Antenna and Models1

8/21/2019 Antenna and Models1

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Antenna

This section contains commonly used antenna-related terms. Logically this is the opening

section since the antenna is the receiver and transmitter of the propagated signal.

DefinitionAntenna TypesInduction and Radiation FieldsPolarizationRadiation PatternAntenna Pattern DistortionReturn LossAntenna Beamwidth (Horizontal!ertical"Front to Bac# RatioAntenna BandwidthRF Feeder LossesAntenna $fficiency$ffects of Antenna Positionin% (P&'&ellular &ommunication 'ystems"Definition

"Strictly speaking, an antenna is a device which converts an electric wave guided by aconductor into a free-space, unguided electromagnetic wave, and vice versa. Electrical

energy is fed to the antenna via a transmission line, a conductor which passes electrical

energy from one point to another. matching device is usually re!uired to ease the abrupttransition between the guided and the free wave. The wave guided by the line is radiated

into space by the antenna."

Antenna Types

There a do#ens of antenna types and variations of each. The type of antenna selected for

use depends on the propagation characteristics re!uired. $ollowing is a short listing of

antenna types.
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$or a description of each, it is recommended that the reader locate a source which would

contain antenna pattern, polari#ation, gain, directivity, efficiency and more details.

Some ntenna Types

%& 'ave (ipole

)agi*orn

Leaky +oa

*elices

)agi-da

$re!uency ndependent

Log-/eriodic

Loops

Slot ntennas

/rinted +ircuit ntennas

ntenna rrays

Induction and Radiation Fields

"There are two different electromagnetic field areas associated with an antenna. The first,

called the induction field is of importance only in the immediate vicinity of the antenna.

This field consists of the lines of force which are set up by the voltage and current in theantenna conductors and which collapse back into the antenna twice each cycle. The

induction field contains only reactive energy because the electric and magnetic fields are

012 out of time phase.

The second field is the radiation field. This field consists of the lines of force which have

become detached from the antenna and are moving out into space as an electromagnetic

wave. The radiation field contains real power that can be measured with specialinstruments. The electric and magnetic fields are in time phase, so the actual power is

removed from the antenna and carried away by the field.

The intensity of the induction field varies as the inverse s!uare of the distance from the

antenna and the radiation field intensity varies inversely as the distance. t is the radiation

field which is principally important for communication purposes, as it etends to greatdistances with sufficient intensity to be useful for transmitting information.

The intensity of the electric field is usually measured in volts per meter and the intensityof the magnetic field in ampers per meter. 3ne half of the wave energy is contained in the

electric field and the remaining half is contained in the magnetic field. The product of the

electric and magnetic field, with a given area in space, will have the units of watts pers!uare meter. ...n interesting point is that the impedance of free space to an


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electromagnetic wave is 455 ohms 6pure resistance7. The fact that the impedance of free

space is resistive supports the statement that the electric and magnetic fields are in time

phase much in the same manner that voltage and current are in time phase in a resistivenetwork."41

Polarization

"The polari#ation of the wave is, by definition, determined by the position of the E phasor

6electric field phasor 8vector97 with respect to a reflecting surface. n most instances the

reflected surface will be the earth. 8$or eample, if the E phasor is parallel to the earth

6reflecting plane7 then9 the wave in this case is said to be hori#ontally polari#ed." 41

Linear - E vector contained in one plane.

*ori#ontal - E vector parallel to hori#ontal plane.

:ertical - E vector parallel to vertical plane.

+ircular&Elliptical - "n electomagnetic wave is linearly polari#ed when the electric field

lies wholly in one plane containing the direction of propagation. plane electromagneticwave, at a given fre!uency, is elliptically polari#ed when the etremity of the electric

vector describes an ellipse in a plane perpendicular to the direction of propagation,

making one complete revolution during one period of the wave. f the rotation isclockwise looking in the direction of propagation, the sense is right-hand. ;ore

generally, any field vector, electric, magnetic, or other, is elliptically polari#ed if its

etremity describes an ellipse."0

+ross-/olari#ed ntenna - Two E vectors which may or may not propagate in-phase. s

the phase between the two E vectors varies, the polari#ation changes from linear to

circular 6or elliptical7 polari#ation.

(ual-/olari#ed ntenna - n antenna which is described as being dual-polari#ed, is,

infact, two antennas occupying the same space. These antennas are normally used fordiversity.

Radiation Pattern

" radiation pattern is a plot of electric field intensity, at a fied distance, as a function of

direction from the antenna or antenna array. lthough radiation patterns 8can be9

determined mathematically, it is possible to obtain patterns by taking actual fieldmeasurements. $or eample, the pattern in the hori#ontal plan may be determined by

taking readings from an


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indicating instrument is constructed to give readings that bear a linear relation to the

electric field intensity, a plot of those readings against a#imuth angles will be the

radiation pattern in the hori#ontal plan.

