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 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 1.10 1.11 1.12 1.13 1.14

2.0

Environment 2.1 2.2 2.3

3.0

22

Clutter Data (Electronic) 22 Some Clutter and Terrain Descriptions Line-of-Site (LOS) 24

23

Large-Scale Propagation Models - Path Loss 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 3.16 3.17 3.18

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4

Definition 4 Antenna Types 4 Induction and Radiation Fields 5 Polarization 5 Radiation Pattern 6 Antenna Pattern Distortion 9 Antenna Gain 9 Return Loss 10 Antenna Beamwidth (Horizontal/Vertical) 11 Front to Back Ratio 12 Antenna Bandwidth 13 RF Feeder Losses 13 Antenna Efficiency 15 Effects of Antenna Positioning (PCS/Cellular Communication Systems) 15

24

Free Space Propagation Model 25 Fresnel Zones 27 Propagation Over a Plane Earth 30 Rough Surface Criterion 33 Refraction and Equivalent Earth’s Radius 33 Transmission Over a Smooth Spherical Earth 34 XLOS 35 Knife Edge Diffraction 37 Log-distance Path Loss Model and Log-normal Shadowing Longley-Rice (Irregular Terrain Model) 42 Okumura 43 Hata 45 COST-231-Hata 46 Slope and Intercept 48 Walfish-Ikegami Cost 231 49 Walfisch-Xia JTC 49 Bullington 49 dn Pathloss Model 51

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3.19 3.20

4.0

4.3 4.4 4.5 4.6 4.7 4.8

69

Multiple-Carrier Intermodulation (IM) Products 69 Intermodulation Distortion 70 Inter-Symbol Interference (ISI) 71 Inter-System Interference (ISI) 71 Adjacent Channel Interference - Land-Mobile 72 Man-Made Noise and Interference 72

Standards and Units 6.1 6.2 6.3 6.4

56

Fade Margin 56 Doppler Spread and Coherence Time, Coherence Bandwidth, Symbol Period 56 Flat Fading (i.e. no frequency selective behavior) 57 Frequency-Selective Fading 59 Fast Fading (observed at approximately 1/2 wavelength i.e. Rayleigh) 61 Slow Fading (observed at distances greater than 1/2 wavelength i.e. log normal) 62 Rayleigh Fading/Multipath 63 Ricean Fading Distribution 68

Interference 5.1 5.2 5.3 5.4 5.5 5.6

6.0

53

Small-Scale Propagation Models - Fading 4.1 4.2

5.0

Diffracting Screens Model Building Penetration 55

74

VSWR (Voltage Standing Wave Ratio): Watts to dBm Conversion32: 74 dBi to dBd Conversion 74 Speed of Light : Wavelength 74

7.0

References

8.0

Other Useful References

74

75 76

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Propagation Basics

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-space, unguided electromagnetic wave, and vice versa. Electrical energy is fed to the antenna via a transmission line, a conductor which passes electrical energy from one point to another. A matching device is usually required to ease the abrupt transition between the guided and the free wave. The wave guided by the line is radiated into space by the antenna.”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.] 1.2

Antenna Types

There a dozens of antenna types and variations of each. The type of antenna selected for use depends on the propagation characteristics 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 pattern, polarization, 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.gov/fs1037/dir-001/_0018.htm.].

Some Antenna Types 1/2 Wave Dipole Yagi Horn Leaky Coax Helices Yagi-Uda

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Frequency Independent Log-Periodic Loops Slot Antennas Printed Circuit Antennas Antenna Arrays

1.3

Induction and Radiation Fields

“There are two different electromagnetic field areas associated with an antenna. The first, called the induction field is of importance only in the immediate vicinity of the antenna. This field consists of the lines of force which are set up by the voltage and current in the antenna conductors and which collapse back into the antenna twice each cycle. The induction field contains only reactive energy because the electric and magnetic fields are 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 the antenna and are moving out into space as an electromagnetic wave. The radiation field contains real power that can be measured with special instruments. The electric and magnetic fields are in time phase, so the actual power is removed from the antenna and carried away by the field. The intensity of the induction field varies as the inverse square of the distance from the antenna and the radiation field intensity varies inversely as the distance. It is the radiation field which is principally important for communication purposes, 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 ampers per meter. One half of the wave energy is contained in the electric field and the remaining half is contained in the magnetic field. The product of the electric and magnetic field, with a given area in space, will have the units of watts per square meter. ...An interesting point is that the impedance of free space to an electromagnetic wave is 377 ohms (pure resistance). The fact that the impedance of free space is resistive supports the statement that the electric and magnetic fields are in time phase much in the same manner that voltage and current are in time phase in a resistive network.”30 [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.academy.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 [vector]) with respect to a reflecting surface. In most instances the reflected surface will be the earth. [For example, if the E phasor 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.

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Circular/Elliptical - “An electomagnetic wave is linearly polarized when the electric field lies wholly in one plane containing the direction of propagation. A plane electromagnetic wave, at a given frequency, is elliptically polarized when the extremity of the electric vector describes an ellipse in a plane perpendicular to the direction of propagation, making one complete revolution during one period of the wave. If the rotation is clockwise looking in the direction of propagation, the sense is right-hand. More generally, any field vector, electric, magnetic, or other, is elliptically polarized if its extremity describes an ellipse.”9 Cross-Polarized Antenna - Two E vectors which may or may not propagate in-phase. As the phase between the two E vectors 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 occupying the same 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.] [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.academy.jccbi.gov/catalog/html/40152.htm.] 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 antenna or antenna array. Although radiation patterns [can be] determined mathematically, it is possible to obtain patterns by taking actual field measurements. For example, the pattern in the horizontal plan may be determined by taking readings from an RF indicating instrument at various azimuth angles. It is essential that the readings be taken at a constant distance from the center of the array. If the RF indicating instrument is constructed to give readings that bear a linear relation to the electric field intensity, a plot of those readings against azimuth angles will be the radiation pattern in the horizontal plan. The figure below (right) illustrates measured data plotted in rectangular coordinates, while the figure on the left shows the same 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 field intensity is zero are called nulls. Portions of the pattern between adjacent nulls are called lobes. Maximums are the points of greatest field intensity. The maximums in our example plots occur at 45°, 135°, 225°, and 315°. The pattern consists of four lobes.

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Y

90°

Direction 1000

E

E

0°

180° 500 1000

X

0°

90°

180°

270°

360°

Direction

270°

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°.

90°

180°

0°

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.

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90° Minimum

180°

0°

Minimum

270° 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 radiation 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 [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.academy.jccbi.gov/catalog/html/40152.htm.]

Non-Directional (Omni-Directional) (Isotropic)

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Bi-Directional

Uni-Directional

Propagation Basics

1/2 Wave Dipole

1.6

Antenna Pattern Distortion

“The real world performance of an antenna is different from that listed in the manufacturer’s antenna pattern specifications. The manufacturer’s specifications are based on measurements in an ideal environment of an antenna range. However, the actual implementation of the antenna in the system is not the same as on the antenna range. In the real system, factors such as how the antenna is mounted (such as on the side of a building or tower) or its relative location with respect to surrounding clutter has an effect on the antenna pattern. If the antenna is mounted below the majority of the surrounding clutter, the signal will be reflected due to this clutter which in effect distorts the antenna pattern, reducing the effective protection from the directivity of the pattern. Since the mounting of the antennas and the surrounding ground clutter vary from site to site, 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 clutter reflections. The amount and placement of tall buildings in the antenna’s main lobe will affect the amount of reflections which propagate behind the antenna. This effect is seen most often in dense urban and urban areas since there are more tall building in these environments. The antenna pattern distortion can affect the capacity of a site. If significant clutter exists in the area of an antenna’s main 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 a reference antenna in the same direction for equal power input. Usually this gain is referenced to either an isotropic antenna or a 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 directions. When used as a gain reference, the isotropic antenna has a power of 0 dBi. The halfwave dipole (dBd) is an antenna which is center fed as to have equal current distribution in both halves. When used as a theoretical reference antenna it has a power gain of 0 dBd, which equates to a 2.14 dB difference compared to an Isotropic antenna.

