction

CONS: Increased handover rateLess effective “trunking” leads to

performnce impairments

Sector 1Laa ff ,1,

Sector 2LaLa ff 2,1,

Sector 3LaLa ff 3,12,

CELL a

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CCI reduction via CCI reduction via sectorizationsectorizationthree sectors casethree sectors case

CB D

E

CB D

EF

G

CD

EF

EF

G AE

FG

CB

A

FG

CB

AD

FG

Inferference from 2 cells, onlyInstead of 6 cells

A

A

A

A

77.4

32

120

120

dBI

SdB

I

S

I

S

D

R

I

S

omni

omni

o

o

With usual approxs (specifically, Dint ~ D)

Conclusion: 3 sectors = 4.77 dB improvement

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6 sectors6 sectors

60o Directional antennas

CCI reduction:1 interfereer only6 x S/I in the omni caseImprovement: 7.78 dB

giuseppe bianchi wireless cellular networks (basics) part 1 – propagation for dummies

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