The figure below 6right7 illustrates measured data plotted in rectangular coordinates,

while the figure on the left shows the same data plotted in polar coordinates.

n either figure, the relative field intensity is #ero at 12, 012 %=12 or at 512. /oints on the

pattern where the relative field intensity is #ero are called nulls. /ortions of the patternbetween ad>acent nulls are called lobes. ;aimums are the points of greatest field

intensity. The maimums in our eample plots occur at ?@2, %4@2, @2, and 4%@2. The

pattern consists of four lobes.

slightly more complicated pattern is shown below. This pattern also contains four lobesbut the maimums that occur at 012 and 512 have less field intensity than the maimumsthat occur at 12 and %=12. The lobes of a pattern having the greatest intensity are called

ma>or lobesA minor lobes are those having smaller maimum values. Thus in the pattern

below, the ma>or lobes occur at 12 and %=12 and minor lobes at 012 and 512.


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nother term used in describing a radiation pattern is minimum. The figure below

illustrates a pattern having minimums at 012 and 512. Bote the field intensity at these

minimums has a value greater than #ero.

radiation pattern may be described according to the shape and phase of the field orfields it represents. The description according to the shape of the pattern generallyincludes the locations of maimums and nulls. The locations of minor lobes and

minimums, if any, may or may not be of importance. There are several types of patterns

that may be named according to the manner in which energy is radiated from the antennasthey represent. 'hen an antenna, or array of antennas, radiates energy e!ually well in all

directions, the pattern is described as non-directional 6i.e. omni-directional7. n antenna,

or array, which radiates chiefly in two directions has a bi-directional pattern. f theradiation is concentrated chiefly in one direction, the pattern is uni-directional. The figure

below illustrates these three types of patterns. radiation patter is classified by phase by

comparing the phase of the electric field at two or more points within the pattern. t is

essential that the points under comparison be located e!ui-distant from the center of thearrayA however, this is usually not stated but must be assumed. f the phase of the electric

field at all points in a pattern is the same, the pattern is described as a uni-phase pattern.

f there are two phase possibilities in a pattern, and if the phase is constant within eachlobe, the pattern is a biphase-pattern. nder certain conditions it is possible for the phase

of the field to vary within a single lobe. $or this case, the pattern is said to be a variable-

phase pattern."41
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Antenna Pattern Distortion

"The real world performance of an antenna is different from that listed in themanufacturerCs antenna pattern specifications. The manufacturerCs specifications are based

on measurements in an ideal environment of an antenna range. *owever, the actual

implementation of the antenna in the system is not the same as on the antenna range. nthe real system, factors such as how the antenna is mounted 6such as on the side of a

building or tower7 or its relative location with respect to surrounding clutter has an effect

on the antenna pattern. f the antenna is mounted below the ma>ority of the surroundingclutter, the signal will be reflected due to this clutter which in effect distorts the antenna

pattern, reducing the effective protection from the directivity of the pattern. Since the

mounting of the antennas and the surrounding ground clutter vary from site to site, theantenna pattern distortion will also vary from site to site, as well as from sector to sector.

The ground clutter type and location with respect to the antenna is the important factor in

determining ground clutter reflections. The amount and placement of tall buildings in theantennaCs main lobe will affect the amount of reflections which propagate behind the

antenna. This effect is seen most often in dense urban and urban areas since there aremore tall building in these environments.

The antenna pattern distortion can affect the capacity of a site. f significant clutter eists

in the area of an antennaCs main lobe causing reflections which propagate behind theantenna, this in effect reduces the front-to-back ratio of the antenna."%?

ntenna Dain

"This is often referred to as "power gain" and is the ratio of the maimum radiation in a

given direction to that of a reference antenna in the same direction for e!ual power input.

sually this gain is referenced to either an isotropic antenna or a half wave dipole in freespace at 1 degrees elevation.

sotropic 6di7 generally refers to a theoretical antenna having a spherical radiation

pattern with e!ual gain in all directions. 'hen used as a gain reference, the isotropic


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antenna has a power of 1 di. The halfwave dipole 6dd7 is an antenna which is center

fed as to have e!ual current distribution in both halves. 'hen used as a theoretical

reference antenna it has a power gain of 1 dd, which e!uates to a .%? d differencecompared to an sotropic antenna.

di F dd G .%? dd F di - .%?

dd :s. di

The gain of an antenna has a direct interaction with other antenna parameters, 6the

technical depth of which is beyond the scope of this document7, the following paragraphs

will provide the system engineer with general guidelinesH

:ertical eamwidth - Denerally, the greater the gain of the antenna, the narrower the

vertical beamwidth. The vertical beam can be used to focus coverage in some

circumstances, but the engineer should ensure that the optimum vertical beamwidth isused to prevent the creation of "nulls" or coverage holes near to the site.