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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 site.”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 reflected from that discontinuity. Return loss can be related to the reflection coefficient VSWR as follows: RLdB = 20 log (1/p)

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Where p = VSWR-1/VSWR+1

Propagation Basics

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

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Degrees Above Horizon -20° 3 dB Pt.

-10° Gain =15 dB

0°

20o

+10° 3 dB Pt.

-3

2

7

10 12

15 dB

+20°

Degrees Below Horizon This particular pattern is a vertical antenna pattern (side view of the antenna) and has a vertical beamwidth of approximately 20 degrees. (Figure above is taken from [Clapp, Scott. March 8, 1995. China Frequency Planning and RF Propagation Analysis Overview, REV B. Motorola, Inc. pp. 18.]. [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.] [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 radiated from the main ray beam forward to that radiated from the back lobe behind the antenna. Front to back ratio is normally expressed in terms of dB, this means that a signal at the back of the antenna should be X dB down on a signal at a mirror angle in front of the antenna. The following illustration show a front to back ratio of 25dB (typical for a PCS antenna).” 13

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0dB Reference Line 5dB Per Ring

25dB Front to Back Ratio [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.] 1.10

Antenna Bandwidth

“The range of frequencies over which the antenna functions efficiently, and over which a reasonable match between the guided and the free waves can be made, is termed the bandwidth of the antenna and is a function of antenna and matching system design. If the transition is smooth and the system design such that the wave characteristics do not undergo a sudden shift, the bandwidth of the antenna may be quite large. But if the transition is abrupt, a region of discontinuity exists in the system and a portion of the guided wave is reflected back down the transmission line, much in the manner that an ocean wave is reflected when it hits a sea wall. The reflected wave is compensated for by the matching device which creates 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 reflected energy at any operating frequency. This limit may be expressed as a voltage standing wave ration (VSWR) or, more simply, SWR. This term is an expression of the ratio of the amplitude of the reflected voltage on the transmission line to the 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 antenna, or with respect to a mobile, all of the losses between the PA and the antenna. Since a majority of subscriber units for a mobility system being sold to customers are portable, there is minimal feeder loss. The feeder loss at the base site can account for several dB of loss.

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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 minimized by reducing the transmission line run between the base station and its antennas, and/or utilizing lower loss transmission lines. Transmission lines can range from 1/2” to 1-5/8” diameter cables. The larger the diameter of the cable, the less lossy the medium, but the sacrifice is more rigid lines, larger bending radius, greater weight, more wind loading and larger area required. Transmission lines are also available with either air or foam dielectrics. The air dielectric cables are more expensive to install and maintain, but are less lossy than the foam lines. The following figure reflects most of the different components that are encountered between the base site antenna and the base station equipment. Typical Components in the RF Feeder Run

Antenna

(A) Top Jumper

(B) Main Transmission Line

Waveguide Entry Port (C) Antenna Surge Protector (D) Jumper to Directional Coupler (E) Directional Coupler (F) Jumper to Duplexer (G) Duplexer (H) Jumper to Tx and Rx Antenna Port BTS

Note:Each Jumper consists of: Two connectors and One line

Transmission cables are more lossy at higher frequencies. At 800 MHz, a 7/8” line may suffice but one may require 1-5/8” line for 1,900 MHz to maintain a similar loss. Refer to the "RF Antenna System" sections13 for additional information on transmission lines.”13

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[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.] 1.12

Antenna Efficiency

“Antennas are transducers that convert electronic signals into electromagnetic fields, and vice versa. They are also used to focus the electromagnetic energy in a desired direction. The larger the antenna aperture (area), the larger is the resulting signal power density in the desired direction. An antenna’s efficiency is described by the ratio of its effective aperture to its physical aperture. Mechanisms contributing to a reduction in efficiency (loss in signal strength) are known as amplitude tapering, aperture blockage, scattering, re-radiation, spillover, edge diffraction, and dissipative loss. Typical efficiencies due to the combined effects of these mechanisms range between 50 and 80%.”26 [Sklar, Bernard. 1988. Digital Communications Fundamentals and Applications. Englewood Cliffs, New Jersey. Prentice-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 frequency of these waves are in the 25 MHz - 50 MHz range. As the frequency increases, the amount of radio wave energy that passes 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 line of sight 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 enables a radio 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 coverage behind and around obstacles. 3) Reflection - the ability of a wave or path of propagation to “bounce” off a certain object or objects (buildings, mountains, etc.). This creates multiple paths that are followed by the transmitted signal and received at the receiver at different 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-building 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:

Poor Frequency Re-use - Range Limited by Downtilt Only

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

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 necessary 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 coverage will be adequate in the area immediately surrounding the cell site down to the side of the town facing the site, coverage within the city may be limited due to signal path obstructions due to buildings on the edge of the town. In other words, reflections off buildings on the edge of the city will provide coverage to areas between the buildings and the cell site, but probably not on the opposite side of the obstructions. An example is shown below:

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Better Location

.

.

.

“Off-grid” Site Locations: As was stated before, following a hexagonal pattern when assigning cell sites is a good starting point in reducing cochannel 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 any type of symmetry. As a result, some interference may appear in some areas regardless of how close you assign sites to the grid. It 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: [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.] Antenna Downtilt:

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By tilting the entire radiation pattern of a particular antenna, one can conceivably control its coverage pattern within a specific 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 effect is know as beamtilt. There are two categories of beamtilt, mechanical and electrical. Electrical beamtilt is obtained by adjusting the phase relationships of radiating elements within the antenna by the factory. [For example, an electrical beamtilt can be adjusted in the field by changing external phasing cables purchased from the vendor.] Mechanical beamtilt may be accomplished by physically tilting the antenna away from the perpendicular by using a shim or downtilt bracket. [For example, some manufacturer’s provide scissor-style brackets that eliminate guesswork about the setting in degrees.] Downtilt of either variety should be specified only after a detailed understanding of the terrain and other propagation factors have been acquired by the designer. Most legitimate uses of beamtilt involve signal coverage restrictions required by cellular repeaters to prevent overlap with adjacent cells. Beamtilt is not a good substitute for null fill below the horizon. A lower gain antenna might well over superior overall performance to a downtilted higher gain model.”2 [Mechanical downtilting will cause the backlobe to tilt upward (parallel to front lobe), while electrical downtilting causes the backlobe to downtilt simultaneously. One other note to make, an electrical downtilt type of antenna could also be downtilted mechanically.] A great deal of caution must be used when downtilting a particular antenna. There are several “side effects” that can occur with excessive downtilting.”3 The following Downtilt Effects graphs are provided by Terry Leonard of the Motorola RF Planning Group.11 The following illustrations show mechanical downtilt effects (the backlobe stays parallel to the front lobe).

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DOWNTILT EFFECTS 3 x SRL410C4R130 Sector Antennas Gain: 10 dB

Vertical Beamwidth: 16°

Ant Ht: 164’ = 50m 153 dB Coverage 0° Downtilt

5° Downtilt

DOWNTILT EFFECTS 3 x SRL410C4R130 Sector Antennas Gain: 10 dB

Vertical Beamwidth: 16°

Ant Ht: 164’ = 50m 10° Downtilt

153 dB Coverage

15° Downtilt Peanut Effect

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DOWNTILT EFFECTS PD1132 Sector Antennas Gain: 16 dB

Vertical Beamwidth: 8°

Ant Ht: 164’ = 50m

153 dB Coverage

0° Downtilt

2° Downtilt

DOWNTILT EFFECTS PD1132 Sector Antennas Gain: 16 dB Vertical Beamwidth: 8° Ant Ht: 164’ = 50m 153 dB Coverage 4° Downtilt

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6° Downtilt

Propagation Basics

DOWNTILT EFFECTS PD1132 Sector Antennas Gain: 16 dB

Vertical Beamwidth: 8°

Ant Ht: 164’ = 50m

153 dB Coverage

8° Downtilt

10° Downtilt

“ERP and Downtilt Limitations: As mentioned above, when adjusting ERP and downtilt at particular site in order to control interference, special considerations 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:

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Propagation Basics

0° Downtilt Angle θ Side Lobe

3dB Beamwidth

Main Lobe

h Usable Signal Area

Rapidly Decreasing Signal Strength Region

Shadow Area

Dmax 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 above ground 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”, physical characteristics of the propagation environment will effect a signal’s ability to traverse through space. Environment descriptions 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 the propagation predictions will be. The most common source of clutter data is from the U.S. Geological Survey (USGS)*. It is

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Propagation Basics

easily obtained and is available digitally. However, there are certain limitations with this data. The USGS data categorizes 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 imagery 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/ [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.] 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 vegetation 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 environment. 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 environment. 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, desert, water (ocean, lake, stream), etc.

