propagation basics

September 30, 1998

Propagation Basics

James Demetriou and Rebecca MacKenzie

This is a quick reference to propagation topics commonly used in the communications industry

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Table of Contents

1.0 Antenna 41.1 Definition 41.2 Antenna Types 41.3 Induction and Radiation Fields 51.4 Polarization 51.5 Radiation Pattern 61.6 Antenna Pattern Distortion 91.7 Antenna Gain 91.8 Return Loss 101.9 Antenna Beamwidth (Horizontal/Vertical) 111.10 Front to Back Ratio 121.11 Antenna Bandwidth 131.12 RF Feeder Losses 131.13 Antenna Efficiency 151.14 Effects of Antenna Positioning (PCS/Cellular Communication Systems) 15

2.0 Environment 222.1 Clutter Data (Electronic) 222.2 Some Clutter and Terrain Descriptions 232.3 Line-of-Site (LOS) 24

3.0 Large-Scale Propagation Models - Path Loss 243.1 Free Space Propagation Model 253.2 Fresnel Zones 273.3 Propagation Over a Plane Earth 303.4 Rough Surface Criterion 333.5 Refraction and Equivalent Earth’s Radius 333.6 Transmission Over a Smooth Spherical Earth 343.7 XLOS 353.8 Knife Edge Diffraction 373.9 Log-distance Path Loss Model and Log-normal Shadowing 393.10 Longley-Rice (Irregular Terrain Model) 423.11 Okumura 433.12 Hata 453.13 COST-231-Hata 463.14 Slope and Intercept 483.15 Walfish-Ikegami Cost 231 493.16 Walfisch-Xia JTC 493.17 Bullington 493.18 dn Pathloss Model 51

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3.19 Diffracting Screens Model 533.20 Building Penetration 55

4.0 Small-Scale Propagation Models - Fading 564.1 Fade Margin 564.2 Doppler Spread and Coherence Time, Coherence Bandwidth,

Symbol Period 564.3 Flat Fading (i.e. no frequency selective behavior) 574.4 Frequency-Selective Fading 594.5 Fast Fading (observed at approximately 1/2 wavelength i.e. Rayleigh) 614.6 Slow Fading (observed at distances greater than 1/2 wavelength

i.e. log normal) 624.7 Rayleigh Fading/Multipath 634.8 Ricean Fading Distribution 68

5.0 Interference 695.1 Multiple-Carrier Intermodulation (IM) Products 695.2 Intermodulation Distortion 705.3 Inter-Symbol Interference (ISI) 715.4 Inter-System Interference (ISI) 715.5 Adjacent Channel Interference - Land-Mobile 725.6 Man-Made Noise and Interference 72

6.0 Standards and Units 746.1 VSWR (Voltage Standing Wave Ratio): 746.2 Watts to dBm Conversion32: 746.3 dBi to dBd Conversion 746.4 Speed of Light : Wavelength 74

7.0 References 75

8.0 Other Useful References 76

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There are numerous books dealing with propagation basics and volumes of papers focusing on specific aspects with regards to propagation. This paper is not intended to cover, in depth, the physics and mathematics behind the theory, nor is it intended to encompass all subject matters associated with propagation. Provided are brief descriptions of propagation topics most commonly used in the communications industry. References for expanded detail are given. Unless specified, the information provided can be applied generally across technologies (wireline, wireless (analog and digital)).

1.0 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.

1.1 Definition

“Strictly speaking, an antenna is a device which converts an electric wave guided by a conductor into a free-spacunguided electromagnetic wave, and vice versa. Electrical energy is fed to the antenna via a transmission line, ator which passes electrical energy from one point to another. A matching device is usually required to ease the a

transition between the guided and the free wave. The wave guided by the line is radiated into space by the anten22

[Orr, William, and Cowan, Stuart. 1993. The Beam Antenna Handbook. Lakewood: Radio Amateur Callbook (an imprint of Watson-Guptill Publications, a division of BPI Communications, Inc.). pp. 6-7.]

1.2 Antenna Types

There a dozens of antenna types and variations of each. The type of antenna selected for use depends on the pcharacteristics required. Following is a short listing of antenna types.

For a description of each, it is recommended that the reader locate a source which would contain antenna patterntion, gain, directivity, efficiency and more details. For example, see Section 32 of [Jordon, Edward C. 1989. Reference Data for Engineers: Radio, Electronics, Computer, and Communications. Seventh Edition. Indianapolis. Howard W. Sams & Company. pp. 32-10.].

Or online:

[Antennas. [Electronic database]. August 7, 1996. U.S. Federal Government. Directory: http://www.its.bldrdoc.g1037/dir-001/_0018.htm.].

Some Antenna Types

1/2 Wave Dipole

Yagi

Horn

Leaky Coax

Helices

Yagi-Uda

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1.3 Induction and Radiation Fields

“There are two different electromagnetic field areas associated with an antenna. The first, called the induction fieimportance only in the immediate vicinity of the antenna. This field consists of the lines of force which are set upvoltage and current in the antenna conductors and which collapse back into the antenna twice each cycle. The infield contains only reactive energy because the electric and magnetic fields are 90° out of time phase.

The second field is the radiation field. This field consists of the lines of force which have become detached from antenna and are moving out into space as an electromagnetic wave. The radiation field contains real power thatmeasured with special instruments. The electric and magnetic fields are in time phase, so the actual power is refrom the antenna and carried away by the field.

The intensity of the induction field varies as the inverse square of the distance from the antenna and the radiationintensity varies inversely as the distance. It is the radiation field which is principally important for communicationposes, as it extends to great distances with sufficient intensity to be useful for transmitting information.

The intensity of the electric field is usually measured in volts per meter and the intensity of the magnetic field in aper meter. One half of the wave energy is contained in the electric field and the remaining half is contained in thenetic field. The product of the electric and magnetic field, with a given area in space, will have the units of watts square meter. ...An interesting point is that the impedance of free space to an electromagnetic wave is 377 ohmsresistance). The fact that the impedance of free space is resistive supports the statement that the electric and m

fields are in time phase much in the same manner that voltage and current are in time phase in a resistive netwo30

[USDOT Federal Aviation Administration. August 1990. FAA Academy Training Manual. pp. 1-1 thru 1-7. Antennas and Radiation Patterns. 40152, Common Principles, Antennas, and Transmission Lines Course. http://www.acad-emy.jccbi.gov/catalog/html/40152.htm.]

1.4 Polarization

“The polarization of the wave is, by definition, determined by the position of the E phasor (electric field phasor [vewith respect to a reflecting surface. In most instances the reflected surface will be the earth. [For example, if the Er

is parallel to the earth (reflecting plane) then] the wave in this case is said to be horizontally polarized.”30

Linear - E vector contained in one plane.

Horizontal - E vector parallel to horizontal plane.

Vertical - E vector parallel to vertical plane.

Frequency Independent

Log-Periodic

Loops

Slot Antennas

Printed Circuit Antennas

Antenna Arrays

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Circular/Elliptical - “An electomagnetic wave is linearly polarized when the electric field lies wholly in one plane cotaining the direction of propagation. A plane electromagnetic wave, at a given frequency, is elliptically polarized wthe extremity of the electric vector describes an ellipse in a plane perpendicular to the direction of propagation, mone complete revolution during one period of the wave. If the rotation is clockwise looking in the direction of proption, the sense is right-hand. More generally, any field vector, electric, magnetic, or other, is elliptically polarized s

extremity describes an ellipse.”9

Cross-Polarized Antenna - Two E vectors which may or may not propagate in-phase. As the phase between thevectors varies, the polarization changes from linear to circular (or elliptical) polarization.

Dual-Polarized Antenna - An antenna which is described as being dual-polarized, is, infact, two antennas occupysame space. These antennas are normally used for diversity.

[Jordon, Edward C. 1989. Reference Data for Engineers: Radio, Electronics, Computer, and Communications. Seventh Edition. Indianapolis. Howard W. Sams & Company. pp. 32-10.]


1.5 Radiation Pattern

“A radiation pattern is a plot of electric field intensity, at a fixed distance, as a function of direction from the antenn antenna array. Although radiation patterns [can be] determined mathematically, it is possible to obtain patterns bactual field measurements. For example, the pattern in the horizontal plan may be determined by taking readingsRF indicating instrument at various azimuth angles. It is essential that the readings be taken at a constant distanthe center of the array. If the RF indicating instrument is constructed to give readings that bear a linear relation toelectric field intensity, a plot of those readings against azimuth angles will be the radiation pattern in the horizonta

The figure below (right) illustrates measured data plotted in rectangular coordinates, while the figure on the left shsame data plotted in polar coordinates.

In either figure, the relative field intensity is zero at 0°, 90° 180° or at 270°. Points on the pattern where the relative fielintensity is zero are called nulls. Portions of the pattern between adjacent nulls are called lobes. Maximums are tof greatest field intensity. The maximums in our example plots occur at 45°, 135°, 225°, and 315°. The pattern consists offour lobes.

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A slightly more complicated pattern is shown below. This pattern also contains four lobes but the maximums that occur at 90° and 270° have less field intensity than the maximums that occur at 0° and 180°. The lobes of a pattern having the greatest intensity are called major lobes; minor lobes are those having smaller maximum values. Thus in the pattern below, the major lobes occur at 0° and 180° and minor lobes at 90° and 270°.

Another term used in describing a radiation pattern is minimum. The figure below illustrates a pattern having minimums at 90° and 270°. Note the field intensity at these minimums has a value greater than zero.

270°

0°

90°

180°

500

1000

EE

0° 90° 180° 270° 360°

1000

Y

X

Direction

Direction

0°

90°

180°

270°

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A radiation pattern may be described according to the shape and phase of the field or fields it represents. The description according to the shape of the pattern generally includes the locations of maximums 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 antennas they represent. When an antenna, or array of antennas, radiates energy equally well in all directions, the pattern is described as non-directional (i.e. omni-directional). An antenna, or array, which radiates chiefly in two directions has a bi-directional pattern. If the radiation is concentrated chiefly in one direction, the pattern is uni-directional. The figure below illustrates these three types of patterns. A radia-tion patter is classified by phase by comparing the phase of the electric field at two or more points within the pattern. It is essential that the points under comparison be located equi-distant from the center of the array; however, this is usually not stated but must be assumed. If the phase of the electric field at all points in a pattern is the same, the pattern is described as a uni-phase pattern. If there are two phase possibilities in a pattern, and if the phase is constant within each lobe, the pattern is a biphase-pattern. Under certain conditions it is possible for the phase of the field to vary within a single lobe.

For this case, the pattern is said to be a variable-phase pattern.”30


0°

90°

180°

270°

Minimum

Minimum

Non-Directional(Omni-Directional)

Bi-Directional Uni-Directional

(Isotropic)

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1.6 Antenna Pattern Distortion

“The real world performance of an antenna is different from that listed in the manufacturer’s antenna pattern spections. The manufacturer’s specifications are based on measurements in an ideal environment of an antenna rangever, the actual implementation of the antenna in the system is not the same as on the antenna range. In the reafactors such as how the antenna is mounted (such as on the side of a building or tower) or its relative location withto surrounding clutter has an effect on the antenna pattern. If the antenna is mounted below the majority of the sing clutter, the signal will be reflected due to this clutter which in effect distorts the antenna pattern, reducing the eive protection from the directivity of the pattern. Since the mounting of the antennas and the surrounding ground clutfrom site to site, the antenna 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 clureflections. The amount and placement of tall buildings in the antenna’s main lobe will affect the amount of reflecwhich propagate behind the antenna. This effect is seen most often in dense urban and urban areas since theretall building in these environments.

The antenna pattern distortion can affect the capacity of a site. If significant clutter exists in the area of an antennin lobe causing reflections which propagate behind the antenna, this in effect reduces the front-to-back ratio of the

antenna.”14

[Motorola. 1997. CDMA RF System Design Procedure. Version 2.0. [Online serial]. http://www.pamd.cig.mot.com/nds/cts/rftech/public_html/Documents/DsgnProc2/bookTOC.html. pp. 3-1, 3-9, 3-12.]

Antenna Gain

“This is often referred to as "power gain" and is the ratio of the maximum radiation in a given direction to that of aence antenna in the same direction for equal power input. Usually this gain is referenced to either an isotropic ana half wave dipole in free space at 0 degrees elevation.

Isotropic (dBi) generally refers to a theoretical antenna having a spherical radiation pattern with equal gain in all tions. When used as a gain reference, the isotropic antenna has a power of 0 dBi. The halfwave dipole (dBd) is anwhich is center fed as to have equal current distribution in both halves. When used as a theoretical reference antea power gain of 0 dBd, which equates to a 2.14 dB difference compared to an Isotropic antenna.

1/2 Wave Dipole

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Propagation Basics

site.”

flected

dBi = dBd + 2.14 dBd = dBi - 2.14

dBd Vs. dBi

The gain of an antenna has a direct interaction with other antenna parameters, (the technical depth of which is beyond the scope of this document), the following paragraphs will provide the system engineer with general guidelines:

Vertical Beamwidth - Generally, 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 is used to prevent the creation of "nulls" or coverage holes near to the site.

Physical Size - The size 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 required to reach the desired gain.

Height of Antenna - In general the 6 dB 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 6 dB. The system engineer should compare this possible gain

increase with the effects of doubling the transmission line loss and the possible appearance of nulls close to the 13

A few gain equations:27

Gain of a 1/2 Wave Dipole:

G(dBi) = 10*log(Gr) = 10*log(1.64) = 2.148 dB

Gr = directivity of resonant dipole

Parabolic Dish Antenna Gain:

G(dBi) = 20*log(f(MHz)) + 20*log(D(feet)) - 52.6

f = frequency in MegaHertz

D = aperture diameter in feet

for 54% illumination.

[Motorola. RF Planning Guide V2.0 [Online serial]. May 29, 1998. http://www.pamd.cig.mot.com/nds/cts/rftech/public_html/Documents/RFPG2/rfguideV2.html.]

[Stedman, Robert. Handy Formulas [Online serial]. June 2, 1995. http://www.acpg.cig.mot.com/w3/APD/SuperCell_Dev./Tech_Notes/Ants_Fs/Ants_Fields.html.]

1.7 Return Loss

“Return loss is the decibel difference between the power incident upon a mismatched continuity and the power refrom that discontinuity. Return loss can be related to the reflection coefficient VSWR as follows:

RLdB = 20 log (1/p) Where p = VSWR-1/VSWR+1

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na,

VSWR = Vmax/Vmin

In other words, the return loss of an antenna can be considered as the difference in power in the forward and reverse direc-tions due to impedance mismatches in the antenna design.

All other things being equal, the higher the antenna return loss, the better the antenna. The system engineer should choose an antenna with a return loss of 14 dB or better. Note that 14 dB corresponds to a VSWR of 1.5:1 as per the following

example:”13

VSWR = 1.5/1 = 1.5 p = 1.5 - 1/1.5 + 1 = 0.5/2.5 = 0.2

RLdB = 20log (1/0.2)

RLdB = 13.979 dB


1.8 Antenna Beamwidth (Horizontal/Vertical)

“Antenna beamwidth is measured in degrees between the half power points (3 dB) of the major lobe of the anten

Beamwidth can be expressed in terms of azimuth (horizontal or H-plane) and elevation (vertical or E-plane).”13

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na).”

(Figure above is taken from [Clapp, Scott. March 8, 1995. China Frequency Planning and RF Propagation Analysis Overview, REV B. Motorola, Inc. pp. 18.].