/hysical Si#e - The si#e of an antenna will generally be greater as an antenna gain

increases. This is due to the greater number of dipole array and electrical elements

re!uired to reach the desired gain.

*eight of ntenna - n general the I d per octave rule will apply to the cell site antenna

height in a flat terrain, that is doubling the antenna height causes a gain increase of I d.

The system engineer should compare this possible gain increase with the effects ofdoubling the transmission line loss and the possible appearance of nulls close to the site."

%4

few gain e!uationsH5

Dain of a %& 'ave (ipoleH

D6di7 F %1Jlog6Dr7 F %1Jlog6%.I?7 F .%?= d

Dr F directivity of resonant dipole

/arabolic (ish ntenna DainH

D6di7 F 1Jlog6f6;*#77 G 1Jlog6(6feet77 - @.I

f F fre!uency in ;ega*ert#
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( F aperture diameter in feet

for @?K illumination.

Return Loss

"


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Front to Bac# Ratio

"The front to back ratio of an antenna is an important measure of performance. t is theratio of the power radiated from the main ray beam forward to that radiated from the back

lobe behind the antenna. $ront to back ratio is normally epressed in terms of d, this

means that a signal at the back of the antenna should be d down on a signal at a

mirror angle in front of the antenna. The following illustration show a front to back ratio

of @d 6typical for a /+S antenna7."%4


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Antenna Bandwidth

"The range of fre!uencies over which the antenna functions efficiently, and over which areasonable match between the guided and the free waves can be made, is termed the

bandwidth of the antenna and is a function of antenna and matching system design. f the

transition is smooth and the system design such that the wave characteristics do notundergo a sudden shift, the bandwidth of the antenna may be !uite large. ut if thetransition is abrupt, a region of discontinuity eists in the system and a portion of the

guided wave is reflected back down the transmission line, much in the manner that an

ocean wave is reflected when it hits a sea wall. The reflected wave is compensated for bythe matching device which creates e!ual and opposite reflection conditions to smooth the

transition.

The operating bandwidth of an antenna is relative and one way of specifying it is to

define the maimum limit of reflected energy at any operating fre!uency. This limit may

be epressed as a voltage standing wave ration 6:S'


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Transmission cables are more lossy at higher fre!uencies. t =11 ;*#, a 5&=" line may

suffice but one may re!uire %-@&=" line for %,011 ;*# to maintain a similar loss.

Antenna $fficiency

"ntennas are transducers that convert electronic signals into electromagnetic fields, and

vice versa. They are also used to focus the electromagnetic energy in a desired direction.The larger the antenna aperture 6area7, the larger is the resulting signal power density in

the desired direction. n antennaCs efficiency is described by the ratio of its effective

aperture to its physical aperture. ;echanisms contributing to a reduction in efficiency

6loss in signal strength7 are known as amplitude tapering, aperture blockage, scattering,re-radiation, spillover, edge diffraction, and dissipative loss. Typical efficiencies due to

the combined effects of these mechanisms range between @1 and =1K."I

$ffects of Antenna Positionin% (P&'&ellular &ommunication 'ystems"

"ackgroundH


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shields thus limiting coverage area. $urthermore, reflection from these buildings will also

provide coverage to areas that normally would not be reachable through line-of-sight

paths. These additional paths would conse!uently increase in-building penetration withinthe contained area.

n order to achieve these results, it is important that antenna&base sites are chosenaccordingly. $irst of all, the highest point in the area will probably do more harm than

good as a cell site location if the area can be considered as suburban or urban. The reason

why is that it will cause more interference to surrounding sites due to the fact that signalswill propagate out over the other, lower buildings into other coverage areas. $urthermore,

street coverage and in-building penetration immediately surrounding the site will

probably be more limited due to the lack of reflections off surrounding buildings.

Eamples of these situations are shown belowH

The choice of the highest point in an area for a cell site would most likely only work in

low-density suburban or rural areas where the overall number of sites needed to meetsubscriber demands is small. $re!uency reuse would not be necessary and these sites

could be considered as "broadcast"sites.

*ill-Top +ell SitesH

s another eample, consider the placement of a cell site at the top of a hill overlooking atown or city. 'hile coverage will be ade!uate in the area immediately surrounding the

cell site down to the side of the town facing the site, coverage within the city may be

limited due to signal path obstructions due to buildings on the edge of the town. n otherwords, reflections off buildings on the edge of the city will provide coverage to areas

between the buildings and the cell site, but probably not on the opposite side of the

obstructions. n eample is shown belowH


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"3ff-grid" Site LocationsH

s was stated before, following a heagonal pattern when assigning cell sites is a goodstarting point in reducing cochannel interference as much as possible. *owever, due to

possible limitations of ade!uate cell space for sites, locations may need to be assigned

that are "off grid." n eample of such a situation is shown belowH

n any case, the heagonal grid reflects an ideal situation. Terrain effects will obviouslyskew the pattern out of any type of symmetry. s a result, some interference may appear

in some areas regardless of how close you assign sites to the grid. t is at this point where

the engineer will consider ways to control this interference.

