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    Radio Propagation -

    Large-Scale Path Loss

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    EEE5302

    Basics - Propagation

    Radio waves are Easy to generate Can travel long distances Can penetrate bildings

    !hey are both sed "or indoor and otdoor co##nication !hey are o#ni-directional$ can travel in all directions !hey can be narrowly "ocsed at high "re%encies &greater

    than '00()*+ sing parabolic antennas &li,e satellite dishes+ Properties o" radio waves are "re%ency dependent

     t low "re%encies. they pass throgh obstacles well. bt thepower "alls o"" sharply with distance "ro# sorce

     t high "re%encies. they tend to travel in straight lines andbonce o" obstacles &they can also be absorbed by rain+

    !hey are sb/ect to inter"erence "ro# other radio wave sorces

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    EEE5303

    Basics - Propagation t VLF, LF, and MF bands. radio

    waves "ollow the grond ( radiobroadcasting ses (1 band

     t HF bands. the grond

    waves tend to be absorbed by the

    earth !he waves that reach ionosphere

    &'00-500,# above earth sr"ace+.are re"racted and sent bac, to

    earth

    absorption

    re"lection

      Ionosphere

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    EEE530

    Basics - Propagation

    LS path

    Re"lected 4ave

    -Directional antennas are used-Waves follow more direct paths

    - LOS Line-of-Si!ht "ommunication- #eflected wave interfere with the

    ori!inal si!nal

    VHF $ransmission

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    EEE5305

    Basics - Propagation

    4aves behave #ore li,e light at higher

    "re%encies i""iclty in passing obstacles

    (ore direct paths

    !hey behave #ore li,e radio at lower

    "re%encies Can pass obstacles

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    EEE5306

    Propagation (odels

    4e are interested in propagation

    characteristics and #odels "or waves with

    "re%encyy in range$ "ew ()* to a "ew 7)*

    (odeling radio channel is i#portant "or$ eter#ining the coverage area o" a trans#itter 

    eter#ine the trans#itter power re%ire#ent

    eter#ine the battery li"eti#e

    1inding #odlation and coding sche#es to i#prove the

    channel %ality

    eter#ine the #a8i## channel capacity

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    Radio Propagation (odels

     s the #obile #oves away "ro# the trans#itter overlarger distances. the local average received signalwill gradally decrease !his is called large-scalepath loss

    !he #odels that predict the #ean signal strength "oran arbitrary-receiver trans#itter &!-R+ separationdistance are called large-scale propagation #odels

    :se"l "or esti#ating the coverage area o" trans#itters

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    S#all-Scale and Large-Scale 1ading

    ' '6 '; 20 22 2 26 2;

    !-R Separation eters+

    -90

    -60

    -50

    -0

    -30

    Received Power &dB#+

    !his "igre is /st an illstration

    to show the concept

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    4hat is ecibel &dB+

    4hat is dB &decibel+$   logarith#ic nit that is sed to describe a ratio

    Let say we have two vales P' and P2 !he di""erence &ratio+

    between the# can be e8pressed in dB and is co#pted as

    "ollows$ '0 log &P'>P2+ dB

    E8a#ple$ trans#it power P' ? '004.

    received power P2 ? ' 4

    !he di""erence is '0log&'00>'+ ? 20dB

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    dB

    dB nit can describe very big ratios withn#bers o" #odest si*e

    See so#e e8a#ples$

    !8 power ? '004. Received power ? '4 !8 power is '00 ti#es o" received power  i""erence is 20dB

    !8 power ? '004. Received power ? '#4 !8 power is '00.000 ti#es o" received power 

    i""erence is 50dB !8 power ? '0004. Received power ? '#4

    !8 power is #illion ti#es o" received power  i""erence is 60dB

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    dB#

    1or power di""erences. dB# is sed to denote

    a power level with respect to '#4 as the

    re"erence power level Let say !8 power o" a syste# is '004 @estion$ 4hat is the !8 power in nit o" dB#A

     nswer$ !8power&dB#+ ? '0log&'004>'#4+ ?