[Clapp, Scott. March 8, 1995. China Frequency Planning and RF Propagation Analysis Overview, REV B. Motorola, Inc. pp. 18.]

1.9 Front to Back Ratio

“The front to back ratio of an antenna is an important measure of performance. It is the ratio of the power radiatethe main ray beam forward to that radiated from the back lobe behind the antenna. Front to back ratio is normallyexpressed in terms of dB, this means that a signal at the back of the antenna should be X dB down on a signal a

angle in front of the antenna. The following illustration show a front to back ratio of 25dB (typical for a PCS anten13

Degrees Below Horizon

15 dB10 122-3

-20°

+20°

-10°

+10°

0°

3 dB Pt.

3 dB Pt.

7

Gain=15 dB

Degrees Above Horizon

20o

This particular pattern is a vertical antenna pattern (side view of the antenna) andhas a vertical beamwidth of approximately 20 degrees.

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1.10 Antenna Bandwidth

“The range of frequencies over which the antenna functions efficiently, and over which a reasonable match betweguided and the free waves can be made, is termed the bandwidth of the antenna and is a function of antenna andsystem design. If the transition is smooth and the system design such that the wave characteristics do not underden shift, the bandwidth of the antenna may be quite large. But if the transition is abrupt, a region of discontinuitin the system and a portion of the guided wave is reflected back down the transmission line, much in the mannerocean wave is reflected when it hits a sea wall. The reflected wave is compensated for by the matching device wates equal 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 maximum limit of reenergy at any operating frequency. This limit may be expressed as a voltage standing wave ration (VSWR) or, mply, SWR. This term is an expression of the ratio of the amplitude of the reflected voltage on the transmission lin

amplitude of the direct voltage.”22

[Orr, William, and Cowan, Stuart. 1993. The Beam Antenna Handbook. Lakewood: Radio Amateur Callbook (an imprint of Watson-Guptill Publications, a division of BPI Communications, Inc.). pp. 6-7.]

1.11 RF Feeder Losses

“RF feeder losses include all of the losses that are encountered between the base station cabinet and the base awith respect to a mobile, all of the losses between the PA and the antenna. Since a majority of subscriber units fority system being sold to customers are portable, there is minimal feeder loss. The feeder loss at the base site cafor several dB of loss.

0dB Reference Line5dB Per Ring

25dB Front to Back Ratio

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Various items contained within the base station RF feeder loss are: top jumper, main transmission line, bottom jumper, lightning arrestors, connectors, duplexers, splitters, combiners, etc. The loss associated with the RF feeder system is min-imized by reducing the transmission line run between the base station and its antennas, and/or utilizing lower loss trans-mission lines. Transmission lines can range from 1/2” to 1-5/8” diameter cables. The larger the diameter of the caless lossy the medium, but the sacrifice is more rigid lines, larger bending radius, greater weight, more wind loadlarger area required. Transmission lines are also available with either air or foam dielectrics. The air dielectric cabmore expensive to install and maintain, but are less lossy than the foam lines. The following figure reflects most oferent components that are encountered between the base site antenna and the base station equipment.

Typical Components in the RF Feeder Run

Transmission cables are more lossy at higher frequencies. At 800 MHz, a 7/8” line may suffice but one may requirline for 1,900 MHz to maintain a similar loss.

Refer to the "RF Antenna System" sections13 for additional information on transmission lines.”13

Antenna

(A) Top Jumper

(B) Main Transmission Line

(C) Antenna Surge Protector

(D) Jumper to Directional Coupler

(E) Directional Coupler

(F) Jumper to Duplexer

(H) Jumper to Tx and Rx Antenna Port

BTS

Waveguide Entry Port

Note:Each Jumper consists of:Two connectors andOne line

(G) Duplexer

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1.12 Antenna Efficiency

“Antennas are transducers that convert electronic signals into electromagnetic fields, and vice versa. They are ato focus the electromagnetic energy in a desired direction. The larger the antenna aperture (area), the larger is thing signal power density in the desired direction. An antenna’s efficiency is described by the ratio of its effective a to its physical aperture. Mechanisms contributing to a reduction in efficiency (loss in signal strength) are known atude tapering, aperture blockage, scattering, re-radiation, spillover, edge diffraction, and dissipative loss. Typical n-

cies due to the combined effects of these mechanisms range between 50 and 80%.”26

[Sklar, Bernard. 1988. Digital Communications Fundamentals and Applications. Englewood Cliffs, New Jersey. Pren-tice-Hall, Inc. pp. 192.]

1.13 Effects of Antenna Positioning (PCS/Cellular Communication Systems)

“Background:

RF propagation is the transmitting of radio waves through a medium such as the atmosphere or a building. How a radio wave propagates depends on its frequency, the medium its passing through and its energy.

Radio waves travel from a transmitting site either by ground waves of by sky waves. RF energy that remains near the ground after leaving or propagating from an antenna results in ground waves. For frequency ranges between 150-2000 MHz, ground waves are more predominant for users of two-way radio communications.

Sky waves propagate up from the earth’s surface towards outer space and are reflected off the ionosphere. The of these waves are in the 25 MHz - 50 MHz range. As the frequency increases, the amount of radio wave energypasses through and that is absorbed by the ionosphere increases.

Cellular radio uses direct ground waves as its mode of travel. Direct waves contain not only waves following a linsight path but also waves due to:

1) Refraction - the bending of a wave or path of propagation at the boundary of two different mediums. This enablradio transmission to extend beyond the line of site.

2) Diffraction - bending around obstacles such as the edge of a roof on a building. This allows radio wave coverageand around obstacles.

3) Reflection - the ability of a wave or path of propagation to “bounce” off a certain object or objects (buildings, motains, etc.). This creates multiple paths that are followed by the transmitted signal and received at the receiver at times.

Note that both refraction and diffraction decrease as frequency increases.

Site Locations and Antenna Heights:

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If it all possible, it is necessary to choose locations for cell sites and antennas carefully and consider issues such as proper containment of coverage, alignment of sites into a specific hexagonal pattern, etc. Again, choices for sites may be limited due to availability of space for equipment and antennas, accessibility for maintenance, and availability of links to the base stations (either radio or physical) from the switch. Nevertheless, it is important to address certain considerations when selecting a cell site. At least, by simply mounting antennas at a lower level (< 40 m), one can essentially reduce a cells coverage area and increase the effectiveness of frequency reuse.

Containment of Coverage Through Reflection from Buildings:

In urban/suburban areas, where: 1) several cell sites may be required, 2) frequency reuse is unavoidable, and 3) in-build-ing penetration is a must, selected sites should offer contained coverage. While downtilt and variations in ERP may help to reduce the effective radius of each cell site, they nonetheless may not be sufficient enough. However, one can also rely on the presence of buildings in the area to serve as radio-path shields thus limiting coverage area. Furthermore, 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 consequently increase in-building penetration within the contained area.

In order to achieve these results, it is important that antenna/base sites are chosen accordingly. First 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 signals will propagate out over the other, lower buildings into other coverage areas. Furthermore, street coverage and in-building penetration immediately surrounding the site will probably be more limited due to the lack of reflections off surrounding buildings.

Examples of these situations are shown below:

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 meet subscriber demands is small. Frequency reuse would not be neces-sary and these sites could be considered as “broadcast”sites.

Hill-Top Cell Sites:

As another example, consider the placement of a cell site at the top of a hill overlooking a town or city. While covwill be adequate in the area immediately surrounding the cell site down to the side of the town facing the site, covwithin the city may be limited due to signal path obstructions due to buildings on the edge of the town. In other wreflections off buildings on the edge of the city will provide coverage to areas between the buildings and the cell sprobably not on the opposite side of the obstructions. An example is shown below:

Poor Frequency Re-use - Range Limited by Downtilt Only Better Frequency Re-use - Range Limited by Downtilt and Buildings

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y type o the grid.

“Off-grid” Site Locations:

As was stated before, following a hexagonal pattern when assigning cell sites is a good starting point in reducing cochan-nel interference as much as possible. However, due to possible limitations of adequate cell space for sites, locations may need to be assigned that are “off grid.” An example of such a situation is shown below:

In any case, the hexagonal grid reflects an ideal situation. Terrain effects will obviously skew the pattern out of anof symmetry. As a result, some interference may appear in some areas regardless of how close you assign sites tIt is at this point where the engineer will consider ways to control this interference.

Link Budgets and System Balance:

For more detail on link budgets please refer to the RF Planning Guide:


Antenna Downtilt:

...

BetterLocation

..

..

. .. .

..

..

..

..

. .. .

..

..

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By tilting the entire radiation pattern of a particular antenna, one can conceivably control its coverage pattern within a spe-cific area. Controlling the beam path will allow the provider to focus the coverage area and, in some cases, eliminate interference caused when the beam is allowed to propagate beyond its desirable coverage area.

Downtilt can be achieved in two ways, through mechanical as well as electrical downtilt.

Downtilt (Beamtilt):

“When the main radiation lobe is intentionally adjusted above or below [its plane of propagation], the resultant effknow as beamtilt. There are two categories of beamtilt, mechanical and electrical. Electrical beamtilt is obtainedadjusting the phase relationships of radiating elements within the antenna by the factory. [For example, an electrbeamtilt can be adjusted in the field by changing external phasing cables purchased from the vendor.] Mechanicbeamtilt may be accomplished by physically tilting the antenna away from the perpendicular by using a shim or dbracket. [For example, some manufacturer’s provide scissor-style brackets that eliminate guesswork about the sdegrees.] Downtilt of either variety should be specified only after a detailed understanding of the terrain and othegation factors have been acquired by the designer. Most legitimate uses of beamtilt involve signal coverage restrequired by cellular repeaters to prevent overlap with adjacent cells. Beamtilt is not a good substitute for null fill b

the horizon. A lower gain antenna might well over superior overall performance to a downtilted higher gain mode2

[Mechanical downtilting will cause the backlobe to tilt upward (parallel to front lobe), while electrical downtilting cathe backlobe to downtilt simultaneously. One other note to make, an electrical downtilt type of antenna could alsdowntilted mechanically.]

A great deal of caution must be used when downtilting a particular antenna. There are several “side effects” that c

with excessive downtilting.”3

The following Downtilt Effects graphs are provided by Terry Leonard of the Motorola RF Planning Group.11 The follow-

ing illustrations show mechanical downtilt effects (the backlobe stays parallel to the front lobe).

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0° Downtilt

DOWNTILT EFFECTS 3 x SRL410C4R130 Sector Antennas

Gain: 10 dB Vertical Beamwidth: 16°

Ant Ht: 164’ = 50m 153 dB Coverage 5° Downtilt

DOWNTILT EFFECTS

10° Downtilt

3 x SRL410C4R130 Sector Antennas


Ant Ht: 164’ = 50m 153 dB Coverage 15° Downtilt

Peanut Effect

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2° Downtilt

DOWNTILT EFFECTS

PD1132 Sector Antennas


Ant Ht: 164’ = 50m 153 dB Coverage

0° Downtilt

DOWNTILT EFFECTS

4° Downtilt 6° Downtilt




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Propagation Basics

“ERP and Downtilt Limitations:

As mentioned above, when adjusting ERP and downtilt at particular site in order to control interference, special consider-ations must be taken into account. There are limitations as to the amount of downtilt and ERP that is used at a given site. For example, one does not want to increase the ERP of a particular base station significantly past the level that assures a balanced path between it and the subscriber unit. If frequency reuse is present in the system, such a level would threaten to cause cochannel and/or adjacent interference with nearby sites. On the other hand, there is also a lower limit to effective use of ERP.

If used properly and carefully, downtilt can be an effective way to control the coverage area of a sectorized cell site and thus reduce possible interference. Generally, large angles (greater than 5 degrees) 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 adjacent sectors in the site which could cause additional, unnecessary port changes. Also, as a rule, there should be no more than 2 degrees difference in downtilt between adjacent sectors in any one site. Please refer to the diagram below:

DOWNTILT EFFECTS

8° Downtilt 10° Downtilt




21 of 76

Propagation Basics

ove

hysical nt

the prop-*. It is

As one can see, coverage decreases dramatically outside of the main lobe of the transmitted signal. We can therefore aim the outer edge of the main lobe at our cell boundary (which can be determined from a best server plot for system) to limit coverage outside. If you can determine the approximate cell radius and are aware of the site’s antenna height abground level, you can determine an approximate downtilt to use by the equation:

Downtilt = arctan(h/Dmax) + (Vertical Beamwidth/2)”3

[Celwave. 1997. Product Selection Guide 197. Radio Frequency Systems. Inc. pp. 320.]

[Clapp, Scott. March 8, 1995. China Frequency Planning and RF Propagation Analysis Overview, REV B. Motorola, Inc. pp. 18.]

[Leonard, Terry. Downtilt Effects Presentation. RF Planning Group. Motorola. pp 5-9.]

2.0 Environment

In an ideal situation, estimating propagation paths and signal fade would be straight forward. In the “real world”, pcharacteristics of the propagation environment will effect a signal’s ability to traverse through space. Environmedescriptions have been standardized in the communications industry.

2.1 Clutter Data (Electronic)

“There are various sources of clutter (morphological) data. The more current the clutter data, the more accurate agation predictions will be. The most common source of clutter data is from the U.S. Geological Survey (USGS)

AreaShadow

3dBBeamwidth

Downtilt0°

Main Lobe

UsableSignalDecreasingRapidly

StrengthRegionSignal

Area

Angle θ

SideLobe

h

Dmax

22 of 76

Propagation Basics

sert,

easily obtained and is available digitally. However, there are certain limitations with this data. The USGS data catego-rizes the land by how it is used (commercial, industrial, etc.), which does not necessarily coincide with categorizing the land by its propagation characteristics. Also, the USGS data may not account for newly developed areas. In order to obtain a more accurate determination for coverage, it is recommended that enhanced clutter data based on satellite imag-ery and aerial photography be used when generating propagation studies. This data is more expensive and requires more

time to acquire than the USGS data, but provides more reliable results.”14

*U.S. Geological Survey web site is located at: http://www.usgs.gov/


2.2 Some Clutter and Terrain Descriptions

“Dense Urban:

Consists of densely built areas with mainly high buildings (over 20 stories). Typically there is little or no trees and vege-tation within this area due to the density of buildings. Central parts of Chicago and New York are examples of dense urban areas.

Urban:

Consist of metropolitan regions, industrial areas and closely spaced residential homes and multi-storied apartments. Building density is high but may be interspersed with trees and other vegetation. Business centers of medium size cities such as Tulsa and Indianapolis as well as portions of the outer areas of New York and Chicago are examples of this envi-ronment.

Suburban:

Consists mainly of single family homes, shopping malls and office parks. Significant vegetation, trees and parking lots are intermixed with buildings. Most buildings are 1 to 3 stories but significant exceptions do occur. Significant areas within small and medium cities along with suburban communities surrounding major cities are examples of this environ-ment.

Rural/Quasi-Open:

Consist generally of open space with few buildings or residences. Major 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.”14

Open Rural/Open: Bare or open areas

Water: Lakes, rivers, ctc.

Terrain:

Terrain descriptions are literally focused on the land mass. Examples of terrain description are: mountainous, dewater (ocean, lake, stream), etc.

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Propagation Basics

stand the sts wo . Often structions.

con- damagl line of

are used sands of ver very

Forest:

Foliage descriptions focus on the tree density and tree height.