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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 primary 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. [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.] 2.3

Line-of-Site (LOS)

“Radio transmission requires a clear path between antennas known as radio line of sight. It is necessary to understand the requirements for radio line of sight when designing a network . Line of sight is the direct free-space path that exists between two points. Using binoculars on a clear day, it is easy to determine if visual line of sight exists between two points that are miles apart. To have a clear line of sight there must be no obstructions between the two locations. Often this means that the observation points must be high enough to allow the viewer to see over any ground-based obstructions. 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 also consider the Fresnel effect. If a hard object, such as a mountain ridge or building, is too close to the signal path, it can damage the radio signal or reduce its strength. This happens even though the obstacle does not obscure the direct, visual line of 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 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

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Propagation Basics

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 be found in 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.

λ 2 P R = P T ⋅ G ⋅ G R ⋅  ----------   4πd  T 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 between the effective transmitted power and the received power and may or may not include the effects of the antenna gains. The path loss for the free space model when the antennas are assumed to have unity gain is provided by the following equation.

PT 4πdf 2 4πd 2 ------- =  ----------  =  ------------  c λ PR Expressed in dB as:

 P T 4πdf 2 4πdf L ( dB ) = 10 log  ------- = 10 log  ------------ = 20 log  ------------    P c  c  R 8 = 20 log ( 4π ) + 20 log ( d ) + 20 log ( f ) – 20 log ( 3 × 10 )

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Propagation Basics

= 21.98 + 20 log ( d ) + 20 log ( f ) – 169.54 = – 147.56 + 20 log ( d ) + 20 log ( f ) Where: d

is in meters

f

is in Hertz

c

is equal to the speed of light (

8 3X10 meters per second)

If: d

is in kilometers

f

is in MegaHertz (

c

is

10

6 Hertz)

km MHz km -  ---------------8 )  6  = 0.3 -----------( 3X10 )meter ⋅ Hertz ( ---------------MHz 1000m 10 Hz

L dB = 21.98 + 20 log ( d km ) + 20 log ( f MHz ) – 20 log ( 0.3 ) = 21.98 + 20 log ( d km ) + 20 log ( f MHz ) – ( – 10.46 ) = 32.44 + 20 log ( d km ) + 20 log ( f MHz ) 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 encountered.”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.]

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Propagation Basics

3.2

Fresnel Zones

“Fresnel zone: In radio communications, one of a (theoretically infinite) number of a concentric ellipsoids of revolution which define volumes in the radiation pattern of a (usually) circular aperture. Note 1: The cross section of the first Fresnel zone is circular. Subsequent Fresnel zones are annular in cross section, and concentric with the first. Note 2: Odd-numbered Fresnel zones have relatively intense field strengths, whereas even numbered Fresnel zones are nulls. Note 3: 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 zones. Fresnel zones represent successive regions where secondary waves have a path length from the transmitter to receiver which are nλ/2 greater than the total path length of a line-of-sight path. [The figure below] demonstrates a transparent plane located between a transmitter and receiver. The concentric circle on the plan represent the loci of the origins of secondary wavelets which propagate to the receiver such that the total path length increases by λ/2 for successive circles. These circles are called Fresnel zones. The successive Fresnel zones have the effect of alternately proving constructive and 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

rn =

nλd 1 d 2 ------------------d1 + d2

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 path traveling through the smallest circle corresponding to n = 1 in the figure will have an excess path length of λ/2 as compared 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 maximum radii if the plane is midway between the transmitter and receiver, and the radii become smaller when the plane is moved towards either the transmitter or the receiver. This effect illustrates how shadowing is sensitive to the frequency as well as 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 transmitter and receiver by joining all the points for which the excess path delay is an integer multiple of half wavelengths. The ellipsoids represent Fresnel zones. Note that the Fresnel zones are elliptical in shape with the transmitter and receiver antenna at their foci.”25

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Propagation Basics

T d1

h O 1 2 3

R d2

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

R FZ = 17.3X ( d 1 × d 2 ) ⁄ ( d × f ) 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.

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Propagation Basics

Microwaves do not normally propagate within the atmosphere in straight lines; they ordinarily travel in curved paths (usually 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 radius of the earth 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 percent of the Fresnel zone radius for K = 4/3 (the most usual value that approaches a “flat earth”), then the obstacle generally causes negligible loss. When, however, an obstacle protrudes into the path of the link by more than 50 percent of the first Fresnel zone, an adjustment must be made for the additional losses incurred. The terrain loss LTR (in dB) can be calculated as

L TR = 10 – ( C ⁄ R FZ ) × 20 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 values of K increase the attenuation due to obstructions, particularly on longer path lengths. You should check to ensure that potential variations in K will not degrade the service.

C

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

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Propagation Basics

 1  C C = 0.078 × d1 × d 2 ×  0.75 –  ----  K  

meters

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. Directory: http://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 estimating the effects of propagation over actual paths. The complex analytical results for propagation over a plane earth derived by Norton have been simplified by Bullington38 by decomposing the solution of Norton into a set of waves consisting of direct, reflected, and surface waves. The formula relating the power transmitted to the power received following the approach of Bullington38 is

2 j∆ j∆ λ 2 P r = P t ---------- gb g m 1 + Re + ( 1 – R )Ae + … 4πd Within the absolute value symbols, the first term (unity) represents the direct wave, the second term represents the reflected wave, the third term represents the surface wave, and the remaining terms represent the induction field and secondary effects of the ground. The reflection coefficient, R, of the ground depends on the angel of incidence, θ, the polarization of the wave, and the ground characteristics; it is given by

sin θ – zR = ------------------sin θ + z where

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Propagation Basics

2

ε 0 – cos θ z = ----------------------ε0

2

z = ε 0 – cos θ

for vertical polarizaion,

for horizontal polarizaion,

ε 0 = 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. 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

2 2π h b + h m ∆ = ------  -------------------- + 1 λ  d 

1--2

2 2πd h b + h m – ----------  -------------------- + 1 λ  d 

1--2

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

4πhb h m ∆ ≈ --------------------λd Since the earth is not a perfect conductor, some energy is transmitted into the ground, setting up ground currents that distort the field distribution relative to what it would have been over a perfectly reflecting surface. The surface wave attenuation factor, A, depends on frequency, polarization, and the ground constants. An approximate expression for A is given by

–1 A ≈ -------------------------------------------------------------2 1 + j ( 2πd ⁄ λ ) ( sin θ + z ) which is valid for |A| < 0.1. More accurate values are given by Norton. Since the effect of this surface wave is only significant in a region a few wavelengths above the ground, this effect can be neglected in most applications of microwave mobile communications.

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Propagation Basics

hb

θ

hm d

Propagation paths over a plane earth.

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]) and for vertical polarization, |R| exceeds 0.9 for angles less than 10º above the horizon. For horizontal polarization above 100 MHz, |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.

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

Under the conditions where R equals -1 and A can be neglected, then [the power received equation] reduces to 2 2πh b h m P r = 4P 0 sin  ---------------------  λd  where P0 is the expected power over a free space path. In most mobile radio applications, except very near the base station antenna, sin 1/2 ∆ ≈ 1/2 ∆; thus the transmission loss over a plane earth is given by the approximation

 h b h m 2 P r = 4P t g b g m  --------------  d2  yielding an inverse fourth-power relationship of received power with distance from the base station antenna.