    '0log&'004>000'4+ ? '0log&'00.0000+ ? 50dB#

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    dB4

    1or power di""erences. dB4 is sed to

    denote a power level with respect to '4 as

    the re"erence power level Let say !8 power o" a syste# is '004 @estion$ 4hat is the !8 power in nit o" dB4A

     nswer$ !8power&dB4+ ? '0log&'004>'4+ ? '0log&'00+ ?

    20dB4

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    1ree-Space Propagation (odel

    :sed to predict the received signal strengthwhen trans#itter and receiver have clear.nobstrcted LS path between the#

    !he received power decays as a "nction o"!-R separation distance raised to so#epower

    Path Loss$ Signal attenation as a positive%antity #easred in dB and de"ined as thedi""erence &in dB+ between the e""ectivetrans#itter power and received power

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    1ree-Space Propagation (odel

    1ree space power received by a receiver antennaseparated "ro# a radiating trans#itter antenna by adistance d is given by 1riis "ree space e%ation$

     Pr &d+ ? &Pt7t7r λ2+ > &&π+2d2L+ E%ation 'D

    Pt is trans#ited power  Pr &d+ is the received power  7t is the tras#itter antenna gain &di#ensionless %antity+ 7r  is the receiver antenna gain &di#ensionless %antity+ d is !-R separation distance in #eters L is syste# loss "actor not related to propagation &L ? '+

    L ? ' indicates no loss in syste# hardware &"or or prposes wewill ta,e L ? '. so we will igonore it in or calclations+

    λ is wavelength in #eters

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    1ree-Space Propagation (odel

    !he gain o" an antenna 7 is related to its a""ective

    apertre e by$

    7 ? π e > λ2   E%ation 2D

    !he e""ective apertre o" e is related to the physical si*e o"the antenna.

    λ is related to the carrier "re%ency by$

    λ ? c>" ? 2πc > ωc  E%ation 3D

    " is carrier "re%ency in )ert*

    ωc is carrier "re%ency in radians per second

    c is speed o" light in #eters>sec

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    1ree-Space Propagation (odel

    Path loss. which represents signal attenationas positive %antity #easred in dB. is de"inedas the di""erence &in dB+ between the e""ective

    trans#itted power and the received power

    PL&dB+ ? '0 log &Pt>Pr + ? -'0log&7t7r λ2+>&π+2d2D E%ation D

    &Fo can drive this "ro# e%ation '+

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    ';

    1ree-Space Propagation (odel G

    Re"erence istance d0

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    '=

    1ree-Space Propagation (odel

    E8pressing the received power in dB# and dB4 Pr &d+ &dB#+ ? '0 log Pr &d0+>000'4D H 20log&d0>d+

    where d ? d0 ? d" and Pr &d0+ is in nits o" watts 

    E%ation 9D

    Pr &d+ &dB4+ ? '0 log Pr &d0+>'4D H 20log&d0>d+where d ? d0 ? d" and Pr &d0+ is in nits o" watts 

    E%ation ;D

    Re"erence distance d0 "or practical syste#s$ 1or "re%ncies in the range '-2 7)*

    ' # in indoor environ#ents

    '00#-',# in otdoor environ#ents

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    E8a#ple @estion

      trans#itter prodces 504 o" power  + E8press the trans#it power in dB#

    B+ E8press the trans#it power in dB4

    C+

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    2'

    Soltion

     + Pt&4+ is 504

    Pt&dB#+ ? '0logPt+>'#4+D

    Pt&dB#+ ? '0log&508'000+Pt&dB#+ ? 9 dB#

    B+

    Pt&dB4+ ? '0logPt&4+>'4+DPt&dB4+ ? '0log&50+

    Pt&dB4+ ? '9 dB4

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    Soltion

    Pr &d+ ? Pr &d0+&d0>d+2

    Sbstitte the vales into the e%ation$ Pr &'0,#+ ? Pr &'00#+&'00#>'0,#+2

    Pr &'0,#+ ? 00035#4&'0-+

    Pr &'0,#+ ? 358'0-'04

    Pr&'0,#+ dB#D ? '0log&358'0-'04>'#4+

      ? '0log&358'0-9

    +  ? -65dB#

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    !wo #ain channel design isses