Roads:

Roads are normally described in terms of their capacity to carry traffic. For example, highways are described as being pri-mary if they are heavily traveled multi-lane roads (such as toll roads and inter-state highways). Smaller roads in and around the city or town would be described as secondary roads, and rural roads or those less travelled would be described as tertiary roads.


2.3 Line-of-Site (LOS)

“Radio transmission requires a clear path between antennas known as radio line of sight. It is necessary to underrequirements for radio line of sight when designing a network . Line of sight is the direct free-space path that exibetween two points. Using binoculars on a clear day, it is easy to determine if visual line of sight exists between tpoints that are miles apart. To have a clear line of sight there must be no obstructions between the two locationsthis means that the observation points must be high enough to allow the viewer to see over any ground-based ob

The following obstructions might obscure a visual link:

1. Topographic features, such as mountains

2. The curvature of the earth

3. Buildings and other man-made objects

4. Trees

If any of these obstructions rise high enough to block the view from end to end, there is no visual line of sight.

Obstructions that can interfere with visual line of sight can also interfere with radio line of sight. But one must alsosider the Fresnel effect. If a hard object, such as a mountain ridge or building, is too close to the signal path, it cane the radio signal or reduce its strength. This happens even though the obstacle does not obscure the direct, visua

sight.”29

[Solectek White Paper. Line of Site. [Online serial]. http://corfu.forthnet.gr/solectek/los.htm.]

3.0 Large-Scale Propagation Models - Path Loss

Propagation models are usually divided into large-scale or small-scale models. The large scale models normallyto predict the mean signal strength for transmitter-receiver separation distances of several hundred or even thoumeters apart. Small scale models, or fading models, describe rapid fluctuations of the received signal strength o

short distances (a few wavelengths) or short time durations.25

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Propagation Basics

found

the effec-path loss n.

There are many path loss models available for use, however certain models or combinations of models are preferred. The best models are those which are continuously compared against actual field data and adjusted for accuracy. The model used in Motorola’s NetPlan tool is XLOS. XLOS has been developed utilizing other models; its description can bein this section.

[Rappaport, Theodore S. 1996. Wireless Communications Principles and Practice. Upper Saddle River, New Jersey: Prentice Hall, Inc. pp. 70, 102-106, 110-111, 116-118, 163-167, 170-176, 188-189.]

3.1 Free Space Propagation Model

“The free space power received by a receiver antenna which is a distance of d from the transmitter antenna is given by Friis free space equation.

Where:

PT is the transmitted power

GT is the transmitting antenna gain

GR is the receiving antenna gain

d is the separation distance between antennas

The path loss which represents the signal attenuation as a positive quantity is defined as the difference betweentive transmitted power and the received power and may or may not include the effects of the antenna gains. The for the free space model when the antennas are assumed to have unity gain is provided by the following equatio

Expressed in dB as:

PR PT G⋅T

GRλ

4πd----------

2

⋅ ⋅=

PTPR-------

4πdλ

---------- 2 4πdf

c------------

2

==

L dB( ) 10PTPR-------

104πdf

c------------

220

4πdfc

------------ log=log=log=

20 4π( ) 20 d( ) 20 f( ) 20 3 108×( )log–log+log+log=

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Propagation Basics

Where:

d is in meters

f is in Hertz

c is equal to the speed of light ( meters per second)

If:

d is in kilometers

f is in MegaHertz ( Hertz)

c is

One is able to see from the above free space equations that 6 dB of loss is associated with a doubling of the frequency. This same relationship also holds for the distance, if the distance is doubled, 6 dB of additional loss will be encoun-

tered.”13


21.98 20 d( )log 20 f( )log 169.54–+ +=

147.56– 20 d( )log+= 20 f( )log+

3X108

106

3X108( )meter Hertz⋅

km1000m-----------------( ) MHz

106

Hz----------------

0.3km

MHz-------------=

LdB 21.98 20 dkm( )log 20 fMHz( )log 20 0.3( )log–+ +=

21.98 20 dkm( )log 20 fMHz( )log 10.46–( )–+ +=

32.44 20 d( km ) 20 f( MHz )log+log+=

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Propagation Basics

tion Fresnel d-num-te 3:

zones. eceiver rent s of sec-

structive

mum moved s well as

and ipsoids enna at

3.2 Fresnel Zones

“Fresnel zone: In radio communications, one of a (theoretically infinite) number of a concentric ellipsoids of revoluwhich define volumes in the radiation pattern of a (usually) circular aperture. Note 1: The cross section of the first zone is circular. Subsequent Fresnel zones are annular in cross section, and concentric with the first. Note 2: Odbered Fresnel zones have relatively intense field strengths, whereas even numbered Fresnel zones are nulls. No

Fresnel zones result from diffraction by the circular aperture.”6

The concept of diffraction loss as a function of the path difference around an obstruction is explained by Fresnel Fresnel zones represent successive regions where secondary waves have a path length from the transmitter to rwhich are nλ/2 greater than the total path length of a line-of-sight path. [The figure below] demonstrates a transpaplane located between a transmitter and receiver. The concentric circle on the plan represent the loci of the originondary wavelets which propagate to the receiver such that the total path length increases by λ/2 for successive circles. These circles are called Fresnel zones. The successive Fresnel zones have the effect of alternately proving conand destructive interference to the total received signal. The radius of the nth Fresnel zone circle is denoted by rn and can be expressed in terms of n, λ, d1, and d2 by

This approximation is valid for d1, d2 >> rn.

The excess total path length traversed by a ray passing through each circle is nλ/2, where n is an integer. Thus, the pathtraveling through the smallest circle corresponding to n = 1 in the figure will have an excess path length of λ/2 as com-pared to a line-of-sight path, and circles corresponding to n = 2,3,etc. will have and excess path length of λ, 3λ/2, etc. The radii of the concentric circles depend on the location of the plane. The Fresnel zones of the figure will have maxiradii if the plane is midway between the transmitter and receiver, and the radii become smaller when the plane istowards either the transmitter or the receiver. This effect illustrates how shadowing is sensitive to the frequency a the location of obstructions with relation to the transmitter or receiver.

An obstacle may block the transmission path and a family of ellipsoids can be constructed between a transmitterreceiver by joining all the points for which the excess path delay is an integer multiple of half wavelengths. The ellrepresent Fresnel zones. Note that the Fresnel zones are elliptical in shape with the transmitter and receiver ant

their foci.”25

rn

nλd1d2d1 d2+-------------------=

27 of 76

Propagation Basics

erence dle of the

Fresnel Zone in a Microwave Link:

“In a microwave link, the radio transmission exhibits wavelike characteristics, and the zone where wavelike interfcan affect the propagation path can be approximated by the Fresnel zone. The Fresnel zone is widest in the midlink and can be calculated from the formula:

where

RFZ = Fresnel zone radius

d1 = distance zone base 1 (km)

d2 = distance zone base 2 (km)

d = d1 + d2 or the length of the hop

f - frequency in GHz

the figure below show the calculation of the first Fresnel zone radius.

O123

hT R

d1 d2

RFZ 17.3X d1 d2×( ) d f×( )⁄=

28 of 76

Propagation Basics

of the

ercent of ly causes Fresnel

alues of at poten-

Microwaves do not normally propagate within the atmosphere in straight lines; they ordinarily travel in curved paths (usu-ally curved downward) due to atmospheric refraction. The amount of curvature is usually defined with respect to the earth’s curvature, which is designated as K, where K X R (R = the earth’s actual radius) gives the effective radiusearth as seen by the microwave path.

If the Fresnel zone is obstructed, some additional path losses will occur. When there are no obstacles within 50 pthe Fresnel zone radius for K = 4/3 (the most usual value that approaches a “flat earth”), then the obstacle generalnegligible loss. When, however, an obstacle protrudes into the path of the link by more than 50 percent of the firstzone, an adjustment must be made for the additional losses incurred.

The terrain loss LTR (in dB) can be calculated as

where

C = the clearance in meters of the obstacle in the Fresnel zone (as shown in the figure)

RFZ = Fresnel zone radius

Notice that

C can be negative if it protrudes into the Fresnel zone.

This approximation is valid only for -1.5 ≤ C/RFZ ≤ +0.5.

Because of changes in the refractive index of the atmosphere, the effective value of K varies with time. Smaller vK increase the attenuation due to obstructions, particularly on longer path lengths. You should check to ensure thtial variations in K will not degrade the service.

The change in clearance (CC) for changes in K can be approximated by

LTR 10 C RFZ⁄( )– 20×=

C

29 of 76

Propagation Basics

ry:

ting the ed by

the

he and sec-

The limiting values of K are

K = 1 for wet climates

K = 0.9 for temperate climates

K = 0.6 for desert climates

It is normal to check the path profile for the extremes of K = 4/3 to K = 0.8.”1

[Boucher, Neil J. 1995. The Cellular Radio Handbook. A Reference for Cellular System Operation. Third Edition. Mill Valley. Quantum Publishing, Inc. pp. 73-74, 185-186.]

[Glossary of Telecommunication Terms. [Electronic database]. August 7, 1996. U.S. Federal Government. Directohttp://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm.]

[Rappaport, Theodore S. 1996. Wireless Communications Principles and Practice. Upper Saddle River, New Jersey: Prentice Hall, Inc. pp. 102-106, 110-111, 116-118, 167, 170-176, 188-189.]

3.3 Propagation Over a Plane Earth

“Knowing the propagation characteristics over a smooth, conducting, flat earth provides a starting point for estimaeffects of propagation over actual paths. The complex analytical results for propagation over a plane earth deriv

Norton have been simplified by Bullington38 by decomposing the solution of Norton into a set of waves consisting ofdirect, reflected, and surface waves. The formula relating the power transmitted to the power received following

approach of Bullington38 is

Within the absolute value symbols, the first term (unity) represents the direct wave, the second term represents treflected wave, the third term represents the surface wave, and the remaining terms represent the induction fieldondary effects of the ground.

The reflection coefficient, R, of the ground depends on the angel of incidence, θ, the polarization of the wave, and the ground characteristics; it is given by

where

CC 0.078 d1 d2 0.751K----

–

×××= meters

Pr Ptλ

4πd----------

2gbgm 1 Re

j∆1 R–( )Ae

j∆ …+ + +2

=

R θ z–sinθ z+sin

--------------------=

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Propagation Basics

The quantity ∆ is the phase difference between the reflected and the direct paths between transmitting and receiving antennas, illustrated in [the figure below]. Let hb and hm be the heights of the base and mobile antennas; then ∆ is given

by

For d greater than 5hbhm [∆ is given by],

Since the earth is not a perfect conductor, some energy is transmitted into the ground, setting up ground currents that dis-tort the field distribution relative to what it would have been over a perfectly reflecting surface. The surface wave attenu-ation factor, A, depends on frequency, polarization, and the ground constants. An approximate expression for A is given by

which is valid for |A| < 0.1. More accurate values are given by Norton. Since the effect of this surface wave is only sig-nificant in a region a few wavelengths above the ground, this effect can be neglected in most applications of microwave mobile communications.

zε0 θcos–

ε0-----------------------= for vertical polarizaion,

2

z ε0 θcos–= for horizontal polarizaion,2

ε0 ε j60σλ–= ,

ε = the dielectric constant of the ground relative to unity in free space,

σ = the conductivity of the earth in mhos per meter.

∆ 2πλ

------hb hm+

d--------------------

2

1+

12---

2πdλ

----------hb hm+

d--------------------

2

1+

12---

–=

∆4πhbhm

λd---------------------≈

A1–

1 j 2πd λ⁄( ) θ z+sin( )2+--------------------------------------------------------------≈

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Propagation Basics

and for e 100

ase sta-

It is of interest to note that in the limit of grazing angle of incidence the value of the reflection coefficient, R, approaches -1 independent of the polarization. For frequencies above 100 MHz and for an “average” earth (see table [below])vertical polarization, |R| exceeds 0.9 for angles less than 10º above the horizon. For horizontal polarization abovMHz, |R| exceeds 0.5 for angles less than 5º, but must be of the order of a degree or less for |R| to exceed 0.9.

Under the conditions where R equals -1 and A can be neglected, then [the power received equation] reduces to

where P0 is the expected power over a free space path. In most mobile radio applications, except very near the btion antenna, sin 1/2 ∆ ≈ 1/2 ∆; thus the transmission loss over a plane earth is given by the approximation

yielding an inverse fourth-power relationship of received power with distance from the base station antenna.

Typical Ground Constants

Type of Surface s(mho/m) e

Poor ground 0.001 4

Average ground 0.005 15

Good ground 0.02 25

Sea water 5 81

Fresh water 0.01 81

hmhb

d

θ

Propagation paths over a plane earth.

Pr 4P0

2πhbhmλd

--------------------- sin=

2

Pr 4Ptgbgm

hbhm

d2

-------------- 2

=

32 of 76

Propagation Basics

gulari-ing the

C<0.1 lues of C

range

heric con- variation

The ground constants over the path of interest enter into both the calculations for line-of-sight and for diffraction attenua-tion. At microwave frequencies it is usually the dielectric constant, ε, which has the dominant effect on propagation. [The table above] gives values of typical ground constants. Applying these values to the formulas for the reflection coef-ficient over a plane earth just derived, we find that for frequencies above 100 MHz the effect of the ground constants are

slight.”8

[Jakes, William C. 1974. Microwave Mobile Communications. An IEEE Press Classic Reissue. Picataway. American Telephone and Telegraph Company. pp. 80-88.]

3.4 Rough Surface Criterion

“At the higher microwave frequencies the assumption of a plane earth may no longer be valid, due to surface irreties. A measure of the surface “roughness” that provides an indication of the range of validity of [the formula relat

power transmitted to the power received following the approach of Bullington38]

is given by the Rayleigh criterion, which is

where σ is the standard deviation of the surface irregularities relative to the mean height of the surface, λ is the wave-length, θ is the angle of incidence measured in radians from the horizontal. Experimental evidence shows that forspectacular reflection results, and the surface may be considered smooth. Surfaces are considered “rough” for va

exceeding 10, and under these conditions the reflected wave is very small in amplitude. Bullington38 has found experi-mentally that most practical paths at microwave frequencies are relatively “rough” with reflection coefficients in the

of 0.2-0.4.”8


3.5 Refraction and Equivalent Earth’s Radius

“Because the index of refraction of the atmosphere is not constant, but decreases (except during unusual atmospditions) with increasing height above the earth (h), electromagnetic waves are bent as they propagate. The meanin refractive index (n) can be considered linear with a constant gradient g of the form

In a medium where there are abrupt changes in index of refraction, Descarte’s law applies:

Pr Ptλ

4πd----------

2gbgm 1 Re

j∆1 R–( )Ae

j∆ …+ + +2

=

C 4πσθλ

--------------=

n n0 gh+=

33 of 76

Propagation Basics

nd the s. Gener-

where α and α0 are the angles at the discontinuity at height h, above the surface of the earth of radius a. Note if the atmo-

sphere is uniform the equation for rectilinear propagation is

When n has a constant gradient the propagation is given approximately by

If we replace the earth’s radius a by a fictitious value a’, where

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

Since the index of refraction in the troposphere is very nearly unity, the N-unit has been defined for convenience,

where n is the index of refraction in the atmosphere. Values of the minimum monthly mean value of Ns throughout the

world have been published. The most commonly used value for Ns is 301. This gives a value for the effective earth’s radius a’ which corresponds to four-thirds of the actual earth’s radius. The empirical formula for a’ is given by

where 6370 km is used for the earth’s radius.”8


3.6 Transmission Over a Smooth Spherical Earth

“At microwave frequencies, diffraction due to the earth severely limits the amount of energy that propagates beyohorizon. Considerable work has been done in an attempt to predict the signal attenuation over transhorizon path

n a h+( ) αcos n0 α0acos=

1 ha---+

αcos a0cos=

1 h 1a--- g+

+ αcos α0cos≈

a′ 1a--- g+

1–=

Ns n 1–( ) 106×=

a′ 6370 1 0.04665 0.005577Ns( )exp–[ ] 1–= km

34 of 76

Propagation Basics

by orithms uter a model

ht over nditions. irtual s are itional

with each ht. The ive an

terms. tion is o

ure-lutter

l

ally speaking, these predictions are semiempirical formulas which apply for frequencies below 1000 MHz. It is possible to obtain analytic expressions for the diffraction over a perfectly conducting sphere; however, the expressions are not sim-ple relationships between the factors of frequency, conductivity of the earth, antenna height, and distance which govern the attenuation. ...Estimations of the attenuation due to diffraction over a smooth earth are particularly difficult in regions just beyond line-of-sight. Furthermore, surface roughness again seriously affects propagation. It is, of course, desirable to be able to estimate signal strengths beyond the horizon, particularly for cases where the same frequencies are being

used at separate base stations. Bullington38 has reduced the involved analytic relationships for the propagation over a

smooth spherical earth to various asymptotic forms.”8


3.7 XLOS

“The workhorse of the NetPlan tool is the XLOS propagation model developed and refined over the last 15 yearsMotorola engineers. The method used to refine estimate coverage is based on the diffraction and line of sight algfound in Longley and Rice, "Prediction of Tropospheric Radio Transmission Loss Over Irregular Terrain. A CompMethod" - 1968, for rough terrain conditions. As the terrain flattens out the range estimates approach the Okumurpredictions, "Field Strength and Its Variability in VHR and UHF Land-Mobile Radio Service" -1968.