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Propagation Basics

The ground constants over the path of interest enter into both the calculations for line-of-sight and for diffraction attenuation. 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 coefficient 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 irregularities. A measure of the surface “roughness” that provides an indication of the range of validity of [the formula relating the power transmitted to the power received following the approach of Bullington38]

2 j∆ j∆ λ 2 P r = P t ---------- gb g m 1 + Re + ( 1 – R )Ae + … 4πd is given by the Rayleigh criterion, which is

C = 4πσθ -------------λ where σ is the standard deviation of the surface irregularities relative to the mean height of the surface, λ is the wavelength, θ is the angle of incidence measured in radians from the horizontal. Experimental evidence shows that for C<0.1 spectacular reflection results, and the surface may be considered smooth. Surfaces are considered “rough” for values of C exceeding 10, and under these conditions the reflected wave is very small in amplitude. Bullington38 has found experimentally that most practical paths at microwave frequencies are relatively “rough” with reflection coefficients in the range of 0.2-0.4.”8 [Jakes, William C. 1974. Microwave Mobile Communications. An IEEE Press Classic Reissue. Picataway. American Telephone and Telegraph Company. pp. 80-88.] 3.5

Refraction and Equivalent Earth’s Radius

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

n = n0 + gh In a medium where there are abrupt changes in index of refraction, Descarte’s law applies:

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Propagation Basics

n ( a + h ) cos α = n 0 acos α 0 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 atmosphere is uniform the equation for rectilinear propagation is

 1 + h--- cos α = cos a  0 a When n has a constant gradient the propagation is given approximately by

1 + h  1--- + g cos α ≈ cos α0 a If we replace the earth’s radius a by a fictitious value a’, where

–1 a′ =  1--- + g a 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,

N s = ( n – 1 ) × 10

6

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

a′ = 6370 [ 1 – 0.04665 exp ( 0.005577N s ) ]

–1

km

where 6370 km is used for the earth’s radius.” 8 [Jakes, William C. 1974. Microwave Mobile Communications. An IEEE Press Classic Reissue. Picataway. American Telephone and Telegraph Company. pp. 80-88.] 3.6

Transmission Over a Smooth Spherical Earth

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

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Propagation Basics

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 simple 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 [Jakes, William C. 1974. Microwave Mobile Communications. An IEEE Press Classic Reissue. Picataway. American Telephone and Telegraph Company. pp. 80-88.] 3.7

XLOS

“The workhorse of the NetPlan tool is the XLOS propagation model developed and refined over the last 15 years by Motorola engineers. The method used to refine estimate coverage is based on the diffraction and line of sight algorithms found in Longley and Rice, "Prediction of Tropospheric Radio Transmission Loss Over Irregular Terrain. A Computer Method" - 1968, for rough terrain conditions. As the terrain flattens out the range estimates approach the Okumura model predictions, "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 height over and above the existing terrain which is varied to correspond to urban, suburban, rural, foliage, water and other conditions. The overlay (or obstruction) code is determined from maps which typically show this information as colors. This virtual height is then scanned to find the major, or controlling, obstacles for each mobile position. Single diffraction points are separated from extended obstructions and are treated in different ways to obtain an estimate of the degree of additional transmission 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 with each new mobile position. This straight line approximation is used to obtain an equivalent adjusted base antenna height. The adjusted base antenna height is further corrected for earth curvature and is applied to the line of sight routine to give an estimated reflection loss term. The final estimated total attenuation for each mobile position is a varying mix of both reflection and diffraction loss terms. Adjustments are made by corrections applied to each loss term as a function of whether single or multiple diffraction is taking place. Antenna horizontal and vertical patterns, downtilt angles, and sector power levels are also taken into account. Although the XLOS propagation model is based on Longley, Rice and Okumura algorithms, extensive field measurements, in varying terrain conditions, have been used to modify the algorithms and to model local environmental clutter (obstruction height).”17 The following slides taken from an Xlos Propagation Model18 presentation, depict the process and evolution of the tool and shows the general mix formula used.

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Propagation Basics

T h e ge n e r a l “ p a t h ” lo ss e qu a t io n is gi v e n be lo w :

LP = AFS + C 1 AD + C 2 AD + AN T H V + P S w h ere: LP

= “ p a th ” l o ss be t w e e n d i p o l e s

A FS

= fr e qu e n cy + fr e e sp a ce co m p o n e n t

AD

= d i ffr a cti o n l o ss

AR

= r e fl e ct io n lo ss

A N T H V = a n t e n n a h o r i z o n ta l a n d v e r ti ca l p a tt e r n PS

= p o w e r a d ju st m e n t (r e l . T o 50 d Bm ) by se ct o r

C

= m ixi n g co e ffi ci e n ts

A l th o u gh t h e Xlo s m o d e l i s ba se d o n Lo n gle y a n d R ice , a n d O k u m u r a a lgo r it h m s, e xt e n si v e fie l d m e a su r e m e n t s, in v a r yin g te r r a i n co n d i ti o n s, w e r e u se d to m o d i fy t h e a lgo r it h m s a n d to m o d e l lo ca l e n v i r o n m e n t a l clu tt e r (v ir tu a l o bst r u ct io n h e igh t ). ‡ 8 6 * 6 / 8 / &  ' , * , 7 $ / ' $ 7 $ ‡ 6 $ 7 ( / / , 7 ( , 0 $ * (

&/877(5 '$7$

6 , 7 ( ' $ 7 $

‡ ' , * , 7 , = ( ' 9 ( 5 7 , & $ / ‡ 8 6 * 6   $ 5 & 6 ( & 2 1 ' ' ( 0

$ 1 ' + 2 5 , = 2 1 7 $ / 

‡ % , / ) 2 5 0 $ 7

3 $ 7 7 ( 5 1 6

$17(11$ 3$77(51

7 ( 5 5 $ ,1 '$7$

;/2 6

XLOS PROCESS DIAGRAM

‡ 6 , 7 ( & 2 2 5 ' , 1 $ 7 ( 6 ‡ $ 1 7 ( 1 1 $ + ( , * + 7

287387 ,0 $ * ( 6

‡ 6 ( & 7 2 5 ' 2 : 1 7 , / 7 ‡ 6 ( & 7 2 5 + ( $ ' , 1 * ‡ 6 ( & 7 2 5 ( 5 3 ‡ & 2 1 7 2 8 5 ‡ 6 , * 1 $ / 6 7 5 ( 1 * 7 + ‡ % ( 6 7 6 ( 5 9 ( 5 ‡ &  ,

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Propagation Basics

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

ON GOING DEVELOPMENT

352727<3( &20387(502'(/

),(/'7(676 ‡7HUUDLQ

;/26

XLOS EVOLUTION

:DVKLQJWRQ%DOWLPRUH7HVW%HG 6DQ)UDQFLVFR +RXVWRQ ‡'LIIHUHQW&OXWWHU

[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 such as hills, trees, and buildings. When the shadowing is caused by a single object such as a hill, it is instructive to treat the object as a diffracting knife edge to estimate the amount of signal attenuation. The exact solution to the problem of diffraction 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

E = A exp ( i∆ ) -----E0 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:

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Propagation Basics

S+1⁄2 A = ---------------------------------2 sin  ∆ + π --- 4 -1 S + 1 ⁄ 2 ∆ = tan  -------------------- – π --C+1⁄2 4 where

h0

∫

C =

π 2 cos  --- v  dv 2 

0 h0 S =

π 2

∫ sin  --2- v  dv 0

where (from Fresnel zone geometry):

π 2 φ = --- v 2

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

2 ( d 1 + d2 ) v = h -------------------------λd 1 d 2 1 1- = h --2-  ----- + ---- λ  d1

d 2

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,

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Propagation Basics

d 1, d 2 » h » λ then the diffracted power can be given by the expression

P- = --------------1 ----P0 2 2 2π h0 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 edge diffraction for such cases is treated by Anderson and Trolese35. Closer agreement with data over measured paths has been obtained by calculations that better describe the geometry of the diffracting obstacle.”8

Geometry for propagation over a knife edge. h d1

d2

[Jakes, William C. 1974. Microwave Mobile Communications. An IEEE Press Classic Reissue. Picataway. American Telephone and Telegraph Company. pp. 80-88.] 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 distribution follows a curve that is a normally distributed curve, provided the field strength is measured logarithmically.”1

.