    Co##nication engineers are generally concernedwith two #ain radio channel isses$

    Lin, Bdged esign Lin, bdget design deter#ines "nda#ental %antities sch as

    trans#it power re%ire#ents. coverage areas. and battery li"e

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    EEE5302

    Lin, Bdged esign :sing Path Loss

    (odels Radio propagation #odels can be derived

    By se o" e#pirical #ethods$ collect#easre#ent. "it crves

    By se o" analytical #ethods (odel the propagation #echanis#s #athe#atically and

    derive e%ations "or path loss

    Long distance path loss #odel

    E#pirical and analytical #odels show thatreceived signal power decreases logarith#icallywith distance "or both indoor and otdoorchannels

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    EEE53025

    Long distance path loss #odel

    !he average large-scalepath loss "or an arbitrary !-

    R separation is e8pressed

    as a "nction o" distance by

    sing a path loss e8ponent

    n$

    !he vale o" n depends on

    the propagation

    environ#ent$ "or "ree space

    it is 2I when obstrctionsare present it has a larger

    vale

    )log(10)()(

    )()(

    0

    0

    0

    d nd  PLdB PL

    d d  PL

      n

    +=

    dB)in(denotedddistanceaat

    loss pathscale-largeaveragethedenotes)(d  PL

    E%ation ''

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    EEE53029

    Selection o" "ree space re"erence

    distance

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    EEE5302;

    Log-nor#al Shadowing

    E%ation '' does not consider the "act thesrronding environ#ent #ay be vastlydi""erent at two locations having the sa#e !-R

    separation !his leads to #easre#ents that are di""erent

    than the predicted vales obtained sing theabove e%ation

    (easre#ents show that "or any vale d. thepath loss PL&d+ in dB# at a particlar locationis rando# and distribted nor#ally

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    EEE5302=

     X σ   is a *ero-#ean 7assian &nor#al+ distribted rando# variable &in dB+

    with standard deviation σ &also in dB+

    Log-nor#al Shadowing- Path Loss

    )(d  PL

    σ  

    σ  

     X d 

    d nd  PLdBd  PL

     X d  PLdBd  PL

    ++=

    +=

    )log(10)(][)(

    )(][)(

    0

    0

    !hen adding this rando# "actor$

    denotes the average large-scale path loss &in dB+ at a distance d

    )( 0d  PL is sally co#pted ass#ing "ree space propagation #odel between

    trans#itter and d0 &or by #easre#ent+

    E%ation '2 ta,es into accont the shadowing a""ects de to clttering on the

    propagation path

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    EEE53030

    Log-nor#al Shadowing- Received

    Power  !he received power in log-nor#al shadowing

    environ#ent is given by the "ollowing "or#la

    &derivable "ro# E%ation '2+

     

    !he antenna gains are inclded in PL&d +

    ++−=

    −=

    ][)log(10])[(][])[(

    ])[(][])[(

    0

    0   dB X d 

    d ndBd  PLdBm P dBmd  P 

    dBd  PLdBm P dBmd  P 

    t r 

    t r 

    σ  

    E%ation '2

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    EEE5303'

    Log-nor#al Shadowing. n and σ

    !he log-nor#al shadowing #odel indicatesthe received power at a distance d isnor#ally distribted with a distance

    dependent #ean and with a standarddeviation o" σ

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    EEE53032

    E8a#ple o" deter#ining n and σ

     ss#e Pr &d0+ ? 0dB#

    and d0 is '00#

     ss#e the receiver

    power Pr  is #easredat distances '00#.