Link udgets and System alanceH

$or more detail on link budgets please refer to the


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(owntilt 6eamtilt7H

"'hen the main radiation lobe is intentionally ad>usted above or below 8its plane ofpropagation9, the resultant effect is know as beamtilt. There are two categories of

beamtilt, mechanical and electrical. Electrical beamtilt is obtained by ad>usting the phase

relationships of radiating elements within the antenna by the factory. 8$or eample, anelectrical beamtilt can be ad>usted in the field by changing eternal phasing cables

purchased from the vendor.9 ;echanical beamtilt may be accomplished by physically

tilting the antenna away from the perpendicular by using a shim or downtilt bracket. 8$oreample, some manufacturerCs provide scissor-style brackets that eliminate guesswork

about the setting in degrees.9 (owntilt of either variety should be specified only after a

detailed understanding of the terrain and other propagation factors have been ac!uired bythe designer. ;ost legitimate uses of beamtilt involve signal coverage restrictions

re!uired by cellular repeaters to prevent overlap with ad>acent cells. eamtilt is not a

good substitute for null fill below the hori#on. lower gain antenna might well over

superior overall performance to a downtilted higher gain model."

8;echanical downtilting will cause the backlobe to tilt upward 6parallel to front lobe7,

while electrical downtilting causes the backlobe to downtilt simultaneously. 3ne othernote to make, an electrical downtilt type of antenna could also be downtilted

mechanically.9

great deal of caution must be used when downtilting a particular antenna. There are

several "side effects" that can occur with ecessive downtilting."4

The following (owntilt Effects graphs are provided by Terry Leonard of the ;otorola


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"Eusting E


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6greater than @ degrees7 are not recommended, for at this point, a peanut shaped coverage

may start to result, depending on the type and height of antenna being used. This may

cause patchy coverage between ad>acent sectors in the site which could cause additional,unnecessary port changes. lso, as a rule, there should be no more than degrees

difference in downtilt between ad>acent sectors in any one site. /lease refer to the

diagram belowH

s one can see, coverage decreases dramatically outside of the main lobe of the

transmitted signal. 'e can therefore aim the outer edge of the main lobe at our cellboundary 6which can be determined from a best server plot for system7 to limit coverage

outside. f you can determine the approimate cell radius and are aware of the siteCs

antenna height above ground level, you can determine an approimate downtilt to use bythe e!uationH

(owntilt F arctan6h&(ma7 G 6:ertical eamwidth&7"4

$nironment

n an ideal situation, estimating propagation paths and signal fade would be straight

forward. n the "real world", physical characteristics of the propagation environment will

effect a signalCs ability to traverse through space. Environment descriptions have been

standardi#ed in the communications industry.

&lutter Data ($lectronic"'ome &lutter and Terrain DescriptionsLine)of)'ite (L*'"
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&lutter Data ($lectronic"

"There are various sources of clutter 6morphological7 data. The more current the clutter

data, the more accurate the propagation predictions will be. The most common source of

clutter data is from the .S. Deological Survey 6SDS7J. t is easily obtained and is

available digitally. *owever, there are certain limitations with this data. The SDS datacategori#es the land by how it is used 6commercial, industrial, etc.7, which does not

necessarily coincide with categori#ing the land by its propagation characteristics. lso,the SDS data may not account for newly developed areas. n order to obtain a more

accurate determination for coverage, it is recommended that enhanced clutter data based

on satellite imagery and aerial photography be used when generating propagation studies.This data is more epensive and re!uires more time to ac!uire than the SDS data, but

provides more reliable results."%?

J.S. Deological Survey web site is located atH httpH&&www.usgs.gov&

'ome &lutter and Terrain Descriptions

"(ense rbanH

+onsists of densely built areas with mainly high buildings 6over 1 stories7. Typically

there is little or no trees and vegetation within this area due to the density of buildings.+entral parts of +hicago and Bew )ork are eamples of dense urban areas.

rbanH

+onsist of metropolitan regions, industrial areas and closely spaced residential homes and

multi-storied apartments. uilding density is high but may be interspersed with trees andother vegetation. usiness centers of medium si#e cities such as Tulsa and ndianapolis as

well as portions of the outer areas of Bew )ork and +hicago are eamples of this

environment.

SuburbanH

+onsists mainly of single family homes, shopping malls and office parks. Significantvegetation, trees and parking lots are intermied with buildings. ;ost buildings are % to 4

stories but significant eceptions do occur. Significant areas within small and medium

cities along with suburban communities surrounding ma>or cities are eamples of thisenvironment.