The model adjusts for built up or natural environments on top of the terrain by assuming a virtual obstruction heigand above the existing terrain which is varied to correspond to urban, suburban, rural, foliage, water and other coThe overlay (or obstruction) code is determined from maps which typically show this information as colors. This vheight is then scanned to find the major, or controlling, obstacles for each mobile position. Single diffraction pointseparated from extended obstructions and are treated in different ways to obtain an estimate of the degree of addtransmission loss expected over free space.

At the same time that the obstruction search is going on, a straight line estimate of the average terrain is updated new mobile position. This straight line approximation is used to obtain an equivalent adjusted base antenna heigadjusted base antenna height is further corrected for earth curvature and is applied to the line of sight routine to gestimated reflection loss term.

The final estimated total attenuation for each mobile position is a varying mix of both reflection and diffraction loss Adjustments are made by corrections applied to each loss term as a function of whether single or multiple diffractaking place. Antenna horizontal and vertical patterns, downtilt angles, and sector power levels are also taken intaccount.

Although the XLOS propagation model is based on Longley, Rice and Okumura algorithms, extensive field measments, in varying terrain conditions, have been used to modify the algorithms and to model local environmental c

(obstruction height).”17

The following slides taken from an Xlos Propagation Model18 presentation, depict the process and evolution of the tooand shows the general mix formula used.

35 of 76

Propagation Basics

T h e gen e r a l “p a th ” lo ss equ at io n is giv en be lo w :

LP = AFS + C 1AD + C 2AD + AN TH V + PS

w h ere :

L P = “p a th ” lo ss be tw een d ip o les

A FS = frequ en cy + free sp ace co m p o n en t

A D = d i ffr act io n lo ss

A R = r e flect io n lo ss

A N T H V = an ten n a h o r izo n ta l an d v er t ica l p a tte rn

PS = p o w er ad ju stm en t (re l . T o 50 d Bm ) by secto r

C = m ixin g co e fficien ts

A lth o u gh th e Xlo s m o d e l i s ba sed o n Lo n gle y a n d R ice , a n d O k u m u r aa lgo r i th m s, e xten siv e fie ld m e a su r e m e n ts, in v a r yin g te r r a in co n d i t io n s,w e r e u sed to m o d ify th e a lgo r i th m s an d to m o d e l lo ca l en v i r o n m e n ta l clu t te r(v ir tu a l o bst r u ct io n h e igh t ).

6 ,7 ( �' $ 7$

� �& 2 1 72 8 5

� �% ( 67 �6 ( 5 9 ( 5� �& � ,

& /8 7 7 ( 5' $ 7$

7 ( 5 5$ ,1' $ 7$

$ 1 7 (1 1 $3$ 7 7 ( 51

; /2 6

2 8 7 38 7,0 $ * ( 6

� �6 ,* 1 $ / �67 5 (1 * 7+

� �6 ,7 ( �& 2 2 5' ,1 $ 7 ( 6� �$ 1 7 (1 1 $ �+ ( ,* + 7� �6( & 72 5 �' 2: 1 7 ,/ 7� �6( & 72 5 �+ ($ ' ,1 *� �6( & 72 5 �( 5 3

� �8 6* 6 �/ 8 /& ��' ,* ,7 $ / �' $ 7$� �6$ 7 ( / / ,7 ( �,0 $ * (

� �8 6* 6 �� $ 5 & �6( & 2 1 ' �' (0� �% ,/ �)2 50 $ 7

� �' ,* ,7 ,= (' �9 ( 5 7 ,& $ /��$ 1 ' ��+ 2 5 ,= 2 1 7$ / ��3 $ 7 7 ( 5 1 6

XLOS PROCESS DIAGRAM

36 of 76

Propagation Basics

ch as t the of dif-

[Motorola NetPlan Group. XLOS Propagation Model [Online serial]. http://www.sesd.cig.mot.com/xlos.html.]

[Motorola NetPlan Gourp. Xlos Propagation Model. Slide Presentation.]

3.8 Knife Edge Diffraction

“Very often in the mobile radio environment a line-of-sight path to the base station is obscured by obstructions suhills, trees, and buildings. When the shadowing is caused by a single object such as a hill, it is instructive to treaobject as a diffracting knife edge to estimate the amount of signal attenuation. The exact solution to the problemfraction over a knife edge is well known as is discussed in many textbooks.

Within the shadow region of the knife edge, the electric field strength E, can be represented as

where E0 is the value of the electric field at the knife edge, A is the amplitude, ∆ is the phase angle with respect to the direct path. The expressions for A and ∆ are obtained in terms of the Fresnel integrals:

Based on:/21*/(<��5,&(��2.8085$%8//,1*721

),(/'�7(676��7HUUDLQ��:DVKLQJWRQ�%DOWLPRUH�7HVW�%HG��6DQ�)UDQFLVFR��+RXVWRQ��'LIIHUHQW�&OXWWHU

;/26352727<3(

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ON GOING DEVELOPMENT

XLOS EVOLUTION

EE0------ A i∆( )exp=

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Propagation Basics

where

where (from Fresnel zone geometry):

For most microwave mobile radio applications several assumptions can be made to simplify the calculations. Consider an infinite completely absorbing (rough) half-plane that divides space into two parts as in [the following figure]. When the distances d1 and d2 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, λ, that is,

A S 1 2⁄+

2 ∆ π4---+

sin

----------------------------------=

∆ S 1 2⁄+C 1 2⁄+--------------------

π4---–tan=

-1

Cπ2---v

2 cos vd

0

h0

∫=

Sπ2---v

2 sin vd

0

h0

∫=

φ π2---v

2= : Phase difference between the direct path and the diffracted path.

v h2 d1 d2+( )

λd1d2---------------------------=

h2λ--- 1

d1------ 1

d2------+

=

38 of 76

Propagation Basics

dge dif-

en

istribu-

ases loga-n the lit-nction of

then the diffracted power can be given by the expression

This result can be considered independent of polarization as long as the conditions of d1,d2>>h>>l, are met. In cases where the earth’s curvature has an effect, there can be up to four paths. A simplified method of computing knife e

fraction for such cases is treated by Anderson and Trolese35. Closer agreement with data over measured paths has be

obtained by calculations that better describe the geometry of the diffracting obstacle.”8


3.9 Log-distance Path Loss Model and Log-normal Shadowing

“[The figure below] shows log normal fading. This process is called log normal fading because the field strength d

tion follows a curve that is a normally distributed curve, provided the field strength is measured logarithmically.”1

“Both theoretical and measurement-based propagation models indicate that average received signal power decrerithmically with distance, whether in outdoor or indoor radio channels. Such models have been used extensively ierature. The average large-scale path loss for an arbitrary T-R (transmit-receive) separation is expressed as a fudistance by using a path loss exponent, n.

d1 d2, h λ» »

PP0------ 1

2π2h0

2----------------=

d1 d2

h

Geometry for propagation over a knife edge.

.

Log normal fading that is due to obstruction is known as “shadowing” or “diffraction losses.”

39 of 76

Propagation Basics

or

where n is the path loss exponent which indicates the rate at which the path loss increases with distance, d0 is the close-in reference distance which is determined from measurements close to the transmitter, and d is the T-R separation distance. The bars in (the above) equations denote the ensemble average of all possible path loss values for a given value of d. When plotted on a log-log scale, the modeled path loss is a straight line with a slope equal to 10n dB per decade. The value of n depends on the specific propagation environment. For example, in free space, n is equal to 2, and when obstructions are present, n will have a larger value.

It is important to select a free space reference distance that is appropriate for the propagation environment. In large cover-age cellular systems, 1 km reference distances are commonly used, whereas in microcellular systems, much smaller dis-tances (such as 100 m or 1 m) 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 path loss is calculated using the free space path loss formula... or through field measurements at distance d0. [The table below] lists typical path loss exponents obtained in

various mobile radio environments.

The model in [the log-distance] equation does not consider the fact that the surrounding environmental clutter may be vastly different at two different locations having the same T-R separation. This leads to measured signals which are vastly different than the average value predicted by [the log-distance] equation. Measurements have shown that at any value of d, the path loss PL(d) at a particular location is random and distributed log-normally (normal in dB) about the mean dis-tance-dependent value. That is

3DWK�/RVV�([SRQHQWV�IRU�'LIIHUHQW�(QYLURQPHQWV

(QYLURQPHQW 3DWK�/RVV�([SRQHQW��Q

Free space 2

Urban area cellular radio 2.7 to 3.5

Shadowed urban cellular radio 3 to 5

In building line-of-sight 1.6 to 1.8

Obstructed in building 4 to 6

obstructed in factories 2 to 3

PL d( ) dd0------

n∝

PL dB( ) PL d0( ) 10nd

d0------

log+=

40 of 76

Propagation Basics

and

where Xσ is a zero-mean Gaussian distributed random variable (in dB) with standard deviation σ (also in dB).

The log-normal distribution describes the random shadowing effects which occur over a large number of measurement locations which have the same T-R (transmit-receive) 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 that mea-sured signal levels at a specific T-R separation have a Gaussian (normal) distribution about the distance-dependent mean of [the previously mentioned PL equation], where the measured signal levels have values in dB units. The standard devi-ation of the Gaussian distribution that describes the shadowing also has units in dB. Thus, the random effects of shadow-ing are accounted for using the Gaussian distribution which lends itself readily to evaluation.

The close-in reference distance d0, the path loss exponent n, and the standard deviation σ, statistically describe the path loss model for an arbitrary location having a specific T-R separation, and this model may be used in computer simulation to provide received power levels for random locations in communication system design and analysis.

In practice, the values of n and σ are computed from measured data, using linear regression such that the difference between the measured and estimated path losses is minimized in a mean square error sense over a wide range of measure-ment locations and T-R separations. The value of PL(d0) in [the previously mentioned path loss equation] is based on

either close-in measurements or on a free space assumption from the transmitter to d0. An example of how the path loss exponent is determined from measured data follows.

Since PL(d) is a random variable with a normal distribution in dB about the distance-dependent mean, so is Pr(d), and the Q-function or error function (erf) may be used to determine the probability that the received signal level will exceed (or fall below) a particular level. The Q-function is defined as

where

the probability that the received signal level will exceed a certain value γ can be calculated from the cumulative density function as

PL d( ) dB[ ] PL d( ) Xσ+ PL d0( ) 10nd

d0------

log Xσ+ += =

Pr d( ) dBm[ ] Pt dBm[ ] PL d( ) dB[ ]–=(antenna gains included in PL(d))

Q z( ) 1

2π---------- x

2

2------–

exp xdz

∞∫

12--- 1 erf

z

2-------

–= =

Q z( ) 1 Q z–( )–=

41 of 76

Propagation Basics

Hz to terrain odel)

ted using g dis-er

ss rela-on path, activity, on path-ance, ter-

ific

param-

impor-is mod-ceiving

similarly, the probability that the received signal level will be below γ is given by”25



3.10 Longley-Rice (Irregular Terrain Model)

“The Longley-Rice model, is applicable to point-to-point communication systems in the frequency range from 40 M100 GHz, over different kinds of terrain. The median transmission loss is predicted using the path geometry of theprofile and the refractivity of the troposphere. Geometric optics techniques (primarily the 2-ray ground reflection mare used to predict signal strengths within the radio horizon. Diffraction losses over isolated obstacles are estimathe Fresnel-Kirchoff knife-edge models. Forward scatter theory is used to make troposcatter predictions over lontances, and far field diffraction losses in double horizon paths are predicted using a modified Van der Pol-Bremmmethod. The Longley-Rice propagation prediction model is also referred to as the ITS irregular terrain model.

The Longley-Rice model is also available as a computer program to calculate large-scale median transmission lotive to free space loss over irregular terrain for frequencies between 20 MHz and 10 GHz. For a given transmissithe program takes as its input the transmission frequency, path length, polarization, antenna heights, surface refreffective radius of earth, ground conductivity, ground dielectric constant, and climate. The program also operatesspecific parameters such as horizon distance of the antennas, horizon elevation angle, angular trans-horizon distrain irregularity and other specific inputs.

The Longley-Rice method operates in two modes. When a detailed terrain path profile is available, the path-specparameters can be easily determined and the prediction is called a point-to-point mode prediction. On the other hand, if the terrain path profile is not available, the Longley-Rice method provides techniques to estimate the path-specificeters, and such a prediction is called an area mode prediction.

There have been many publications and corrections to the Longley-Rice model since its original publication. Onetant modification deals with radio propagation in urban areas, and this is particularly relevant to mobile radio. Thification introduces an excess term as an allowance for the additional attenuation due to urban clutter near the reantenna. This extra term, called the urban factor (UF), has been derived by comparing the predictions by the originalLongley-Rice model with those obtained by Okumura.

Pr Pr d( ) γ>[ ] Qγ Pr d( )–

σ---------------------

=

Pr Pr d( ) γ<[ ] QPr d( ) γ–

σ-------------------------

=

42 of 76

Propagation Basics

MHz, the Bull-

base and ce from th loss

s are

ra

.