Log normal fading that is due to obstruction is known as “shadowing” or “diffraction losses.” “Both theoretical and measurement-based propagation models indicate that average received signal power decreases logarithmically with distance, whether in outdoor or indoor radio channels. Such models have been used extensively in the literature. The average large-scale path loss for an arbitrary T-R (transmit-receive) separation is expressed as a function of distance by using a path loss exponent, n.

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Propagation Basics

d n PL ( d ) ∝  ------ d0 or

d PL ( dB ) = PL ( d 0 ) + 10n log  ------ d  0 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 coverage cellular systems, 1 km reference distances are commonly used, whereas in microcellular systems, much smaller distances (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 d 0. [The table below] lists typical path loss exponents obtained in various mobile radio environments.

3DWK/RVV([SRQHQWVIRU'LIIHUHQW(QYLURQPHQWV (QYLURQPHQW

Free space Urban area cellular radio Shadowed urban cellular radio In building line-of-sight

3DWK/RVV([SRQHQWQ

2 2.7 to 3.5 3 to 5 1.6 to 1.8

Obstructed in building

4 to 6

obstructed in factories

2 to 3

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 distance-dependent value. That is

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Propagation Basics

d PL ( d ) [ dB ] = PL ( d ) + X σ = PL ( d 0 ) + 10n log  ------ + X σ d0 and

P r ( d ) [ dBm ] = P t [ dBm ] – PL ( d ) [ dB ] (antenna gains included in PL(d)) 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 measured 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 deviation of the Gaussian distribution that describes the shadowing also has units in dB. Thus, the random effects of shadowing 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 measurement 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

∞  x 2 1 1 z Q ( z ) = ---------- ∫ exp  – ------ dx = --- 1 – erf  ------- 2 2π z 2  2 where

Q ( z ) = 1 – Q ( –z ) the probability that the received signal level will exceed a certain value γ can be calculated from the cumulative density function as

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Propagation Basics

 γ – P r ( d ) Pr [ P r ( d ) > γ ] = Q  --------------------- σ   similarly, the probability that the received signal level will be below γ is given by”25

  P r ( d ) – γ  Pr [ P r ( d ) < γ ] = Q  -------------------------   σ   [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.] [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.] 3.10

Longley-Rice (Irregular Terrain Model)

“The Longley-Rice model, is applicable to point-to-point communication systems in the frequency range from 40 MHz to 100 GHz, over different kinds of terrain. The median transmission loss is predicted using the path geometry of the terrain profile and the refractivity of the troposphere. Geometric optics techniques (primarily the 2-ray ground reflection model) are used to predict signal strengths within the radio horizon. Diffraction losses over isolated obstacles are estimated using the Fresnel-Kirchoff knife-edge models. Forward scatter theory is used to make troposcatter predictions over long distances, and far field diffraction losses in double horizon paths are predicted using a modified Van der Pol-Bremmer method. 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 loss relative to free space loss over irregular terrain for frequencies between 20 MHz and 10 GHz. For a given transmission path, the program takes as its input the transmission frequency, path length, polarization, antenna heights, surface refractivity, effective radius of earth, ground conductivity, ground dielectric constant, and climate. The program also operates on pathspecific parameters such as horizon distance of the antennas, horizon elevation angle, angular trans-horizon distance, terrain irregularity and other specific inputs. The Longley-Rice method operates in two modes. When a detailed terrain path profile is available, the path-specific parameters 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-specific parameters, 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. One important modification deals with radio propagation in urban areas, and this is particularly relevant to mobile radio. This modification introduces an excess term as an allowance for the additional attenuation due to urban clutter near the receiving antenna. This extra term, called the urban factor (UF), has been derived by comparing the predictions by the original Longley-Rice model with those obtained by Okumura.

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One shortcoming of the Longley-Rice model is that it does not provide a way of determining corrections due to environmental 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 [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.] 3.11

Okumura

“The Okumura model is based on data taken from 150 to 1500 MHz with less data taken at 150 MHz. Above 216 MHz, use the Okumura model. Between 132 and 216 MHz, the Okumura and Bullington models are equally valid. Use the Bullington model for frequencies below 132 MHz.”20 “Okumura developed a set of curves giving the median attenuation relative to free space (A mu), 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 the base and mobile, and are plotted as a function of frequency in the range 100 MHz to 1920 MHz and as a function of distance from the base station in the range 1 km to 100 km. To determine path loss using Okumura’s model, the free space path loss between 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

L 50 ( dB ) = L F + A mu (f,d) – G ( h te ) – G ( h re ) – G AREA 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 gains are strictly 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, Okumura 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.

h te G ( h te ) = 20 log  --------- 200

1000 m > hte > 30m

h re G ( h re ) = 10 log  -------- 3

hre ≤ 3m

h re G ( h re ) = 20 log  -------- 3

10 m > hre > 3 m

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Propagation Basics

Other corrections may also be applied to Okumura’s model. Some of the important terrain related parameters are the terrain undulation height (∆h), isolated ridge height, average slope of the terrain and the mixed land-sea parameter. Once the terrain related parameters are calculated, the necessary correction factors can be added or subtracted as required. All these correction factors are also available as Okumura curves. Okumura’s model is wholly based on measured data and does not provide any analytical explanation. For many situations, extrapolations of the derived curves can be made to obtain values outside the measurement range, although the validity of such extrapolations depends on the circumstances and the smoothness of the curve in question.

35

Uban Area ht = 200 m hr = 3 m Correction Factor, GAREA (dB)

100 Median Attenuation, A(f,d) (dB)

80

d (km)

30

70 60 50 40 30 20 10

25

ea Ar n e Op

20

Qu

pe O i as

rea A n

15 10

b Su

ea Ar n a ur b

5

5

2 1

70 100

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

0

100

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

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

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[Mozaik Web Page. Okumura Propagation Model. [Online serial]. http://rdeserver.comm.mot.com/mozaik/okumura.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.] 3.12

Hata

“Among the many technical reports that are concerned with propagation prediction methods for mobile radio, Okumura’s2 report is believed to be the most comprehensive one. In his report, many useful curves to predict a median value of the received signal strength are presented based on the data collected in the Tokyo area. The Tokyo urban area was then used as a basic predictor for urban areas. The correction factors for suburban and open areas are determined based on the transmit frequency. Based on Okumura’s prediction curves, empirical formulae for the median path loss, Lp, between two isotropic 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 cell radius and a reverse link cell radius. For Urban Area:

L U = 69.55 + 26.16 × log ( fc ) – 13.82 × log ( H b ) – A Hm + [ 44.9 – 6.55 × log ( H b ) ] × log ( r ) For Suburban Area:

fc 2  ----L S = L U – 2 × log - –5.4  28 For Quasi Open Area:

2 L q = L U – 4.78 × [ log ( f c ) ] + 18.33 × log ( f c ) – 35.94 For Open Rural Area:

2 L q = L U – 4.78 × [ log ( f c ) ] + 18.33 × log ( f c ) – 40.94 where: AHm Correction Factor For Vehicular Station Antenna Height For a Medium-Small City:

A Hm = [ 1.1 × log ( f c ) – 0.7 ] × H m – [ 1.56 × log ( f c ) – 0.8 ] 45 of 76

Propagation Basics

For a Large City:

2 A Hm = 3.2 × [ log ( 11.75 × H m ) ] – 4.97 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

69.55 + 26.16 log ( f c )

COST-231-Hata yields

46.3 + 33.9 log ( f c )

[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.] 3.13

COST-231-Hata

“The COST 231 Subgroup on Propagation Models proposed an improved propagation model for urban areas to be applied above 1,500 MHz4. Like Hata’s model, the COST-231-Hata model is based on the measurements of Okumura. The COST-231-Hata propagation model has been derived by analyzing Okumura’s propagation curves in the upper frequency band. Hata’s analysis was restricted to frequencies below 1,000 MHz. The COST-231-Hata propagation model extended the range of parameters to include 1,500 to 2,000 MHz. Their modified model was based on Hata’s formula for the basic transmission loss in urban areas (see above). For Urban Area

L U = 46.3 + 33.9 × log ( fc ) – 13.82 × log ( Hb ) – A Hm + [ 44.9 – 6.55 × log ( H b ) ] × log ( r )

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Propagation Basics

For Suburban Area:

fc 2 L S = L U – 2 × log  ------ – 5.4 28 For Quasi Open Area:

2 L q = L U – 4.78 × [ log ( f c ) ] + 18.33 × log ( f c ) – 35.94 For Open Rural Area:

2 L q = L U – 4.78 × [ log ( f c ) ] + 18.33 × log ( f c ) – 40.94 where: AHm Correction Factor For Vehicular Station Antenna Height For a Medium-Small City:

A Hm = [ 1.1 × log ( f c ) – 0.7 ] × H m – [ 1.56 × log ( f c ) – 0.8 ] For a Metropolitan Center:

A Hm = [ 1.1 × log ( f c ) – 0.7 ] × H m – [ 1.56 × log ( f c ) – 0.8 ] – 3 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.