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+onsist generally of open space with few buildings or residences. ;a>or interconnecting

highways, farms, and barren land are found within rural areas. The largest variations in

cell coverage area are found in rural areas due to differences in vegetation and terrain."%?

3pen


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f any of these obstructions rise high enough to block the view from end to end, there is

no visual line of sight.

3bstructions that can interfere with visual line of sight can also interfere with radio line

of sight. ut one must also consider the $resnel effect. f a hard ob>ect, such as a

mountain ridge or building, is too close to the signal path, it can damage the radio signalor reduce its strength. This happens even though the obstacle does not obscure the direct,

visual line of sight."0

Lar%e)'cale Propa%ation +odels ) Path Loss

/ropagation models are usually divided into large-scale or small-scale models. The largescale models normally are used to predict the mean signal strength for transmitter-

receiver separation distances of several hundred or even thousands of meters apart. Small

scale models, or fading models, describe rapid fluctuations of the received signal strengthover very short distances 6a few wavelengths7 or short time durations.@

There are many path loss models available for use, however certain models orcombinations of models are preferred. The best models are those which are continuously

compared against actual field data and ad>usted for accuracy. The model used in

;otorolaCs Bet/lan tool is L3S. L3S has been developed utili#ing other modelsA its

description can be found in this section.

Free 'pace Propa%ation +odelFresnel ,onesPropa%ation *er a Plane $arthRou%h 'urface &riterionRefraction and $-uialent $arth.s RadiusTransmission *er a 'mooth 'pherical $arth/L*'0nife $d%e DiffractionLo%)distance Path Loss +odel and Lo%)normal 'hadowin%Lon%ley)Rice (Irre%ular Terrain +odel"*#umura
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Hata

&*'T)123)Hata'lope and Intercept4alfish)I#e%ami &ost 1234alfisch)/ia 5T&Bullin%tondn Pathloss +odelDiffractin% 'creens +odelBuildin% PenetrationRicean Fadin% Distri6utionFresnel ,ones

"$resnel #oneH n radio communications, one of a 6theoretically infinite7 number of a

concentric ellipsoids of revolution which define volumes in the radiation pattern of a6usually7 circular aperture. Bote %H The cross section of the first $resnel #one is circular.

Subse!uent $resnel #ones are annular in cross section, and concentric with the first. Bote

H 3dd-numbered $resnel #ones have relatively intense field strengths, whereas even

numbered $resnel #ones are nulls. Bote 4H $resnel #ones result from diffraction by thecircular aperture."I

The concept of diffraction loss as a function of the path difference around an obstructionis eplained by $resnel #ones. $resnel #ones represent successive regions where

secondary waves have a path length from the transmitter to receiver which are nl&

greater than the total path length of a line-of-sight path. 8The figure below9 demonstratesa transparent plane located between a transmitter and receiver. The concentric circle on

the plan represent the loci of the origins of secondary wavelets which propagate to the

receiver such that the total path length increases by l& for successive circles. Thesecircles are called $resnel #ones. The successive $resnel #ones have the effect of

alternately proving constructive and destructive interference to the total received signal.

The radius of the nth $resnel #one circle is denoted by rn and can be epressed in terms

of n, l, d%, and d by

This approimation is valid for d%, d OO rn.
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The ecess total path length traversed by a ray passing through each circle is nl&, where

n is an integer. Thus, the path traveling through the smallest circle corresponding to n F %

in the figure will have an ecess path length of l& as compared to a line-of-sight path,and circles corresponding to n F ,4,etc. will have and ecess path length of l, 4l&, etc.

The radii of the concentric circles depend on the location of the plane. The $resnel #ones

of the figure will have maimum radii if the plane is midway between the transmitter andreceiver, and the radii become smaller when the plane is moved towards either the

transmitter or the receiver. This effect illustrates how shadowing is sensitive to the

fre!uency as well as the location of obstructions with relation to the transmitter orreceiver.

n obstacle may block the transmission path and a family of ellipsoids can beconstructed between a transmitter and receiver by >oining all the points for which the

ecess path delay is an integer multiple of half wavelengths. The ellipsoids represent

$resnel #ones. Bote that the $resnel #ones are elliptical in shape with the transmitter and

receiver antenna at their foci."@

$resnel Pone in a ;icrowave LinkH

"n a microwave link, the radio transmission ehibits wavelike characteristics, and the

#one where wavelike interference can affect the propagation path can be approimated by

the $resnel #one. The $resnel #one is widest in the middle of the link and can becalculated from the formulaH
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where

ustment must be made for the additional losses incurred.