One shortcoming of the Longley-Rice model is that it does not provide a way of determining corrections due to environ-mental factors in the immediate vicinity of the mobile receiver, or consider correction factors to account for the effects of

buildings and foliage. Further, multipath is not considered.”25


3.11 Okumura

“The Okumura model is based on data taken from 150 to 1500 MHz with less data taken at 150 MHz. Above 216use the Okumura model. Between 132 and 216 MHz, the Okumura and Bullington models are equally valid. Use

ington model for frequencies below 132 MHz.”20

“Okumura developed a set of curves giving the median attenuation relative to free space (Amu), in an urban area over a

quasi-smooth terrain with a base station effective antenna height (hte) of 200 m and a mobile antenna height (hre) of 3 m. These curves were developed from extensive measurements using vertical omni-directional antennas at both themobile, and are plotted as a function of frequency in the range 100 MHz to 1920 MHz and as a function of distanthe base station in the range 1 km to 100 km. To determine path loss using Okumura’s model, the free space pabetween the points of interest is first determined, and then the value of Amu(f,d) (as read from the curves) is added to it along with correction factors to account for the type of terrain. The model can be expressed as

where L50 is the 50th percentile (i.e. median) value of propagation path loss, LF is the free space propagation loss, Amu is the median attenuation relative to free space, G(hte) is the base station antenna height gain factor, G(hre) is the mobile antenna height gain factor, and GAREA is the gain due to the type of environment. Note that the antenna height gainstrictly a function of height and have nothing to do with antenna patterns.

Plots of Amu(f,d) and GAREA for a wide range of frequencies are shown in [the figures] below. Furthermore, Okumu

found that G(hte) varies at a rate of 20 dB/decade and G(hre) varies at a rate of 10 dB/decade for heights less than 3 m

L50 dB( ) LF Amu f d( , ) G hte( )– G hre( )– GAREA–+=

G hte( ) 20hte200---------

log= 1000 m > hte > 30m

G hre( ) 10hre3

-------- log= hre ≤ 3m

G hre( ) 20hre3

-------- log= 10 m > hre > 3 m

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Propagation Basics

e the ter-nce the . All these

situa-h the

r mature for sys-esponse al areas.

.

Other corrections may also be applied to Okumura’s model. Some of the important terrain related parameters arrain undulation height (∆h), isolated ridge height, average slope of the terrain and the mixed land-sea parameter. Oterrain related parameters are calculated, the necessary correction factors can be added or subtracted as requiredcorrection factors are also available as Okumura curves.

Okumura’s model is wholly based on measured data and does not provide any analytical explanation. For manytions, extrapolations of the derived curves can be made to obtain values outside the measurement range, althougvalidity of such extrapolations depends on the circumstances and the smoothness of the curve in question.

Okumura’s model is considered to be among the simplest and best in terms of accuracy in path loss prediction focellular and land mobile radio systems in cluttered environments. It is very practical and has become a standardtem planning in modern land mobile radio systems in Japan. The major disadvantage with the model is its slow rto rapid changes in terrain, therefore the model is fairly good in urban and suburban areas, but not as good in rur

Common standard deviations between predicted and measured path loss values are around 10 dB to 14 dB.”25

For more information please read Okumura’s paper [Okumura, Y., Ohmori, E., Kawano, T., Fukada, K. 1968. Field strength and ITs Variability in VHF and UHF Land-Mobile Radio Service, Rev. Elec. Commun. Lab., 16. pp. 825-873.]

Frequency f (MHz) Frequency f (MHz)70 100 200 300 500 700 1000 2000 3000 100 200 300 500 700 1000 2000 3000

30

25

20

15

10

5

0

35

Corr

ecti

on F

acto

r, G

AR

EA

(dB

)

Suburban Area

Quasi Open AreaOpen Area

Uban Areaht = 200 mhr = 3 m

100

80

706050

40

30

20105

21

Med

ian

Att

enuat

ion

, A

(f,d

) (d

B)

d (

km

)

44 of 76

Propagation Basics

mura’s of the then used n the trans-

radius

[Mozaik Web Page. Okumura Propagation Model. [Online serial]. http://rdeserver.comm.mot.com/mozaik/oku-mura.htm.]


3.12 Hata

“Among the many technical reports that are concerned with propagation prediction methods for mobile radio, Oku2

report is believed to be the most comprehensive one. In his report, many useful curves to predict a median valuereceived signal strength are presented based on the data collected in the Tokyo area. The Tokyo urban area wasas a basic predictor for urban areas. The correction factors for suburban and open areas are determined based omit frequency. Based on Okumura’s prediction curves, empirical formulae for the median path loss, Lp, between two iso-

tropic antennae were obtained by Hata and are known as the Hata Empirical Formulae for Path Loss3. The Hata propagation formulae are used with the link budget calculation to translate a path loss value to a forward link celland a reverse link cell radius.

For Urban Area:

For Suburban Area:

For Quasi Open Area:

For Open Rural Area:

where:

AHm Correction Factor For Vehicular Station Antenna Height

For a Medium-Small City:

LU 69.55 26.16 fc( )log× 13.82 Hb( )log×–

AHm– 44.9 6.55 Hb( )log× ] r( )log×–[+

+

=

LS LU 2fc28------

log2

×– 5.4–=

Lq LU 4.78 fc( )log[ ]× 2– 18.33 fc( )log× 35.94–+=

Lq LU 4.78 fc( )log[ ]× 2– 18.33 fc( )log× 40.94–+=

AHm 1.1 fc( ) 0.7–log×[ ] Hm× 1.56 fc( ) 0.8–log×[ ]–=

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e applied

e equency xtended e basic

For a Large City:

Lu , Ls , Lq = isotropic path loss values

fc = carrier frequency in MHz (valid 150 to 1,000 MHz)

Hb = base antenna height in meters (valid 30 to 200 meters)

Hm = mobile antenna height in meters (valid 1 to 10 meters)

r = radius of site in kilometers (valid 1 to 20 km)

This model is valid for large and small cells (i.e. base station antenna heights above roof-top levels of buildings adjacent to the base station).

Measurements which have been taken at 1,900 MHz have shown the path loss difference between 800 MHz and 1,900 MHz closer to 11 dB. The COST-231-Hata model was developed to account for this difference.

Hata is similar to COST-231-Hata with the exception of two terms:”13

Hata yields

COST-231-Hata yields


3.13 COST-231-Hata

“The COST 231 Subgroup on Propagation Models proposed an improved propagation model for urban areas to b

above 1,500 MHz4. Like Hata’s model, the COST-231-Hata model is based on the measurements of Okumura. ThCOST-231-Hata propagation model has been derived by analyzing Okumura’s propagation curves in the upper frband. Hata’s analysis was restricted to frequencies below 1,000 MHz. The COST-231-Hata propagation model ethe range of parameters to include 1,500 to 2,000 MHz. Their modified model was based on Hata’s formula for thtransmission loss in urban areas (see above).

For Urban Area

AHm 3.2 11.75 Hm×( ) ]log[× 24.97–=

69.55 26.16 fc( )log+

46.3 33.9 fc( )log+

LU 46.3 33.9 fc( )log× 13.82 Hb( )log×–

AHm– 44.9 6.55 Hb( )log× ] r( )log×–[+

+

=

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Propagation Basics

For Suburban Area:

For Quasi Open Area:

For Open Rural Area:

where:

AHm Correction Factor For Vehicular Station Antenna Height

For a Medium-Small City:

For a Metropolitan Center:

Lu , Ls , Lq = isotropic path loss values

fc = carrier frequency in MHz (valid 1,500 to 2,000 MHz)

Hb = base antenna height in meters (valid 30 to 200 meters)

Hm = mobile antenna height in meters (valid 1 to 10 meters)

r = radius of site in kilometers (valid 1 to 20 km)

This model is valid for large and small cells (i.e. base station antenna heights above roof-top levels of buildings adjacent to the base station).

Measurements which have been taken at 1,900 MHz have shown the path loss difference between 800 MHz and 1,900 MHz closer to 11 dB. The COST-231-Hata model was developed to account for this difference.

LS LU 2fc28------

log2

×– 5.4–=

Lq LU 4.78 fc( )log[ ]× 2– 18.33 fc( )log× 35.94–+=

Lq LU 4.78 fc( )log[ ]× 2– 18.33 fc( )log× 40.94–+=

AHm 1.1 fc( ) 0.7–log×[ ] Hm× 1.56 fc( ) 0.8–log×[ ]–=

AHm 1.1 fc( ) 0.7–log×[ ] Hm× 1.56 fc( ) 0.8–log×[ ]– 3–=

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Propagation Basics

f the Such an

n note.

loss ence

A comparison between the Hata and COST-231-Hata equations show that they are similar except for the following two

terms:”13

Hata yields

COST-231-Hata yields


3.14 Slope and Intercept

There are a number of different kinds of statistical, empirical and custom pathloss models available today. Most omodels are represented by an equation, describing the various parameters that contribute to the pathloss model.expression is shown below, borrowed from the Custom Pathloss Model (CPM) application note.

Where: D is the Diffraction, LU is the Land Use and CSL is the Cover Set Loss as described in the CPM applicatioK1 through K7 parameters are also described in more details in the CPM application note.

(The K1 and K2 parameters are the subject of this discussion.) K1 and K2 are the intercept and slope of the pathmodel respectively. The figure below illustrates the slope and intercept parameters for the HATA 800 Model (refer

from the CPM Application Note15).

69.55 26.16 fc( )log+

46.3 33.9 fc( )log+

PL indBd( ) K1 K2 d( )log K3 Hb( )log K4 Hb( ) d( )loglog K5 Hm( )logK6 f )( ) K7 D LU( ) CSL( )⁄+⋅+log

+ + + ++

=

Log(Distance (km))

Sig

nal S

tren

gth

(dB

m)

1 kmHATA Intercept

Intercept =

K1 27.81 0.7 Hm 4.78 f( )log( )2⋅( )– 4.3–⋅+=

Slope = K2 44.9= dB/decade

HATA 800 MODEL

48 of 76


Propagation Basics

ic and ami is l. and building

ommu- is

e, at, or t the ters:

to be qually

r Com-ber

What the graph shows is that the greater the distance from the serving site the lower the signal strength will be. The K1 value is a constant which is the intercept of the graph with the abscissa. The K1 value for the HATA 800 and COST-231 models can be found in the CPM application note for various environments. The K2 value is the slope of the line and rep-resents the slope in dB per decade that the signal strength (or the Pathloss (PL)) will be diminishing with respect to dis-tance.

[Motorola NetPlan Group. May 12, 1998. NetPlan Application Note Custom Pathloss Model. NetPlan V3.2. Revision 0.1.]

3.15 Walfish-Ikegami Cost 231

“The Walfisch-Ikegami model, also developed by a subgroup of the European Cooperation in the Field of ScientifTechnical Research, factors in parameters that describe obstructions found in urban environments. Walfisch-Ikegsuitable for modeling small cells in the 800-2000 MHz frequency ranges where deployment is above building leveWalfisch-Ikegami uses user-specified area and city qualifications (correction factors) to adapt the model for urbansuburban areas. In addition, users specify values for the following parameters: average building height, average

separation, average street width, and road orientation.”16

[Motorola NetPlan Group. Statistical [Online serial]. http://www.sesd.cig.mot.com/statistical/.]

3.16 Walfisch-Xia JTC

“The Walfisch-Xia JTC model is a new propagation model adopted by the Joint Technical Committee of the Telecnications Industry Association (TIA) and the Exchange Carriers Standards Association (ECSA). Walfisch-Xia JTCsuitable for modeling small, large, and micro cells in the 300-2000 MHz frequency ranges with deployments abovbelow building level. Walfisch-Xia JTC uses user-specified area and city qualifications (correction factors) to adapmodel for urban, suburban, residential, and rural areas. In addition, users specify values for the following parame

average building height, average building separation, and average street width.”16

[Motorola NetPlan Group. Statistical [Online serial]. http://www.sesd.cig.mot.com/statistical/.]

3.17 Bullington

“The Bullington model is based on data taken from 54 to 216 MHz. The Bullington model is generally consideredpreferable at frequencies below 132 MHz. Between 132 and 216 MHz, the Bullington and Okumura models are evalid. Do not use Bullington at frequencies above 216 MHz.

Mozaik(sm)'s Bullington model is based on formulae and techniques described in "Radio Propagation for Vehiculamunications", Kenneth Bullington, IEEE Transactions on Vehicular Technology, Volume VT-26, Number 4, Novem

1977.”19

The following figure is Bullington’s nomograph for calculating the diffraction loss due to an isolated obstacle.23

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50 of 76

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model ll as the e term

).

cade the ible and

km

hysical

ariabil-n log-nor-ndent

[Bullington, Kenneth. November 1997. Radio Propagation for Vehicular Communications. IEEE Transactions on Vehicular Technology. Volume VT-26. Number 4.]

[Mozaik Web Page. Bullington Propagation Model. [Online serial]. http://rdeserver.comm.mot.com/mozaik/bullngtn.htm.]

[Parsons, David. 1996. The Mobile Radio Propagation Channel. London. John Wiley & Sons Ltd. pp. 44, 162-164, 190-195.]

3.18 dn Pathloss Model

“The dn path loss model is generally used to predict the power transfer between a transmitter and a receiver. Thistakes into account the decrease in energy density suffered by the electromagnetic wave due to spreading, as weenergy loss due to the interaction of the electromagnetic wave with the propagation environment. Path loss is thused to quantify the difference (in dB) between the transmitted power, Pt (in dBm), and received power, Pr (in dBm). (The

gains of the transmitting and receiving antennas may be implicitly included or excluded in these power quantities

The dn model predicts that the mean path loss, PL(d) , measured in dB, at a T-R separation d will be

where PL(d0) is the mean path loss in dB at close-in reference distance d0, and n is the empirical quantity - the path lossexponent. Note that when n=2, the path loss is the same as free space - received signals fall off by 20 dB per deincrease in distance. The reference distance, d0, is chosen to be in the far-field of the antenna, at a distance at which propagation can be considered to be close enough to the transmitter such that multipath and diffraction are negligthe link is approximately that of free-space. Typically, d0 is chosen to be 1 m for indoor environments and 100 m or 1

in outdoor environments. The free space distance must be in the far-field of the antenna, which is related to the psize and frequency of the antenna. Without explicit measured information on the close-in receive distance PL(d0), it can be measured or estimated by the following formula:

where λ = c/f is the wavelength of the transmitted signal (c is the speed of light, 3*108 m/s and f is the frequency of thetransmitted signal in Hz).

The path losses at different geographical locations at the same distance d (for d > d0) from a fixed transmitter exhibit a natural variability due to differences in local surroundings, blockage or terrain over which the signals travel. This vity over a large number of independent measured locations the same distance away from the transmitter results imal shadowing and is usually found to follow a Gaussian distribution (with values in dB) about the distance-depemean path loss, PL(d), with standard deviation σ dB about the mean path loss PL(d).

PL dB( ) PL d0( ) 10nd

d0------

dB( )log+=10

PL d0( ) 204πd0

λ------------

log=10

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h/

The path loss exponent, n, is an empirical constant that is often measured, but can also be derived theoretically in some

environments. It varies depending upon the radio propagation environment. [The table below], taken from Rappaport25, gives typical values for n. Typical values for the log-normal shadowing in outdoor environments range between 8 and 14

dB. Path loss exponents for indoor environments are presented [below], which also presents measured values of σ.”24

[Rappaport. dn Path Loss Model - Range vs. Battery/Power Drain. [Online serial]. http://www.mprg.ee.vt.edu/researcglomo/node3.html#SECTION00021000000000000000.]