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A comparison between the Hata and COST-231-Hata equations show that they are similar except for the following two terms:”13 Hata yields

69.55 + 26.16 log ( f c )

COST-231-Hata yields

46.3 + 33.9 log ( f c )

[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.] 3.14

Slope and Intercept

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

PL ( indBd ) = K1 + K2 log ( d ) + K3 log ( Hb ) + K4 log ( Hb ) log ( d ) + K5 log ( Hm ) + K6 log ( f ) ) + K7 ⋅ D + ( LU ) ⁄ ( CSL ) Where: D is the Diffraction, LU is the Land Use and CSL is the Cover Set Loss as described in the CPM application note. K1 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 pathloss model respectively. The figure below illustrates the slope and intercept parameters for the HATA 800 Model (reference from the CPM Application Note15).

Signal Strength (dBm)

HATA 800 MODEL Intercept = 2 K1 = 27.81 + 0.7 ⋅ Hm – ( 4.78 ⋅ ( log ( f ) ) ) – 4.3 Slope = K2 = 44.9 dB/decade

1 km HATA Intercept

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Log(Distance (km))

Propagation Basics

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 represents the slope in dB per decade that the signal strength (or the Pathloss (PL)) will be diminishing with respect to distance. [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 Scientific and Technical Research, factors in parameters that describe obstructions found in urban environments. Walfisch-Ikegami is suitable for modeling small cells in the 800-2000 MHz frequency ranges where deployment is above building level. Walfisch-Ikegami uses user-specified area and city qualifications (correction factors) to adapt the model for urban and suburban areas. In addition, users specify values for the following parameters: average building height, average building 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 Telecommunications Industry Association (TIA) and the Exchange Carriers Standards Association (ECSA). Walfisch-Xia JTC is suitable for modeling small, large, and micro cells in the 300-2000 MHz frequency ranges with deployments above, at, or below building level. Walfisch-Xia JTC uses user-specified area and city qualifications (correction factors) to adapt the model for urban, suburban, residential, and rural areas. In addition, users specify values for the following parameters: 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 considered to be preferable at frequencies below 132 MHz. Between 132 and 216 MHz, the Bullington and Okumura models are equally valid. 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 Vehicular Communications", Kenneth Bullington, IEEE Transactions on Vehicular Technology, Volume VT-26, Number 4, November 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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[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. This model takes into account the decrease in energy density suffered by the electromagnetic wave due to spreading, as well as the energy loss due to the interaction of the electromagnetic wave with the propagation environment. Path loss is the term used 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

d PL ( dB ) = PL ( d 0 ) + 10n log  ------ ( dB ) d 10 0 where PL(d0) is the mean path loss in dB at close-in reference distance d0, and n is the empirical quantity - the path loss exponent. Note that when n=2, the path loss is the same as free space - received signals fall off by 20 dB per decade increase in distance. The reference distance, d0, is chosen to be in the far-field of the antenna, at a distance at which the propagation can be considered to be close enough to the transmitter such that multipath and diffraction are negligible and the link is approximately that of free-space. Typically, d0 is chosen to be 1 m for indoor environments and 100 m or 1 km in outdoor environments. The free space distance must be in the far-field of the antenna, which is related to the physical size 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:

4πd 0 PL ( d 0 ) = 20 log  ------------  λ 

10

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 the transmitted 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 variability over a large number of independent measured locations the same distance away from the transmitter results in log-normal shadowing and is usually found to follow a Gaussian distribution (with values in dB) about the distance-dependent mean path loss, PL(d), with standard deviation σ dB about the mean path loss PL(d).

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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

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

Environment

Freq. (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

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

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3.19

Diffracting Screens Model

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

a

Hb Hm b

d

s

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

Hm

Hb b

d

s

Suburban Propagation between two sites below roof Level The resulting expression for the path propagation Lds, based on the models of Maciel, Bertoni, Xia and Walfisch is written as :

2 b+d Lds = – F – Le1 – Le2 – 18 log 17H ------------------------17H b

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Gm ( θ ) 1 - 2 Le1 = – 10 log ----------------------------------------------------------- ⋅ --1- – ------------------2 2 θ 2⋅π+θ π ⋅ k ⋅ ( b – Hm ) + w F = 32.448 + 20 log ( f ⋅ d )

Parameters for the Diffracting Screens Model

b – Hm θ = atan -----------------w

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)

θ

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

λ

Wavelength

see figure below for the angle θ

2 Le2 = – 10 log [ Gb ⋅ Q ]

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Parameter

Propagation Basics

Q is either Qe or Ql depending on whether the fixed-site antenna is elevated above or lower than the rooftop level. Practically, Qe is chosen when the fixed-site antenna height Hb is more than when Hb is below rooftop level by more than

λ ⋅ s above rooftop level b, and Ql is chosen

0.5 ⋅ λ ⋅ s .”10

b w Hm s

s -----------------------------d ⋅ 1, 000 – s 1 1 Ql = ------------------------------------------------------------------- ⋅ -------------------------------- – ------------------------------------------------b – Hb b – Hb 2 2 atan ---------------2 ⋅ π + atan ---------------2 ⋅ π ⋅ k ⋅ ( b – Hb ) + s s s 0.9 Hb Qe = 2.35 ⋅ atan ---------------------- ⋅ --sd ⋅ 1, 000 λ [Kazimierz Siwiak. Radiowave Propagation and Antennas for Personal Communicationsi. Boston/London: ISBN 089006-755-4. Artech House.] 3.20

Building Penetration

There is a great interest in characterizing the radio communication channel between a base station and a mobile located inside a building. The problem of modeling radiowave penetration into buildings differs from vehicular case in several aspects. The main aspects are: 1.

The problem is three dimensional because at a fixed distance from the base station the mobile can be at a number of heights 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 of materials) close to the mobile.

Building penetration loss is dependent on a number of factors:

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Propagation Basics

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 transmission 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 predominant 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.

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

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 present, the more reliable the wireless link. Fade margin can be calculated during system design and measured during system installation. Because fade margin can be measured, it is possible to install wireless links that are extremely reliable, even exceeding 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 channel in a local area. however, they do not offer information about the time varying nature of the channel caused by either relative motion

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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 components 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 proportional to each other.”25 Coherence Bandwidth: “While the delay spread is a natural phenomenon caused by reflected and scattered propagation paths in the radio channel, the coherence bandwidth is a defined relation derived from the rms delay spread. Coherence bandwidth is a statistical measure of the range of frequencies over which the channel can be considered “flat” (i.e., a channel which passes all spectral components with approximately equal gain and linear phase). IN other words, coherence bandwidth is the range of 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 than the bandwidth of the transmitted signal, then the received signal will undergo flat fading. This type of fading is historically the most common type of fading described in the technical literature. In flat fading, the multipath structure of the channel is such that the spectral characteristics of the transmitted signal are preserved at the receiver. However the strength of the received signal changes with time, due to fluctuations in the gain of the channel caused by multipath. The characteristics of a flat fading channel are illustrated [below].