The terrain loss LT< 6in d7 can be calculated as

where

+ F the clearance in meters of the obstacle in the $resnel #one 6as shown in the figure7


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ecause of changes in the refractive inde of the atmosphere, the effective value of Q

varies with time. Smaller values of Q increase the attenuation due to obstructions,

particularly on longer path lengths. )ou should check to ensure that potential variations inQ will not degrade the service.

The change in clearance 6++7 for changes in Q can be approimated by

The limiting values of Q are

Q F % for wet climates

Q F 1.0 for temperate climates

Q F 1.I for desert climates

t is normal to check the path profile for the etremes of Q F ?&4 to Q F 1.=."%

Propa%ation *er a Plane $arth

"Qnowing the propagation characteristics over a smooth, conducting, flat earth provides a

starting point for estimating the effects of propagation over actual paths. The comple

analytical results for propagation over a plane earth derived by Borton have been

simplified by ullington4=by decomposing the solution of Borton into a set of wavesconsisting of direct, reflected, and surface waves. The formula relating the power

transmitted to the power received following the approach of ullington4=is
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'ithin the absolute value symbols, the first term 6unity7 represents the direct wave, the

second term represents the reflected wave, the third term represents the surface wave, and

the remaining terms represent the induction field and secondary effects of the ground.

The reflection coefficient,


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been over a perfectly reflecting surface. The surface wave attenuation factor, , depends

on fre!uency, polari#ation, and the ground constants. n approimate epression for is

given by

which is valid for M 1.%. ;ore accurate values are given by Borton. Since the effect ofthis surface wave is only significant in a region a few wavelengths above the ground, this

effect can be neglected in most applications of microwave mobile communications.

t is of interest to note that in the limit of gra#ing angle of incidence the value of thereflection coefficient,


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where /1 is the epected power over a free space path. n most mobile radio applications,

ecept very near the base station antenna, sin %& ( U %& (A thus the transmission loss

over a plane earth is given by the approimation

yielding an inverse fourth-power relationship of received power with distance from the

base station antenna.

The ground constants over the path of interest enter into both the calculations for line-of-

sight and for diffraction attenuation. t microwave fre!uencies it is usually the dielectric

constant, e, which has the dominant effect on propagation. 8The table above9 gives valuesof typical ground constants. pplying these values to the formulas for the reflection

coefficient over a plane earth >ust derived, we find that for fre!uencies above %11 ;*#

the effect of the ground constants are slight."=

on satellite imagery and aerial photography be used when generating propagation studies.

This data is more epensive and re!uires more time to ac!uire than the SDS data, butprovides more reliable results."%?

Free 'pace Propa%ation +odel

"The free space power received by a receiver antenna which is a distance of d from the

transmitter antenna is given by $riis free space e!uation.

'hereH

/T is the transmitted power

DT is the transmitting antenna gain

D< is the receiving antenna gain

d is the separation distance between antennas

The path loss which represents the signal attenuation as a positive !uantity is defined asthe difference between the effective transmitted power and the received power and may
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or may not include the effects of the antenna gains. The path loss for the free space model

when the antennas are assumed to have unity gain is provided by the following e!uation.

Epressed in d asH

'hereH

d is in meters

f is in *ert#

c is e!ual to the speed of light 6 meters per second7

fH

d is in kilometers

f is in ;ega*ert# 6 *ert#7

c is


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3ne is able to see from the above free space e!uations that I d of loss is associated with

a doubling of the fre!uency. This same relationship also holds for the distance, if the

distance is doubled, I d of additional loss will be encountered."%4

Rou%h 'urface &riterion

"t the higher microwave fre!uencies the assumption of a plane earth may no longer bevalid, due to surface irregularities. measure of the surface "roughness" that provides an

indication of the range of validity of 8the formula relating the power transmitted to the

power received following the approach of ullington4=9

is given by the


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n a medium where there are abrupt changes in inde of refraction, (escarteCs law

appliesH

where a and a1 are the angles at the discontinuity at height h, above the surface of theearth of radius a. Bote if the atmosphere is uniform the e!uation for rectilinear

propagation is

'hen n has a constant gradient the propagation is given approimately by

f we replace the earthCs radius a by a fictitious value aC, where

we now have an epression in the same form as that for rectilinear propagation.