Environment Path Loss Exponent, n

Free space 2

Urban area cellular radio 2.7 to 3.5

Shadowed urban cellular radio 3 to 5

In building line-of-sight 1.6 to 1.8

Obstructed in building 4 to 6

obstructed in factories 2 to 3

EnvironmentFreq. (MHz) n s (dB)

Indoor-Retail Store 914 2.2 8.7

Indoor-Grocery Store 914 1.8 5.2

Indoor-Hard Partition Office 1500 3.0 7.0

Indoor-Soft Partition Office 900 2.4 9.6

Indoor-Soft Partition Office 1900 2.6 14.1

Indoor-Factory (LOS) 1300 1.6 -2.0

3.0 -5.8

Indoor-Factory (LOS) 4000 2.1 7.0

Indoor-Suburban Home 900 3.0 7.0

Indoor-Factory (Obstructed) 1300 3.3 6.8

Indoor-Factory (Obstructed) 4000 2.1 9.7

Indoor-Office Same Floor 914 2.76 - 3.27

5.2 - 12.9

Indoor-Office Entire Building 914 3.54 - 4.33

12.8 - 13.3

Indoor-Office Wing 914 2.68 - 4.01

4.4 -- 8.1

Indoor-Average 914 3.14 16.3

Indoor-Through One Floor 914 4.19 5.1

Indoor-Through Two Floors 914 5.04 6.5

Indoor-Through Three Floors 914 5.22 6.7

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ity build-he build-ith a d, this

as

is writ-

3.19 Diffracting Screens Model

“The model described here is based on a geometrical generalization. Walfisch and Bertoni modeled the rows of cings as a series of absorbing diffracting screens of uniform height. For the case of a fixed antenna height above ting roofline, they gave an overall propagation model starting with the forward diffraction, along the screens, and wfinal diffraction down to the street level. The model is shown in the figure below. Since absorbing screens are usemodel is essentially polarization independent.

Maciel, Bertoni and Xia extended the Walfisch-Bertoni model to allow the fixed-site antenna to be below as well above the rooftop levels as shown in the figure below.

The resulting expression for the path propagation Lds, based on the models of Maciel, Bertoni, Xia and Walfisch

ten as :

d

Hb

a

b

s

Hm

Wave Propagation in Homogeneous Urban region

d

Hbb

s

Hm

Suburban Propagation between two sites below roof Level

Lds F– Le1– Le2– 18 17Hb d2

+17Hb

--------------------------log–=

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Propagation Basics

see figure below for the angle θ

Parameters for the Diffracting Screens Model

Parameter Definition

Lds Diffracting screens propagation, average signal, dB

F Free-space loss

Le1 Final Diffraction down rooftop level

Le2 Losses due to diffraction along the rooftops

Hb Fixed-site antenna height, m

Hm Mobile antenna height, m

b Building height, m

s Separation between rows of buildings, m

w Distance from mobile to building on street, m

d Range, Km (not beyond radio horizon)

f Frequency, MHz

Gm Mobile antenna gain in the roof-edge direction

k Wave number

Gb Fixed-site antenna gain in the roof direction (usually taken to be unity)

Angle from the roof edge to the mobile found from (see figure below)

Wavelength

F 32.448 20 f d⋅( )log+=

Le1 10Gm θ( )

π k b Hm–( )2 w2

+⋅ ⋅----------------------------------------------------------- 1

θ--- 1

2 π θ+⋅--------------------–

2⋅log–=

θ

λ

θ b Hm–w

------------------atan=

Le2 10 Gb Q2⋅[ ]log–=

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Propagation Basics

located

main

umber of

f mate-

Q is either Qe or Ql depending on whether the fixed-site antenna is elevated above or lower than the rooftop level. Practi-

cally, Qe is chosen when the fixed-site antenna height Hb is more than above rooftop level b, and Ql is chosen

when Hb is below rooftop level by more than .”10

[Kazimierz Siwiak. Radiowave Propagation and Antennas for Personal Communicationsi. Boston/London: ISBN 0-89006-755-4. Artech House.]

3.20 Building Penetration

There is a great interest in characterizing the radio communication channel between a base station and a mobileinside a building.

The problem of modeling radiowave penetration into buildings differs from vehicular case in several aspects. Theaspects are:

1. The problem is three dimensional because at a fixed distance from the base station the mobile can be at a nheights corresponding to the floor of the building on which is located.

2. The local environment within a building consists of a large number of obstructions (constructed of a variety orials) close to the mobile.

Building penetration loss is dependent on a number of factors:

λ s⋅

0.5 λ s⋅⋅

b

w

Hm

s

Ql

sd 1 000 s–,⋅------------------------------

2 π k b Hb–( )2 s2

+⋅ ⋅ ⋅

------------------------------------------------------------------- 1

b Hb–s

----------------atan

--------------------------------- 1

2 π b Hb–s

----------------atan+⋅--------------------------------------------------–⋅=

Qe 2.35Hb

d 1 000,⋅----------------------atan s

λ---⋅

0.9⋅=

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Propagation Basics

sent, the installa-

n exceed-

l in a local motion

1. Mobile orientation with respect to the base station

2. Number and size of the windows

3. Height of the transceiver within the building

4. Propagation conditions along the transmission path

5. Carrier frequency

When the transmitter is outside, the signal within a building can be characterized as follows:

1. The small scale signal variation is Rayleigh distributed.

2. The large scale signal variation is log-normally distributed with a standard deviation related to the condition of trans-mission and the area of the floor.

3. The building penetration loss decreases at higher frequencies.

4. When no line-of-sight path exists between the transmitter and the building concerned (i.e. scattering is the predomi-nant mechanism of wave propagation) the standard deviation of the local mean values is approximately 4 dB. When partial or complete line-of-sight conditions exist, the standard deviation rises to 6-9 dB.

5. The rate of change of penetration loss with height within the building is about 2 dB per floor.


4.0 Small-Scale Propagation Models - Fading

Propagation models are usually divided into large-scale or small-scale models. The large scale 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 strength over very

short distances (a few wavelengths) or short time durations.25

[Rappaport, Theodore S. 1996. Wireless Communications Principles and Practice. Upper Saddle River, New Jersey: Prentice Hall, Inc. pp. 70, 102-106, 110-111, 116-118, 163-167, 170-176, 188-189.]

4.1 Fade Margin

“The fade margin is the amount of "extra" signal that is present between 2 antennae. The more extra signal is premore reliable the wireless link. Fade margin can be calculated during system design and measured during systemtion. Because fade margin can be measured, it is possible to install wireless links that are extremely reliable, eve

ing the reliability of a wired link. Significance - Knowing the fade margin, you can predict system reliability.”33

[Wireless Infonet. [Online serial]. http://www.ask-wi.com/training.html]

4.2 Doppler Spread and Coherence Time, Coherence Bandwidth, Symbol Period

“Delay spread and coherence bandwidth are parameters which describe the time dispersive nature of the channearea. however, they do not offer information about the time varying nature of the channel caused by either relative

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Propagation Basics

channel, tistical s all spec-nge of

n the cally hannel gth of theteristics

between the mobile and base station, or by movement of objects in the channel. Doppler spread and coherence time are parameters which describe the time varying nature of the channel in a small-scale region.

Doppler spread BD is a measure of the spectral broadening caused by the time rate of change of the mobile radio channel and is defined as the range of frequencies over which the received Doppler spectrum is essentially non-zero. When a pure sinusoidal tone of frequency fc is transmitted, the received signal spectrum, called the Doppler spectrum, will have com-ponents in the range fc - fd to fc + fd, where fd is the Doppler shift. The amount of spectral broadening depends on fd which is a function of the relative velocity of the mobile, and the angle θ between the direction of motion of the mobile and direction of arrival of the scattered waves. If the baseband signal bandwidth is much greater than BD, the effects of

Doppler spread are negligible at the receiver. This is a slow fading channel.

Coherence time Tc is the time domain dual of Doppler spread and is used to characterize the time varying nature of the frequency dispersiveness of the channel in the time domain. The Doppler spread and coherence time are inversely propor-

tional to each other.”25

Coherence Bandwidth:

“While the delay spread is a natural phenomenon caused by reflected and scattered propagation paths in the radiothe coherence bandwidth is a defined relation derived from the rms delay spread. Coherence bandwidth is a stameasure of the range of frequencies over which the channel can be considered “flat” (i.e., a channel which passetral components with approximately equal gain and linear phase). IN other words, coherence bandwidth is the ra

frequencies over which two frequency components have a strong potential for amplitude correlation.”25

Symbol Period:

The symbol period is equal to the reciprocal of the bandwidth.25

[Rappaport, Theodore S. 1996. Wireless Communications Principles and Practice. Upper Saddle River, New Jersey: Prentice Hall, Inc. pp. 102-106, 110-111, 116-118, 163-167, 170-176, 188-189.]

4.3 Flat Fading (i.e. no frequency selective behavior)

“Small-Scale Fading (Based on Multipath Time Delay Spread)”25:

1. Bandwidth of Signal < Bandwidth of Channel

2. Delay Spread < Symbol Period

“If the mobile radio channel has a constant gain and linear phase response over a bandwidth which is greater thabandwidth of the transmitted signal, then the received signal will undergo flat fading. This type of fading is historithe most common type of fading described in the technical literature. In flat fading, the multipath structure of the cis such that the spectral characteristics of the transmitted signal are preserved at the receiver. However the stren received signal changes with time, due to fluctuations in the gain of the channel caused by multipath. The characof a flat fading channel are illustrated [below].

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Propagation Basics

It can be seen from [the above illustration] that if the channel gain changes over time, a change of amplitude occurs in the received signal. Over time, the received signal r(t) varies in gain, but the spectrum of the transmission is preserved. In a flat fading channel, the reciprocal bandwidth of the transmitted signal is much larger than the multipath time delay spread of the channel, and hb(t,τ) can be approximated as having no excess delay (i.e., a single delta function with τ = 0). Flat fading channels are also known as amplitude varying channels and are sometimes referred to as narrowband channels, since the bandwidth of the applied signal is narrow as compared to the channel flat fading bandwidth. Typically flat fad-ing channels cause deep fades, and thus may require 20 or 30 dB more transmitter power to achieve low bit error rates during times of deep fades as compared to systems operating over non-fading channels. The distribution of the instanta-neous gain of flat fading channels is important for designing radio links, and the most common amplitude distribution is the Rayleigh distribution. The Rayleigh flat fading channel model assumes that the channel induces an amplitude which varies in time according to the Rayleigh distribution.

To summarize, a signal undergoes flat fading if

and

where TS is the reciprocal bandwidth (e.g. symbol period) and BS is the bandwidth, respectively, of the transmitted modu-

lation, and στ and BC are the rms delay spread and coherence bandwidth, respectively, of the channel.”25


∫ ∫ ∫ ∫ ∫ ∫

s(t) r(t)h(t,τ)

0 TSτ TS+τ τ<<TS

S(f) H(f) R(f)

f

s(t) h(t,τ) r(t)

0 0t t t

fcfcfcff

Flat fading channel characteristics

BS BC«

TS στ»

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Propagation Basics

eived at a as to the that in onsider en the dif-ponents multi-ndwidth uency r fre-ecorrela-ay spreads mall. Sig-ill the signal ing and ncy selec-which

method ity of ssible to irection ed with aeen at A, B

ent time

4.4 Frequency-Selective Fading

“Small-Scale Fading (Based on Multipath Time Delay Spread)”25:

1. Bandwidth of Signal > Bandwidth of Channel

2. Delay Spread > Symbol Period

“The earlier discussion concentrated in general on describing the envelope and phase variations of the signal recmoving vehicle when an unmodulated carrier is radiated by the base station transmitter. The question now arisesadequacy of this channel description when real signals, which occupy a finite bandwidth, are radiated. It is clearpractice we need to consider the effects of multipath propagation on these signals and to illustrate the point we cthe case of two frequency components within the message bandwidth. If these frequencies are close together thferent propagation paths within the multipath medium have approximately the same electrical length for both comand their amplitude and phase variations will be very similar. In other words, although there will be fading due topath, the two frequency components will behave in a very similar way. More generally, provided the message bais sufficiently small, all frequency components within it behave similarly and flat fading is said to exist. As the freqseparation increases, however, the behavior at one frequency tends to become uncorrelated with that at the othequency because the phase shifts along the various paths are different at the two frequencies. The extent of the dtion depends on the spread of time delays since the phase shifts arise from the excess path lengths. For large delthe phases of the incoming components can vary over several radians even if the frequency separation is quite snals which occupy a bandwidth greater than that over which spectral components are affected in a similar way wbecome distorted since the amplitudes and phases of the various spectral components in the received version of are not the same as they were in the transmitted version. The phenomenon is known as frequency-selective fadappears as a variation in received signal strength as a function of frequency. In analogue FM systems the frequetivity limits the maximum usable frequency deviation for a given amount of signal distortion. The bandwidth over the spectral components are affected in a similar way is known as the coherence, or correlation bandwidth.

The fact that the lengths of the individual propagation paths vary with time due to motion of the vehicle provides a of gaining further insight into the propagation mechanism since the changing time of arrival suggests the possibilassociating each delayed version of the transmitted signal with a physical propagation path. However, it is not podistinguish between different paths merely by considering the difference between the time of arrival, the spatial dof arrival also has to be taken into account. If we consider only single-scattered paths then all scatterers associat certain path length can be located on an ellipse with the transmitter and receiver at its foci. Each time delay betwtransmitter and receiver defines a confocal ellipse as shown in [the figure below]. If we consider scatterers locatedand C, then we can distinguish between paths TAR and TBR, which have the same angle of arrival, by their differdelays and between TAR and TCR which have the same time delay, but there are different angles of arrival.

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Propagation Basics

The angles of arrival can be determined by means of Doppler shift. As we have already seen, whenever the receiver or transmitter is in motion the received RF signal experiences a Doppler shift, the frequency shift being related to the cosine of the spatial angle between the direction of arrival of the wave and the direction of motion of the vehicle. If, therefore, we transmitted a short RF pulse and measured both its time of arrival and Doppler shift at the receiver, we could identify the length of the propagation path and the angle of arrival. Of course, there is left/right ambiguity inherent in the Doppler shift measurement but this could be resolved, if necessary, by the use of directional antennas.

. .RxTx

B

A

C

Line of sight

τ+∆τ

Path of Geometry for Single Scattering

Direction of motion

τ

EchoesTransmittedPulse

t = 0

Overallresponse

t

t

Illustrating how the receiver responses to a number of echoes of a transmitted pulse canoverlap, causing intersymbol interference

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Propagation Basics

annel, a

the sym-oppler

creases fast fad-

An important and instructive feature of [the above figure] is that for a particular receiver location, a suitably scaled dia-gram with several confocal ellipses can be produced in the form of a map overlay. Co-ordinated use of this overly, together with experimental results for the location in question allows the identification of significant single scatterers or scattering areas, and gives an indication of the extent of the contribution from multiple scattering.