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s(t)

s(t)

h(t,τ) t

0

0τ

TS

S(f) ∫∫

r(t) t

∫∫

τ<
R(f) f

fc

t TS+τ

0

H(f) f

fc

r(t)

h(t,τ)

∫∫

f fc

Flat fading channel characteristics 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 fading 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 instantaneous 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

BS « BC and

TS » στ where TS is the reciprocal bandwidth (e.g. symbol period) and BS is the bandwidth, respectively, of the transmitted modulation, and στ and BC are the rms delay spread and coherence bandwidth, respectively, of the channel.”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, 167, 170-176, 188-189.]

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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 received at a moving vehicle when an unmodulated carrier is radiated by the base station transmitter. The question now arises as to the adequacy of this channel description when real signals, which occupy a finite bandwidth, are radiated. It is clear that in practice we need to consider the effects of multipath propagation on these signals and to illustrate the point we consider the case of two frequency components within the message bandwidth. If these frequencies are close together then the different propagation paths within the multipath medium have approximately the same electrical length for both components and their amplitude and phase variations will be very similar. In other words, although there will be fading due to multipath, the two frequency components will behave in a very similar way. More generally, provided the message bandwidth is sufficiently small, all frequency components within it behave similarly and flat fading is said to exist. As the frequency separation increases, however, the behavior at one frequency tends to become uncorrelated with that at the other frequency because the phase shifts along the various paths are different at the two frequencies. The extent of the decorrelation depends on the spread of time delays since the phase shifts arise from the excess path lengths. For large delay spreads the phases of the incoming components can vary over several radians even if the frequency separation is quite small. Signals which occupy a bandwidth greater than that over which spectral components are affected in a similar way will become distorted since the amplitudes and phases of the various spectral components in the received version of the signal are not the same as they were in the transmitted version. The phenomenon is known as frequency-selective fading and appears as a variation in received signal strength as a function of frequency. In analogue FM systems the frequency selectivity limits the maximum usable frequency deviation for a given amount of signal distortion. The bandwidth over which 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 method of gaining further insight into the propagation mechanism since the changing time of arrival suggests the possibility of associating each delayed version of the transmitted signal with a physical propagation path. However, it is not possible to distinguish between different paths merely by considering the difference between the time of arrival, the spatial direction of arrival also has to be taken into account. If we consider only single-scattered paths then all scatterers associated with a certain path length can be located on an ellipse with the transmitter and receiver at its foci. Each time delay between transmitter and receiver defines a confocal ellipse as shown in [the figure below]. If we consider scatterers located at A, B and C, then we can distinguish between paths TAR and TBR, which have the same angle of arrival, by their different time delays and between TAR and TCR which have the same time delay, but there are different angles of arrival.

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Propagation Basics

B

τ+∆τ τ

A

.

Tx

Line of sight

C

.

Rx

Direction of motion

Path of Geometry for Single Scattering

Transmitted Pulse

Echoes

t=0

t Overall response

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

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.

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An important and instructive feature of [the above figure] is that for a particular receiver location, a suitably scaled diagram 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 digital 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 [Parsons, David. 1996. The Mobile Radio Propagation Channel. London. John Wiley & Sons Ltd. pp. 44, 162-164, 190-195.] [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.] 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 channel, a channel 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 the symbol period of the transmitted signal. This causes frequency dispersion (also called time selective fading) due to Doppler spreading, which leads to signal distortion. Viewed in the frequency domain, signal distortion due to fast fading increases with increasing Doppler spread relative to the bandwidth of the transmitted signal. Therefore, a signal undergoes fast 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

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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 amplitudes, phases and time delays of any one of the multipath components vary faster than the rate of change of the transmitted signal. In practice, fast fading only occurs for very low data rates.”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, 167, 170-176, 188-189.] 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 baseband signal s(t). In this case, the channel may be assumed to be static over one or several reciprocal bandwidth intervals. in the frequency domain, this implies that the Doppler spread of the channel is much less than the bandwidth of the baseband signal. 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 signaling determines 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 small-scale fading. It should be emphasized that fast and slow fading deal with the relationship between the time rate of change in the channel and the transmitted signal, and not with the propagation path loss models.”25

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Propagation Basics

[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.] 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, limits the coverage of mobile systems when the mobile is moving in a multipath environment. It is not such a dominant factor in hand held mobile usage but, in low-field-strength areas, it can be detected by variations in noise levels as the receiver is moved.”1

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

2 r -   r ⁄ σ 2 exp  – -------- p(r) =   2σ 2     0

(0 ≤ r ≤ ∞) (r < 0)

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 exceed a specified value R is given by the corresponding cumulative distribution function (CDF).

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Propagation Basics

Typical Simulated Rayleigh Fading at the Carrier Receiver Speed = 120 km/hr 10

Signal Level (dB about rms)

5 0 -5 -10 -15 -20

λ/2

-25 -30 -35 -40

0

50

100

150

200

250

Elapsed Time (ms) R P ( R ) = Pr ( r ≤ R ) =

∫ 0

 R2  p ( r ) dr = 1 – exp  – ----------  2σ 2

The mean value rmean of the Rayleigh distribution is given by

∞ r mean = E [ r ] =

∫ rp( r )dr = σ

π --- = 1.2533σ 2

0 and the variance of the Rayleigh distribution is given by

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2 σ r , which represents the ac power in the signal envelope

Propagation Basics

∞ 2 2 2 σr = E [ r ] – E [ r ] =

∫

2 2 σ π r p ( r ) dr – ---------2

0 2 2 2 σr = σ  2 – π --- = 0.4292σ   2 The rms value of the envelope is the square root of the mean square, or

2σ .

The median value of r is found by solving

r median 1--- = 2

∫

p ( r ) dr

0 and is

r median = 1.177σ 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

Received signal envelope voltage r (volts) 65 of 76

Propagation Basics

OBS light clutter, Site C LOS heavy clutter, Site E LOS light clutter, Site D

% Probabilty Signal Level < Abscissa

Log-normal σ=7.5 dB Rayleigh Rician K=6 dB

Signal Level (dB about median) CDF (Cumulative Distribution Function) “Two-Ray Rayleigh Fading Model: Clark’s model and the statistics for Rayleigh fading are for flat fading conditions and do not consider multipath time delay. In modern mobile communication systems with high data rates, it has become necessary to model the effects of multipath delay spread as well as fading. A commonly used multipath model is an independent Rayleigh fading 2-ray model (which is a specific implementation of the generic fading simulator shown in [the figure below].

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Propagation Basics

Signal under test

s(t)

τ1 ... τΝ Rayleigh Fading Simulator

a0

Rayleigh Fading Simulator

a1

Rayleigh Fading Simulator

aN

∑

r(t)

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

[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

hb ( t ) = α 1 exp ( jΦ 1 )δ ( t ) + α 2 ( 1 ) exp ( jΦ 2 ( 1 ) )δ ( t – τ )

input

∑

output

α1exp(jφ1) τ

α2exp(jφ2) Two-ray Rayleigh Fading Model.

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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

hb ( t ) = α 1 exp ( jΦ 1 )δ ( t ) By varying τ, it is possible to create a wide range of frequency selective fading effects. The proper time correlation properties of the Rayleigh random variables α1 and α2 are guaranteed by generating two independent waveforms, each produced from the inverse Fourier transform of the spectrum described [in the section entitled “Simulation of Clarke and Gans Fading Model”].”25 [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.] [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.] 4.8

Ricean Fading Distribution

For an interesting and fun look at Ricean Fading check out the Wireless Communications Web Page by Jean-Paul M.G. 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 small-scale fading envelope distribution is Ricean. In such a situation, random multipath components arriving at different angles are superimposed on a stationary dominant signal. At the output of an envelope detector, this has the effect of adding a dc component 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 with many weaker multipath signals gives rise to the Ricean distribution. As the dominant signal becomes weaker, the composite signal resembles a noise signal which has an envelope that is Rayleigh. Thus, the Ricean distribution degenerates to a Rayleigh distribution when the dominant component fades away. The Ricean distribution is given by

2 2  –( r + A ) --------------------------  Ar  r p ( r ) =  ------ e 2σ 2 I 0  ------  σ 2  σ2 0 

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for (A≥ 0, r ≥ 0) for (r < 0)

Propagation Basics

.