Since the inde of refraction in the troposphere is very nearly unity, the B-unit has been

defined for convenience,

where n is the inde of refraction in the atmosphere. :alues of the minimum monthlymean value of Bs throughout the world have been published. The most commonly used

value for Bs is 41%. This gives a value for the effective earthCs radius aC which

corresponds to four-thirds of the actual earthCs radius. The empirical formula for aC is

given by

where I451 km is used for the earthCs radius."=


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Transmission *er a 'mooth 'pherical $arth

"t microwave fre!uencies, diffraction due to the earth severely limits the amount ofenergy that propagates beyond the hori#on. +onsiderable work has been done in an

attempt to predict the signal attenuation over transhori#on paths. Denerally speaking,

these predictions are semiempirical formulas which apply for fre!uencies below %111;*#. t is possible to obtain analytic epressions for the diffraction over a perfectlyconducting sphereA however, the epressions are not simple relationships between the

factors of fre!uency, conductivity of the earth, antenna height, and distance which govern

the attenuation. ...Estimations of the attenuation due to diffraction over a smooth earth areparticularly difficult in regions >ust beyond line-of-sight. $urthermore, surface roughness

again seriously affects propagation. t is, of course, desirable to be able to estimate signal

strengths beyond the hori#on, particularly for cases where the same fre!uencies are beingused at separate base stations. ullington4=has reduced the involved analytic

relationships for the propagation over a smooth spherical earth to various asymptotic

forms."=

/L*'

"The workhorse of the Bet/lan tool is the L3S propagation model developed and

refined over the last %@ years by ;otorola engineers. The method used to refine estimatecoverage is based on the diffraction and line of sight algorithms found in Longley and

usts for built up or natural environments on top of the terrain by assuminga virtual obstruction height over and above the eisting terrain which is varied to

correspond to urban, suburban, rural, foliage, water and other conditions. The overlay 6or

obstruction7 code is determined from maps which typically show this information ascolors. This virtual height is then scanned to find the ma>or, or controlling, obstacles for

each mobile position. Single diffraction points are separated from etended obstructions

and are treated in different ways to obtain an estimate of the degree of additionaltransmission loss epected over free space.

t the same time that the obstruction search is going on, a straight line estimate of the

average terrain is updated with each new mobile position. This straight lineapproimation is used to obtain an e!uivalent ad>usted base antenna height. The ad>usted

base antenna height is further corrected for earth curvature and is applied to the line of

sight routine to give an estimated reflection loss term.

The final estimated total attenuation for each mobile position is a varying mi of both

reflection and diffraction loss terms. d>ustments are made by corrections applied to each
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loss term as a function of whether single or multiple diffraction is taking place. ntenna

hori#ontal and vertical patterns, downtilt angles, and sector power levels are also taken

into account.

lthough the L3S propagation model is based on Longley,


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8;otorola Bet/lan Dourp. los /ropagation ;odel. Slide /resentation.9

0nife $d%e Diffraction

":ery often in the mobile radio environment a line-of-sight path to the base station is

obscured by obstructions such as hills, trees, and buildings. 'hen the shadowing iscaused by a single ob>ect such as a hill, it is instructive to treat the ob>ect as a diffracting

knife edge to estimate the amount of signal attenuation. The eact solution to the problem

of diffraction over a knife edge is well known as is discussed in many tetbooks.

'ithin the shadow region of the knife edge, the electric field strength E, can be

represented as

where E1 is the value of the electric field at the knife edge, is the amplitude, ( is the

phase angle with respect to the direct path. The epressions for and ( are obtained in

terms of the $resnel integralsH


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where

where 6from $resnel #one geometry7H

$or most microwave mobile radio applications several assumptions can be made tosimplify the calculations. +onsider an infinite completely absorbing 6rough7 half-plane

that divides space into two parts as in 8the following figure9. 'hen the distances d% and

d from the half-plane to the transmitting antenna and the receiving antenna are large

compared to the height h, and h itself is large compared with the wavelength, l, that is,

then the diffracted power can be given by the epression


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This result can be considered independent of polari#ation as long as the conditions of

d%,dOOhOOl, are met. n cases where the earthCs curvature has an effect, there can be upto four paths. simplified method of computing knife edge diffraction for such cases istreated by nderson and Trolese4@. +loser agreement with data over measured paths has

been obtained by calculations that better describe the geometry of the diffracting

obstacle."=

8Vakes, 'illiam +. %05?. ;icrowave ;obile +ommunications. n EEE /ress +lassic


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or

where n is the path loss eponent which indicates the rate at which the path loss increaseswith distance, d1 is the close-in reference distance which is determined from

measurements close to the transmitter, and d is the T-< separation distance. The bars in

6the above7 e!uations denote the ensemble average of all possible path loss values for agiven value of d. 'hen plotted on a log-log scale, the modeled path loss is a straight line

with a slope e!ual to %1n d per decade. The value of n depends on the specific

propagation environment. $or eample, in free space, n is e!ual to , and whenobstructions are present, n will have a larger value.

t is important to select a free space reference distance that is appropriate for thepropagation environment. n large coverage cellular systems, % km reference distances

are commonly used, whereas in microcellular systems, much smaller distances 6such as

%11 m or % m7 are used. The reference distance should always be in the far field of the

antenna so that near-field effects do not alter the reference path loss. The reference pathloss is calculated using the free space path loss formula... or through field measurements

at distance d1. 8The table below9 lists typical path loss eponents obtained in various

mobile radio environments.