It is clear from the above that these time-delayed echoes can overlap, as shown in [the figure above], causing error in dig-ital systems due to intersymbol interference. In this case, increasing the signal-to-noise ratio will not cause a reduction in error rate and so the delay spread sets the lower bound on error performance for a specified data rate. This limit is often termed the irreducible error rate, although in practice the performance can be further improved by the use of channel

equalization techniques.”23



4.5 Fast Fading (observed at approximately 1/2 wavelength i.e. Rayleigh)

“Small-Scale Fading (Based on Doppler Spread):

1. High Doppler Spread

2. Coherence Time < Symbol Period

3. Channel Variations Faster than Baseband Signal Variations

Depending on how rapidly the transmitted baseband signal changes as compared to the rate of change of the chchannel may be classified either as a fast fading or slow fading channel. In a fast fading channel, the channel impulse response changes rapidly within the symbol duration. That is, the coherence time of the channel is smaller than bol period of the transmitted signal. This causes frequency dispersion (also called time selective fading) due to Dspreading, which leads to signal distortion. Viewed in the frequency domain, signal distortion due to fast fading inwith increasing Doppler spread relative to the bandwidth of the transmitted signal. Therefore, a signal undergoesing if

TS > TC

and

BS < BD

Where:

TS = Reciprocal Bandwidth (e.g. Symbol Period)

TC = Coherence Time (Time Domain Dual of Doppler Spread)

BS = Bandwidth

BD= Doppler Spread

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Propagation Basics

and sig-. in the eband

deter-

-scale fad- in the

It should be noted that when a channel is specified as a fast or slow fading channel, it does not specify whether the channel is flat fading or frequency selective in nature. Fast fading only deals with the rate of change of the channel due to motion. In the case of the flat fading channel, we can approximate the impulse response to be simply a delta function (no time delay). Hence, a flat fading, fast fading channel is a channel in which the amplitude of the delta function varies faster than the rate of change of the transmitted baseband signal. In the case of a frequency selective, fast fading channel, the ampli-tudes, phases and time delays of any one of the multipath components vary faster than the rate of change of the transmit-

ted signal. In practice, fast fading only occurs for very low data rates.”25


4.6 Slow Fading (observed at distances greater than 1/2 wavelength i.e. log normal)

“Small-Scale Fading (Based on Doppler Spread):

1. Low Doppler Spread

2. Coherence Time > Symbol Period

3. Channel Variations Slower than Baseband Signal Variations

“In a slow fading channel, the channel impulse response changes at a rate much slower than the transmitted basebnal s(t). In this case, the channel may be assumed to be static over one or several reciprocal bandwidth intervalsfrequency domain, this implies that the Doppler spread of the channel is much less than the bandwidth of the bassignal. Therefore, a signal undergoes slow fading if

TS << TC

and

BS >> BD

Where:

TS = Reciprocal Bandwidth (e.g. Symbol Period)

TC = Coherence Time (Time Domain Dual of Doppler Spread)

BS = Bandwidth

BD= Doppler Spread

It should be clear that the velocity of the mobile (or velocity of objects in the channel) and the baseband signalingmines whether a signal undergoes fast fading or slow fading.

Over the years, some authors have confused the terms fast and slow fading with the terms large-scale and smalling. It should be emphasized that fast and slow fading deal with the relationship between the time rate of change

channel and the transmitted signal, and not with the propagation path loss models.”25

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Propagation Basics

s the tor in eiver is

re of n that

ow] nsity

ed a


4.7 Rayleigh Fading/Multipath

For an interesting and fun look at Raleigh Fading check out the Wireless Communications Web Page by Jean-Paul M.G.

Linnartz5 at:

http://ns.baltzer.nl/wirelesscd/rayleigh.htm

“Multipath, or Rayleigh, fading is a salient feature of mobile communications and, to some significant extent, limitcoverage of mobile systems when the mobile is moving in a multipath environment. It is not such a dominant fachand held mobile usage but, in low-field-strength areas, it can be detected by variations in noise levels as the rec

moved.”1

“In mobile radio channels, the Rayleigh distribution is commonly used to describe the statistical time varying natuthe received envelope of a flat fading signal, or the envelope of an individual multipath component. It is well knowthe envelope of the sum of two quadrature Gaussian noise signals obeys a Rayleigh distribution. [The figure belshows a Rayleigh distributed signal envelope as a function of time. The Rayleigh distribution has a probability defunction (pdf) given by

where σ is the rms value of the received voltage signal before envelope detection, and σ2 is the time-average power the received signal before envelope detection. The probability that the envelope of the received signal does not excespecified value R is given by the corresponding cumulative distribution function (CDF).

p r( ) r σ2⁄ r2

2σ2----------–

exp

0 0 r ∞≤ ≤( )

r 0<( )

=

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Propagation Basics

The mean value rmean of the Rayleigh distribution is given by

and the variance of the Rayleigh distribution is given by , which represents the ac power in the signal envelope

Typical Simulated Rayleigh Fading at the CarrierReceiver Speed = 120 km/hr

Elapsed Time (ms)

Sign

al L

evel

(dB

abo

ut rm

s)

10

5

0

-5

-10

-15

-20

-25

-30

-35

-40 0 50 100 150 200 250

λ/2

P R( ) Pr r R≤( ) p r( ) rd

0

R

∫ 1 R2

2σ2----------–

exp–= = =

rmean E r[ ] rp r( ) rd

0

∞

∫ σ π2--- 1.2533σ= = = =

σr2

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Propagation Basics

The rms value of the envelope is the square root of the mean square, or .

The median value of r is found by solving

and is

Thus the mean and the median differ by only 0.55 dB in a Rayleigh fading signal. Note that the median is often used in practice, since fading data are usually measured in the field and a particular distribution cannot be assumed. By using median values instead of mean values it is easy to compare different fading distributions which may have widely varying means. [The figure below] illustrates the Rayleigh pdf. The corresponding Rayleigh cumulative distribution function

(CDF) is shown in [the figure below].”25

σr2

E r2[ ] E

2r[ ]– r

2p r( ) rd

0

∞

∫ σ2π2

----------–= =

σr2 σ2

2 π2---–

0.4292σ2= =

2σ

12--- p r( ) rd

0

rmedian

∫=

rmedian 1.177σ=

Received signal envelope voltage r (volts)

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Propagation Basics

delay. ultipath

l (which

“Two-Ray Rayleigh Fading Model:

Clark’s model and the statistics for Rayleigh fading are for flat fading conditions and do not consider multipath timeIn modern mobile communication systems with high data rates, it has become necessary to model the effects of mdelay spread as well as fading. A commonly used multipath model is an independent Rayleigh fading 2-ray modeis a specific implementation of the generic fading simulator shown in [the figure below].

CDF (Cumulative Distribution Function)

Signal Level (dB about median)

% ProbabiltySignal Level< Abscissa

OBS light clutter, Site CLOS heavy clutter, Site ELOS light clutter, Site D

Log-normal σ=7.5 dBRayleighRician K=6 dB

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Propagation Basics

[The following illustration] shows a block diagram of the 2-ray independent Rayleigh fading channel model. The impulse response of the model is represented as

∑

...

Signalunder test

s(t)

aN

a1

a0RayleighFadingSimulator

RayleighFadingSimulator

RayleighFadingSimulator

r(t)

A signal may be applied to a Rayleigh fading simulator to determine performance in a wide range ofchannel conditions. Both flat and frequency selective fading conditions may be simulated, dependingon gain and time delay settings.

τ1 τΝ

hb t( ) α1 jΦ1( )δ t( )exp α2 1( ) jΦ2 1( )( )δ t τ–( )exp+=

∑

τ

α2exp(jφ2)

α1exp(jφ1)

input output

Two-ray Rayleigh Fading Model.

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Propagation Basics

and

ul M.G.

all-scale les are g a dc

h many posite es to a

Where α1 and α2 are independent and Rayleigh distributed, ρ1 and ρ2 are independent and uniformly distributed over [0,2π], and τ is the time delay between the two rays. By setting α2 equal to zero, the special case of a flat Rayleigh fading channel is obtained as

By varying τ, it is possible to create a wide range of frequency selective fading effects. The proper time correlation prop-erties of the Rayleigh random variables α1 and α2 are guaranteed by generating two independent waveforms, each pro-duced from the inverse Fourier transform of the spectrum described [in the section entitled “Simulation of Clarke

Gans Fading Model”].”25



4.8 Ricean Fading Distribution

For an interesting and fun look at Ricean Fading check out the Wireless Communications Web Page by Jean-Pa

Linnartz5 at:

http://ns.baltzer.nl/wirelesscd/rice.htm

“When there is a dominant stationary signal component present, such as a line-of-sight propagation path, the smfading envelope distribution is Ricean. In such a situation, random multipath components arriving at different angsuperimposed on a stationary dominant signal. At the output of an envelope detector, this has the effect of addincomponent to the random multipath.

Just as for the case of detection of a sine wave in thermal noise [Ric48], the effect of a dominant signal arriving witweaker multipath signals gives rise to the Ricean distribution. As the dominant signal becomes weaker, the comsignal resembles a noise signal which has an envelope that is Rayleigh. Thus, the Ricean distribution degeneratRayleigh distribution when the dominant component fades away.

The Ricean distribution is given by

hb t( ) α1 jΦ1( )δ t( )exp=

p r( ) r

σ2------e

r2

A2

+( )–

2σ2---------------------------

0

I0Ar

σ2------

=for (A≥ 0, r ≥ 0)

for (r < 0)

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Propagation Basics

”

sult is a nd dif-ts a loss

e effect

ed.

The parameter A denotes the peak amplitude of the dominant signal and I0(.) is the modified Bessel function of the first

kind and zero-order. The Ricean distribution is often described in terms of a parameter K which is defined as the ratio

between the deterministic signal power and the variance of the multipath. It is give by K = A2/(2σ2) or, in terms of dB

The parameter K is known as the Ricean factor and completely specifies the Ricean distribution. As A → 0, K → −∞ dB,

and as the dominant path decreases in amplitude, the Ricean distribution degenerates to a Rayleigh distribution.25


5.0 Interference

5.1 Multiple-Carrier Intermodulation (IM) Products

“When several signals having different carrier frequencies are simultaneously present in a nonlinear device, the remultiplicative interaction between the carrier frequencies which can produce signals at all combinations of sum aference frequencies. The energy apportioned to these spurious signals (intermodulation or IM products) represenin signal energy. In addition, if these IM products appear within the bandwidth region of these or other signals, th

is that of added noise for those signals.”26

Frequencies of Intermodulation Products:

“Frequencies of IM products can be defined in the following manner:

Order - corresponding to the classification of IM products by the number of constituent frequencies (e.g. 2nd, 3rd, 4th,...

Nth). Order is equal to the sum of the harmonics of the constituent frequencies.

Fundamental Frequencies - referring to constituent fundamental frequencies from which the IM products are deriv

Harmonics - corresponding to the whole number multiples of a fundamental frequency.

For example, a 3rd order IM signal centered at frequency C could result from the combination of the 2nd harmonic of a sig-nal whose fundamental center frequency is A and a second signal whose fundamental center frequency is B:

C = 2A + (1)B (where order = 2 + 1 = 3)

Some examples of 2nd through 5th order intermodulation products are provided in [the following table]:

K dB( ) 10A

2

2σ2----------dBlog=

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Propagation Basics

infor-. In ider

l com-s.

nd owave ty in

rized ach ts (dis-t to be

t is ction of ally may be

Note that third and fifth order intermodulation are most prevalent. The signal strength level of harmonic decreases rapidly with its order (e.g. 3A would be weaker than 2A). Higher order IM products are less prevelent due to the low probability of many different transmitters being keyed simultaneously (e.g. A+B+C+2D+2E) for the IM to occur. Even order IM

products may fall out of the local systems’ operating bands.”4

[Clapp, Scott. Inter-Band Interference Control. Motorola. pp. 4.]

[Sklar, Bernard. 1988. Digital Communications Fundamentals and Applications. Englewood Cliffs, New Jersey. Pren-tice-Hall, Inc. pp. 192.]

5.2 Intermodulation Distortion

“Linear circuits are used in communications where it is important that an exact or nearly exact reproduction of anmation bearing signal must be transmitted to a destination. "Good Linearity" is synonymous with "Low Distortion"this paper, the type of linearity being discussed is primarily amplitude linearity, although it is equally valid to consphase linearity.

Examples of signals that require linearity are: human voice, multilevel data signals, a microwave baseband signaposed of FDM channels, or RF signals which are modulated (at least partly amplitude modulated) by such signal

M-QAM microwave transmitters are simultaneously phase and amplitude modulated by multilevel data signals, adepending on the number "M" require some degree of linearity from the circuits which amplify or process the micrsignals. For example, 64-QAM requires much more perfect linearity than 4-QAM, in fact, 64-QAM requires linearithe IF and RF circuits approaching that previously required in the baseband circuits in analog microwave radios.

The term Intermodulation Distortion or IMD indicates that the distortion phenomenon being referred to is characteby multiple signals, or a composite signal with multiple frequency components, where the components mix with eother (intermodulate) in an imperfectly linear electrical circuit and as a result produce undesired signal componentortion). By way of comparison, the more familiar Harmonic Distortion only requires one signal or signal componenpresent, and the undesired products generated are at multiples (harmonics) of the original signal frequency.

IMD is similar to Harmonic Distortion in that both are caused by nonlinear imperfections in an electrical circuit thasupposed to be linear. However, a simple mathematical analysis will show that odd order terms of the transfer funa non-linear circuit will cause the in-band distortion products referred to as IMD, while the even order terms normcause Harmonic Distortion products which, in many cases, fall out of the frequency band or off channel, and thus

Order Intermodulation Products

2nd A+B, A-B

3rd 2A+B, 2A-B, 2B+A, 2B-A, A+B+C

4th 2A+2B, 2A-2B, 3A+B, 3A-B

5th A+4B, A-4B, 4A+B, 4A-B, 2A+3B, 2A-3B...

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Propagation Basics

m/

pread-n e will

re of mea-e recep-e or

ry:

ch as min-

if it is s. Some wer and he

e action ted e best

ns for

removed by filtering. Thus, IMD is usually the more serious of the two types of distortion, since it often falls in or close to the frequency band occupied by the desired signal and cannot be removed easily by filtering.

The term Intermodulation Ratio or IMR indicates the ratio of the desired signal to the undesired (IMD) signal power.

The term Intercept Point is used to describe a fictitious condition where the IMD products of interest (usually the 3rd order products, because they are normally the largest) would be equal to the desired signals, and the IMR would be 0 dB. This condition is not usually achievable, because the circuit becomes highly non-linear or saturates at signal levels lower

than would be necessary.”28

For mathematical descriptions please refer to Robert Stedman’s Intermodulation Distortion Basics paper.28

[Stedman, Robert. Intermodulation Distortion Basics [Online serial]. November 9, 1990. http://www.acpg.cig.mot.cow3/APD/Supercell_Dev./Tech_Notes/Intermod/IMD.html.]

5.3 Inter-Symbol Interference (ISI)

“In a digital transmission system, distortion of the received signal, which distortion is manifested in the temporal sing and consequent overlap of individual pulses to the degree that the receiver cannot reliably distinguish betweechanges of state, i.e. , between individual signal elements. Note 1: At a certain threshold, intersymbol interferenccompromise the integrity of the received data. Note 2: Intersymbol interference attributable to the statistical natuquantum mechanisms sets the fundamental limit to receiver sensitivity. Note 3: Intersymbol interference may besured by eye patterns. 2. Extraneous energy from the signal in one or more keying intervals that interferes with thtion of the signal in another keying interval. 3. The disturbance caused by extraneous energy from the signal in on

more keying intervals that interferes with the reception of the signal in another keying interval.”6

[Glossary of Telecommunication Terms. [Electronic database]. August 7, 1996. U.S. Federal Government. Directohttp://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm.]

5.4 Inter-System Interference (ISI)

“When a CDMA system is designed as an overlay over an existing system, reusing the same frequency band, suCDMA over AMPS in North America, or 900 MHz CDMA over TACS as in China, it is necessary to anticipate andimize any intersystem interference that might result from the deployment.

This is not a problem unique to CDMA, it is a radio-systems issue. The same issues will occur in a GSM system overlaid on a TACS system in the same frequency band. All technologies have the same set of contributing factorkey variables for the interfering transmitter are: ERP (directed towards the receive antenna), Transmit nominal poSideband splatter. A few key variables for the receiver which might be interfered with are: IM (intercept point) of treceiver, Filter protection available and Gain of the receive antenna system.