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

2 A --------K ( dB ) = 10 log dB 2 2σ 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 [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.]

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 result is a multiplicative interaction between the carrier frequencies which can produce signals at all combinations of sum and difference frequencies. The energy apportioned to these spurious signals (intermodulation or IM products) represents a loss in signal energy. In addition, if these IM products appear within the bandwidth region of these or other signals, the effect 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 derived. 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 signal 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]:

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Propagation Basics

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, 2A3B...

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. Prentice-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 an information bearing signal must be transmitted to a destination. "Good Linearity" is synonymous with "Low Distortion". In this paper, the type of linearity being discussed is primarily amplitude linearity, although it is equally valid to consider phase linearity. Examples of signals that require linearity are: human voice, multilevel data signals, a microwave baseband signal composed of FDM channels, or RF signals which are modulated (at least partly amplitude modulated) by such signals. M-QAM microwave transmitters are simultaneously phase and amplitude modulated by multilevel data signals, and depending on the number "M" require some degree of linearity from the circuits which amplify or process the microwave signals. For example, 64-QAM requires much more perfect linearity than 4-QAM, in fact, 64-QAM requires linearity in the 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 characterized by multiple signals, or a composite signal with multiple frequency components, where the components mix with each other (intermodulate) in an imperfectly linear electrical circuit and as a result produce undesired signal components (distortion). By way of comparison, the more familiar Harmonic Distortion only requires one signal or signal component to be present, 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 that is supposed to be linear. However, a simple mathematical analysis will show that odd order terms of the transfer function of a non-linear circuit will cause the in-band distortion products referred to as IMD, while the even order terms normally cause Harmonic Distortion products which, in many cases, fall out of the frequency band or off channel, and thus may be

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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.com/ w3/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 spreading and consequent overlap of individual pulses to the degree that the receiver cannot reliably distinguish between changes of state, i.e. , between individual signal elements. Note 1: At a certain threshold, intersymbol interference will compromise the integrity of the received data. Note 2: Intersymbol interference attributable to the statistical nature of quantum mechanisms sets the fundamental limit to receiver sensitivity. Note 3: Intersymbol interference may be measured by eye patterns. 2. Extraneous energy from the signal in one or more keying intervals that interferes with the reception of the signal in another keying interval. 3. The disturbance caused by extraneous energy from the signal in one or 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. Directory: http://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, such as CDMA over AMPS in North America, or 900 MHz CDMA over TACS as in China, it is necessary to anticipate and minimize 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 if it is overlaid on a TACS system in the same frequency band. All technologies have the same set of contributing factors. Some key variables for the interfering transmitter are: ERP (directed towards the receive antenna), Transmit nominal power and Sideband splatter. A few key variables for the receiver which might be interfered with are: IM (intercept point) of the receiver, 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. Corrective action can be in the form of improving the filtering at the receive site, or it can be related to any of the other variables noted above; improve Tx splatter, adjust ERP, frequency planning, etc. In all cases, the potential for interference, and the best corrective action, are site specific. There is no generic solution and site engineering is required. Recommendations for corrective action is addressed where deemed appropriate.

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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 mitigate the problem.”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.] 5.5

Adjacent Channel Interference - Land-Mobile

“The origin of adjacent channel interference is shown in [the figure below]. The figure portrays two transmissions occurring on adjacent channels. Inevitably some signal components spread beyond the channel boundaries and can be intercepted by receivers tuned to the adjacent channel. When the signal strength of the adjacent channel transmission becomes so large that the power intercepted by an on-channel receiver approaches that of the desired on-channel signal source, interference occurs. The ratio of the signal strengths of the two transmissions at the point at which interference is first noted is called the adjacent channel interference protection ratio (ACIPR).”8

Relative signal strength

ACIPR Desired signal Interfering signal Idealized receiver selectivity Adjacent channel

Desired channel

Frequency

Origin of Adjacent Channel Interference [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 medium and it can often be improved by use of techniques which successfully exploit these characteristics, for example by using an optimum modulation method. As far as the communications engineer is concerned the important characteristics are the frequency and time responses of the channel and the magnitude and nature of the noise. The former characteristics have been discussed in earlier chapters; we now deal with the problem of noise. There are two basic reasons for a study of noise. Firstly there is a need to gain an understanding of the nature of the noise in order to devise methods by which it can be characterized. Knowledge of the sources of noise may also lead to methods by which it can be suppressed. Secondly

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there is a vital need to be able to predict the performance of communication systems that have to operate in noisy environments. 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 Gaussian noise. It can be detected at frequencies up to 7 GHz. ...The characterization of Gaussian noise is fairly straightforward, but impulsive noise is a quite different matter. There are several potential sources of impulsive noise which could play a role in mobile communication systems. The radio is often installed in a vehicle which is itself a source of noise due to its own ignition and other electrical systems and the vehicle commonly operates in urban, suburban and industrial areas where it is close to other noisy vehicles. There are various extraneous sources of noise such as power lines and neon signs, industrial noise from heavy current switches, arch welders and the like, and noise from various items of domestic electrical equipment. These may or may not be significant contributors in any specific situation. In practice the level of man-made noise varies markedly with location and time, so from a limited series of observations it is only possible to derive typical values and obtain some estimate of the variability. In urban areas it is generally conceded that vehicle ignition noise is a major source of interference to VHF mobile radio systems. Throughout the literature, the terms Gaussian and impulsive are used to denote two distinct types of noise. Only the power spectral density of Gaussian noise is affected by linear filtering; the probability density function remains Gaussian. The in-phase and quadrature components of narrowband Gaussian noise are independent, as are the envelope and phase distributions. For any other type of noise, both the power spectral density and the probability density function are changed by filtering; the in-phase and quadrature components, although uncorrelated, are not independent. In the general case, the envelope and phase of random noise are independent, the phase being uniformly distributed in the interval (0,2π). In general terms we may consider an impulse as a transient that contains an instantaneous uniform spectrum over the frequency band for which it is defined, a uniform spectrum requiring that all frequencies are present, of equal strength and in phase over the frequency band. Impulsive noise is the combination of successive impulses which have random amplitudes and random time-spacings; these factors may sometimes be such that adequate separation of successive impulse responses by a narrowband receiver is not possible. Thermal noise can produce an annoying “hiss” on a voice channel, but does not significantly degrade intelligibility unless its RMS value is relatively high. Impulsive noise causes clicks, which, although disturbing, may be tolerable. The degradation of the channel is not easily defined and is usually based on some kind of subjective assessment, although the quasipeak measurement, which will be mentioned later, has been shown to have some correspondence with the subjective annoyance on a.m. radio and television. In some ways digital transmissions are easier to deal with since the bit error rate (BER) provides a good quantitative indication of how well the communication system reproduces the transmitted information. The BER produced by thermal noise is readily available in several textbooks. As far as impulsive noise is concerned we will discuss the methods that exist for expressing the properties of the noise, and to what extent these methods 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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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 with the impedance match of the antenna feed point to the feed or transmission line. The antenna input impedance establishes a load on the transmission line as well as on the radio link transmitter and receiver. To have RF energy produced by the transmitter radiated with minimum loss or the energy picked up by the antenna passed to the receiver with minimum loss, the input or base impedance of the antenna must be matched to the characteristics of the transmission line.”13 VSWR = Vmax/Vmin [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.] Watts to dBm Conversion32:

6.2

Power in dBm = 10 log ( watts × 1000 )

Power in Watts =

 dBm ------------  10  10 -----------------------1000

[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

dBd = dBi – 2.14

dBi = dBd + 2.14

6.4

Speed of Light : Wavelength

c = 3 × 10

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λ = c⁄f λ = wavelength (m) c = speed of light (m/s) f = frequency (Hz) 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. Motorola, 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. Directory: 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. American 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 089006-755-4. 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. Revision 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.

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20.

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

21.

Okumura, Y., Ohmori, E., Kawano, T., Fukada, K. 1968. Field strength and ITs Variability in VHF and UHF LandMobile 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, 162164, 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. Antennas 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 Documentation. 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 Documentation. Directory: http://www.cig.mot.com/Org.new/TED/cellglos.html. Version 1.

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