    500#. '000#. and

    3000#.

    !he table gives the#easred vales o"

    received power

    Distance from$ransmitter 

    #eceived %ower 

    '00# 0dB#

    500# -5dB#

    '000# -''dB#

    3000# -'6dB#

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    EEE53033

    E8a#ple o" deter#ining n and σ

    4e ,now the #easred vales Lets co#pte the esti#ates "or received

    power at di""erent distances sing long-

    distance path loss #odel &E%ation ''+ Pr &d0+ is given as 0dB# and #easred vale

    is also the sa#e #eanPr &d+ ? Pr &d0+ G #eanPL&"ro#d0 tod+

    !hen #eanPr &d+ ? 0 G '0logn&d>d0+ :se this e%ation to co#pter power levels at

    500#. '000#. and 3000#

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    EEE5303

    E8a#ple o" deter#ining n and σ

     veragePr &500#+ ? 0 G '0logn&500>'00+ ? -6==n

     veragePr &'000#+ ? 0 G '0logn&'000>'00+ ? -'0n

     veragePr &3000#+ ? 0 G '0logn&3000>'00+ ? -'99n

    Jow we ,now the esti#ates and also #easred

    actal vales o" the received power at di""erent

    distances

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    EEE53035

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    EEE53036

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    EEE53039

    Path Loss E8ponent and Standard eviation

    (easred "or i""erent Bildings

    &uildin! Fre'uenc( )MH*+ n  )d&+

    Retail Stores =' 22 ;9

    7rocery Store =' '; 52

    ""ice. hard partition '500 30 90

    ""ice. so"t partition =00 2 =6

    ""ice. so"t partition '=00 26 ''

    Factor( LOS

    !e8tile>Che#ical '300 20 30

    !e8tile>Che#ical 000 2' 90

    Paper>Cereals '300 '; 60

    (etalwor,ing '300 '6 5;

    Sbrban )o#e

    Che#ical 000 2' =9

    (etalwor,ing '300 33 6;

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    EEE5303;

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    EEE5303=

    Partition Losses

    !here are two ,ind o" partition at the sa#e

    "loor$ )ard partions$ the walls o" the roo#s

    So"t partitions$ #oveable partitions that does notspan to the ceiling

    !he path loss depends on the type o" the

    partitions

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    EEE5300

    Partition Losses

    Material $(pe Loss )d&+ Fre'uenc( )MH*+

     ll #etal 26 ;'5

     l#ini# Siding 20 ;'5

    Concerete Bloc, 4all 3= '300

    Loss "ro# one 1loor 20-30 '300

    !rning an ngle in a Corridor '0-'5 '300

    Concrete 1loor '0 '300

    ry Plywood &3>in+ G ' sheet ' =600

    4et Plywood &3>in+ G ' sheet '= =600

     l#in# &'>;in+ G ' sheet 9 =600

     verage signal loss #easre#ents reported by varios researches

    "or radio paths obscrcted by so#e co##on bilding #aterial

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    EEE530'

    Partition Losses between 1loors

    !he losses between "loors o" a bilding are

    deter#ined by E8ternal di#ensions and #aterials o" the bilding

    !ype o" constrction sed to create "loors E8ternal srrondings

    J#ber o" windows

    Presence o" tinting on windows

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    EEE5302

    Partition Losses between 1loors

    &uildin! FF )d&+  )d&+

    Office &uildin!

    !hrogh ' 1loor '2= 90

    !hrogh 2 1loors ';9 2;

    !hrogh 3 1loors 2 '9

    !hrogh 1loors 290 '5

    Office &uildin! .

    !hrogh ' 1loor '62 2=

    !hrogh 2 1loors 295 5!hrogh 3 1loors 3'6 92

     verage 1loor ttenation 1actor in dB "or ne. !wo. !hree and1or 1loors in !wo ""ice Bildings

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    EEE5303

    Signal Penetration

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    Signal Penetration