After the potential for interference has been assessed, corrective action, if required, can then be taken. Correctivcan be in the form of improving the filtering at the receive site, or it can be related to any of the other variables noabove; improve Tx splatter, adjust ERP, frequency planning, etc. In all cases, the potential for interference, and thcorrective action, are site specific. There is no generic solution and site engineering is required. Recommendatiocorrective action is addressed where deemed appropriate.

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Propagation Basics

occur-e inter-

n becomes ource, s first

and it g an opti- the fre-s have udy of ich it can Secondly

One additional note, rogue transmitters are rare and illegal occurrences. If they are high enough in power, they may cause problems to one or more sectors of a CDMA system. In some cases, surrounding CDMA cell will increase in size to miti-

gate the problem.”13


5.5 Adjacent Channel Interference - Land-Mobile

“The origin of adjacent channel interference is shown in [the figure below]. The figure portrays two transmissionsring on adjacent channels. Inevitably some signal components spread beyond the channel boundaries and can bcepted by receivers tuned to the adjacent channel. When the signal strength of the adjacent channel transmissioso large that the power intercepted by an on-channel receiver approaches that of the desired on-channel signal sinterference occurs. The ratio of the signal strengths of the two transmissions at the point at which interference i

noted is called the adjacent channel interference protection ratio (ACIPR).”8

[Jakes, William C. 1974. Microwave Mobile Communications. An IEEE Press Classic Reissue. Picataway. American Telephone and Telegraph Company. pp. 80-88, 138-139.]

5.6 Man-Made Noise and Interference

“The performance of any communication system is dependent on the characteristics of the transmission mediumcan often be improved by use of techniques which successfully exploit these characteristics, for example by usinmum modulation method. As far as the communications engineer is concerned the important characteristics arequency and time responses of the channel and the magnitude and nature of the noise. The former characteristicbeen discussed in earlier chapters; we now deal with the problem of noise. There are two basic reasons for a stnoise. Firstly there is a need to gain an understanding of the nature of the noise in order to devise methods by whbe characterized. Knowledge of the sources of noise may also lead to methods by which it can be suppressed.

Desired signalInterfering signal

Idealized receiver selectivity

ACIPR

Adjacent channel Desired channelFrequency

Rel

ativ

e si

gnal

str

engt

h

Origin of Adjacent Channel Interference

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Propagation Basics

Gauss-htfor-

. The ms anhere are hes, arch nificant

ime, so iability. radio

the ussian. and phase e general rval

er the fre-h and in ampli- impulse

unless degra-

the quasi-ctive error rate infor-is con- methods

there is a vital need to be able to predict the performance of communication systems that have to operate in noisy environ-ments.

A mobile radio system is beset with noise from various sources and each source may have different characteristics. Firstly there is receiver noise which is Gaussian in nature and arises from the receiving system itself. Receiver noise is usually expressed in terms of nkT0B, n being the factor by which the total receiver noise exceeds ambient noise. Atmospheric noise may also be present, but it decreases rapidly with frequency and is generally negligible in the VHF range. Galactic noise is also insignificant in the VHF band as it is well below the background noise. By far the most important source of noise as far as mobile communication is concerned is that radiated by electrical equipment of various kinds. This noise, commonly termed ‘man-made’ noise is impulsive in nature, and therefore has characteristics quite different from ian noise. It can be detected at frequencies up to 7 GHz. ...The characterization of Gaussian noise is fairly straigward, but impulsive noise is a quite different matter.

There are several potential sources of impulsive noise which could play a role in mobile communication systemsradio is often installed in a vehicle which is itself a source of noise due to its own ignition and other electrical systed the vehicle commonly operates in urban, suburban and industrial areas where it is close to other noisy vehicles. Tvarious extraneous sources of noise such as power lines and neon signs, industrial noise from heavy current switcwelders and the like, and noise from various items of domestic electrical equipment. These may or may not be sigcontributors in any specific situation. In practice the level of man-made noise varies markedly with location and tfrom a limited series of observations it is only possible to derive typical values and obtain some estimate of the var In urban areas it is generally conceded that vehicle ignition noise is a major source of interference to VHF mobilesystems.

Throughout the literature, the terms Gaussian and impulsive are used to denote two distinct types of noise. Onlypower spectral density of Gaussian noise is affected by linear filtering; the probability density function remains GaThe in-phase and quadrature components of narrowband Gaussian noise are independent, as are the envelope distributions. For any other type of noise, both the power spectral density and the probability density function arechanged by filtering; the in-phase and quadrature components, although uncorrelated, are not independent. In thcase, the envelope and phase of random noise are independent, the phase being uniformly distributed in the inte(0,2π).

In general terms we may consider an impulse as a transient that contains an instantaneous uniform spectrum ovquency band for which it is defined, a uniform spectrum requiring that all frequencies are present, of equal strengtphase over the frequency band. Impulsive noise is the combination of successive impulses which have random tudes and random time-spacings; these factors may sometimes be such that adequate separation of successiveresponses by a narrowband receiver is not possible.

Thermal noise can produce an annoying “hiss” on a voice channel, but does not significantly degrade intelligibilityits RMS value is relatively high. Impulsive noise causes clicks, which, although disturbing, may be tolerable. Thedation of the channel is not easily defined and is usually based on some kind of subjective assessment, althoughpeak measurement, which will be mentioned later, has been shown to have some correspondence with the subjeannoyance on a.m. radio and television. In some ways digital transmissions are easier to deal with since the bit (BER) provides a good quantitative indication of how well the communication system reproduces the transmittedmation. The BER produced by thermal noise is readily available in several textbooks. As far as impulsive noise cerned we will discuss the methods that exist for expressing the properties of the noise, and to what extent these

provide information which is directly useful in predicting performance degradation in communication systems.”23

[Parsons, David. 1996. The Mobile Radio Propagation Channel. London. John Wiley & Sons Ltd. pp. 44, 162-164, 190-195, 255-257.]

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ith the lishes a y the m loss,

6.0 Standards and Units

6.1 VSWR (Voltage Standing Wave Ratio):

“Voltage Standing Wave Ratio (VSWR) is another parameter used to describe an antenna performance. It deals wimpedance match of the antenna feed point to the feed or transmission line. The antenna input impedance estabload on the transmission line as well as on the radio link transmitter and receiver. To have RF energy produced btransmitter radiated with minimum loss or the energy picked up by the antenna passed to the receiver with minimu

the input or base impedance of the antenna must be matched to the characteristics of the transmission line.”13

VSWR = Vmax/Vmin


6.2 Watts to dBm Conversion32:

[Watts to dBm Conversion Chart [Online serial]. http://infonow.ecid.cig.mot.com/EMD/TMG/Watt_dBm/Watts_dBm.html.]

6.3 dBi to dBd Conversion

6.4 Speed of Light : Wavelength

10 watts 1000×( )logPower in dBm =

10

dBm10

------------

1000------------------------Power in Watts =

dBd dBi 2.14–=

dBi dBd 2.14+=

c 3 108×=

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Propagation Basics

7.0 References

1. Boucher, Neil J. 1995. The Cellular Radio Handbook. A Reference for Cellular System Operation. Third Edition. Mill Valley. Quantum Publishing, Inc. pp. 73-74, 185-186.

2. Celwave. 1997. Product Selection Guide 197. Radio Frequency Systems. Inc. pp. 320.

3. Clapp, Scott. March 8, 1995. China Frequency Planning and RF Propagation Analysis Overview, REV B. Motor-ola, Inc. pp. 18.

4. Clapp, Scott. December 15, 1997. Inter-Band Interference Control. Motorola. pp. 4.

5. COST 231 TD (91) 73. September 1991. COST 231 - UHF Propagation, Urban Transmission Loss Models for Mobile Radio in the 900- and 1,800- MHz Bands. The Hagne.

6. Glossary of Telecommunication Terms. [Electronic database]. August 7, 1996. U.S. Federal Government. Direc-tory: http://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm.

7. Hata, M. 1980. Empirical Formula for Propagation Loss in Land Mobile Radio Services. IEEE Trans. on Vehicular and Technology, VT-29. pp. 317-325.

8. Jakes, William C. 1974. Microwave Mobile Communications. An IEEE Press Classic Reissue. Picataway. Ameri-can Telephone and Telegraph Company. pp. 80-88, 138-139.

9. Jordon, Edward C. 1989. Reference Data for Engineers: Radio, Electronics, Computer, and Communications. Seventh Edition. Indianapolis. Howard W. Sams & Company. pp. 32-10.

10. Kazimierz Siwiak. Radiowave Propagation and Antennas for Personal Communicationsi. Boston/London: ISBN 0-89006-755-4. Artech House.

11. Leonard, Terry. Downtilt Effects Presentation. RF Planning Group. Motorola. pp 5-9.

12. Linnertz, Jean_Paul M.G. Wireless Communication. Wireless Channels. Multipath Fading [Online serial]. 1995. http://ns.baltzer.nl/wirelesscd/rayleigh.htm.

13. Motorola. RF Planning Guide V2.0 [Online serial]. May 29, 1998. http://www.pamd.cig.mot.com/nds/cts/rftech/public_html/Documents/RFPG2/rfguideV2.html.

14. Motorola. 1997. CDMA RF System Design Procedure. Version 2.0. [Online serial]. http://www.pamd.cig.mot.com/nds/cts/rftech/public_html/Documents/DsgnProc2/bookTOC.html. pp. 3-1, 3-9, 3-12.

15. Motorola NetPlan Group. May 12, 1998. NetPlan Application Note Custom Pathloss Model. NetPlan V3.2. Revi-sion 0.1.

16. Motorola NetPlan Group. Statistical [Online serial]. http://www.sesd.cig.mot.com/statistical/.

17. Motorola NetPlan Group. XLOS Propagation Model [Online serial]. http://www.sesd.cig.mot.com/xlos.html.

18. Motorola NetPlan Gourp. Xlos Propagation Model. Slide Presentation.

19. Mozaik Web Page. Bullington Propagation Model. [Online serial]. http://rdeserver.comm.mot.com/mozaik/bullngtn.htm.

λ c f⁄=

λ = wavelength (m)c = speed of light (m/s)f = frequency (Hz)

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Propagation Basics

20. Mozaik Web Page. Okumura Propagation Model. [Online serial]. http://rdeserver.comm.mot.com/mozaik/oku-mura.htm.

21. Okumura, Y., Ohmori, E., Kawano, T., Fukada, K. 1968. Field strength and ITs Variability in VHF and UHF Land-Mobile Radio Service, Rev. Elec. Commun. Lab., 16. pp. 825-873.

22. Orr, William, and Cowan, Stuart. 1993. The Beam Antenna Handbook. Lakewood: Radio Amateur Callbook (an imprint of Watson-Guptill Publications, a division of BPI Communications, Inc.). pp. 6-7.

23. Parsons, David. 1996. The Mobile Radio Propagation Channel. London. John Wiley & Sons Ltd. pp. 44, 162-164, 190-195, 255-257.

24. Rappaport. dn Path Loss Model - Range vs. Battery/Power Drain. [Online serial]. http://www.mprg.ee.vt.edu/research/glomo/node3.html#SECTION00021000000000000000.

25. Rappaport, Theodore S. 1996. Wireless Communications Principles and Practice. Upper Saddle River, New Jersey: Prentice Hall, Inc. pp. 70, 93-94, 102-106, 110-111, 116-118, 163-167, 170-176, 188-189.

26. Sklar, Bernard. 1988. Digital Communications Fundamentals and Applications. Englewood Cliffs, New Jersey. Prentice-Hall, Inc. pp. 192.

27. Stedman, Robert. Handy Formulas [Online serial]. June 2, 1995. http://www.acpg.cig.mot.com/w3/APD/SuperCell_Dev./Tech_Notes/Ants_Fs/Ants_Fields.html.

28. Stedman, Robert. Intermodulation Distortion Basics [Online serial]. November 9, 1990. http://www.acpg.cig.mot.com/w3/APD/Supercell_Dev./Tech_Notes/Intermod/IMD.html.

29. Solectek White Paper. Line of Site. [Online serial]. http://corfu.forthnet.gr/solectek/los.htm.

30. USDOT Federal Aviation Administration. August 1990. FAA Academy Training Manual. pp. 1-1 thru 1-7. Anten-nas and Radiation Patterns. 40152, Common Principles, Antennas, and Transmission Lines Course. http://www.academy.jccbi.gov/catalog/html/40152.htm.

31. U.S. Geological Survey [Electronic database]. 1998. Directory: http://www.usgs.gov/.

32. Watts to dBm Conversion Chart [Online serial]. http://infonow.ecid.cig.mot.com/EMD/TMG/Watt_dBm/Watts_dBm.html.

33. Wireless Infonet. [Online serial]. http://www.ask-wi.com/training.html

34. Yang, Samuel C. 1998. CDMA RF System Engineering. Norwood, Massachusettes. Artech House, Inc. pp. 15.

8.0 Other Useful References

35. Anderson, L.J. and Trolese, L.G. July 1958. Simplified Method for Computing Knife Edge Diffraction in the Shadow Region. IRE Trans. Ant. Prop. Vol. 6. pp. 281.

36. Antennas. [Electronic database]. August 7, 1996. U.S. Federal Government. Directory: http://www.its.bldrdoc.gov/fs-1037/dir-001/_0018.htm.

37. Balanis, Constantine A. 1989. Advanced Engineering Electromagnetics. New York. John Wiley and Sons.

38. Bullington, Kenneth. November 1997. Radio Propagation for Vehicular Communications. IEEE Transactions on Vehicular Technology. Volume VT-26. Number 4.

39. Motorola. RF Technology Team Antenna Vendor List. [Online serial]. http://www.pamd.cig.mot.com/nds/cts/rftech/public_html/AntennaVendor.html

40. On-Line CDMA Glossary [Electronic database]. November 9, 1995. Motorola Technical Education and Documen-tation. Directory: http://www.cig.mot.com/Org.new/TED/glossary.html. Version 0.3.

41. On-Line Cellular Glossary [Electronic database]. June 24, 1996. Motorola Technical Education and Documenta-tion. Directory: http://www.cig.mot.com/Org.new/TED/cellglos.html. Version 1.

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http://www.mprg.ee.vt.edu/research/glomo/node3.html#SECTION00021000000000000000

http://corfu.forthnet.gr/solectek/los.htm

http://www.ask-wi.com/training.html

http://www.acpg.cig.mot.com/w3/APD/SuperCell_Dev./Tech_Notes/Ants_Fs/Ants_Fields.html

http://www.cig.mot.com/Org.new/TED/glossary.html

http://www.cig.mot.com/Org.new/TED/cellglos.html

http://www.pamd.cig.mot.com/nds/cts/rftech/public_html/AntennaVendor.html

http://www.acpg.cig.mot.com/w3/APD/Supercell_Dev./Tech_Notes/Intermod/IMD.html

http://infonow.ecid.cig.mot.com/EMD/TMG/Watt_dBm/Watts_dBm.html

http://www.academy.jccbi.gov/catalog/html/40152.htm

http://www.usgs.gov

http://www.its.bldrdoc.gov/fs-1037/dir-001/_0018.htm

propagation basics

Documents

antenna bandwidth

antenna efficiency

antenna conductors

type of antenna

antenna pattern distortion

dozens of antenna types

beam antenna handbook

propagation characteristics