Path Loss $8ponents for Different $nironments

$nironment Path Loss $8ponent9 n$ree space

rban area cellular radio .5 to 4.@

Shadowed urban cellular radio 4 to @

n building line-of-sight %.I to %.=

3bstructed in building ? to I

obstructed in factories to 4

The model in 8the log-distance9 e!uation does not consider the fact that the surrounding

environmental clutter may be vastly different at two different locations having the sameT-< separation. This leads to measured signals which are vastly different than the average

value predicted by 8the log-distance9 e!uation. ;easurements have shown that at any

value of d, the path loss /L6d7 at a particular location is random and distributed log-

normally 6normal in d7 about the mean distance-dependent value. That is


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and

where s is a #ero-mean Daussian distributed random variable 6in d7 with standard

deviation s 6also in d7.

The log-normal distribution describes the random shadowing effects which occur over a

large number of measurement locations which have the same T-< 6transmit-receive7

separation, but have different levels of clutter on the propagation path. This phenomenon

is referred to as log-normal shadowing. Simply put, log-normal shadowing implies thatmeasured signal levels at a specific T-< separation have a Daussian 6normal7 distribution

about the distance-dependent mean of 8the previously mentioned /L e!uation9, where the

measured signal levels have values in d units. The standard deviation of the Daussiandistribution that describes the shadowing also has units in d. Thus, the random effects of

shadowing are accounted for using the Daussian distribution which lends itself readily to

evaluation.

The close-in reference distance d1, the path loss eponent n, and the standard deviation s,

statistically describe the path loss model for an arbitrary location having a specific T-acent channeltransmission becomes so large that the power intercepted by an on-channel receiver

approaches that of the desired on-channel signal source, interference occurs. The ratio of
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the signal strengths of the two transmissions at the point at which interference is first

noted is called the ad>acent channel interference protection ratio 6+/


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There are several potential sources of impulsive noise which could play a role in mobile

communication systems. The radio is often installed in a vehicle which is itself a source

of noise due to its own ignition and other electrical systems and the vehicle commonlyoperates in urban, suburban and industrial areas where it is close to other noisy vehicles.

There are various etraneous sources of noise such as power lines and neon signs,

industrial noise from heavy current switches, arch welders and the like, and noise fromvarious items of domestic electrical e!uipment. These may or may not be significant

contributors in any specific situation. n practice the level of man-made noise varies

markedly with location and time, so from a limited series of observations it is onlypossible to derive typical values and obtain some estimate of the variability. n urban

areas it is generally conceded that vehicle ignition noise is a ma>or source of interference

to :*$ mobile radio systems.

Throughout the literature, the terms Daussian and impulsive are used to denote two

distinct types of noise. 3nly the power spectral density of Daussian noise is affected by

linear filteringA the probability density function remains Daussian. The in-phase and

!uadrature components of narrowband Daussian noise are independent, as are theenvelope and phase distributions. $or any other type of noise, both the power spectral

density and the probability density function are changed by filteringA the in-phase and!uadrature components, although uncorrelated, are not independent. n the general case,

the envelope and phase of random noise are independent, the phase being uniformly

distributed in the interval 61,p7.

n general terms we may consider an impulse as a transient that contains an instantaneous

uniform spectrum over the fre!uency band for which it is defined, a uniform spectrumre!uiring that all fre!uencies are present, of e!ual strength and in phase over the

fre!uency band. mpulsive noise is the combination of successive impulses which have

random amplitudes and random time-spacingsA these factors may sometimes be such thatade!uate separation of successive impulse responses by a narrowband receiver is notpossible.

Thermal noise can produce an annoying "hiss" on a voice channel, but does notsignificantly degrade intelligibility unless its ective assessment,although the !uasi-peak measurement, which will be mentioned later, has been shown to

have some correspondence with the sub>ective annoyance on a.m. radio and television. n

some ways digital transmissions are easier to deal with since the bit error rate 6E


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'tandards and =nits

!'4R (!olta%e 'tandin% 4ae Ratio">4atts to dBm &onersion>dBi to dBd &onersion'peed of Li%ht > 4aelen%th

!'4R (!olta%e 'tandin% 4ae Ratio">

":oltage Standing 'ave

dBi to dBd &onersion
http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.39.html#pgfId=514154http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3a.html#pgfId=498512http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3b.html#pgfId=624180http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3c.html#pgfId=611837http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3d.html#12244http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3d.html#22353http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.39.html#pgfId=514154http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3a.html#pgfId=498512http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3b.html#pgfId=624180http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3c.html#pgfId=611837http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3d.html#12244http://www.pamd.cig.mot.com/~rftech/Documents/Prop_Basics/prop_basics3.3d.html#22353


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