radiowave propagation

I

RADIOWAVE PROPAGATION This chapter is a presentation of the basic principles and algorithms related to radiowave

propagation used in radio-relay transmission. Both loss and attenuation algorithms as well as fade prediction models for different fading mechanisms are presented and discussed. The

chapter also includes a presentation of the basic concepts of main propagation mechanisms, Fresnel zone, equivalent and true Earth radii and the decibel scale. Diversity, hardware failure

and passive repeaters are also presented.

TABLE OF CONTENTS

1 The decibel 1 1.1 A relative comparison 1 1.2 Some motivations for using decibels 1 1.3 Absolute comparisons 1 1.4 The comparison of field quantities 2 1.5 Power and field quantity ratios 3 2 The main propagation mechanisms 3 2.1 Propagation along the earths surface 4 3 The Fresnel zone and clearance 4 3.1 Definition 4 3.2 The Fresnel ellipsoid 4 3.3 Clearance 5 4 Equivalent and true earth radii 6 4.1 Earth-radius factor 6 4.2 Comparing the equivalent and true Earth surface 7 5 Prediction models 7 6 The prediction cycle 8 7 The loss/attenuation block 8 7.1 Free-space loss 8 7.1.1 Definition 8 7.1.2 Free-space loss between two isotropic antennas 9 7.2 Atmospheric gases 10 7.2.1 Definition 10 7.2.2 The troposphere 11 7.2.3 Chemical composition 11 7.2.4 Absorption peaks 11 7.2.5 Calculating total gas attenuation 11 7.2.5.1 Oxygen (dry air) 12 7.2.5.2 Water vapor 13 7.2.5.3 Total gas attenuation 15 7.3 Reflection 16 7.3.1 Ground reflection interference 16 7.3.2 The problems of handling reflection 17 7.3.3 Reflection coefficient 18 7.3.4 The Fresnel reflection coefficient 18 7.3.5 Divergence factor 18 7.3.6 Correction factor 19 7.3.7 Rough estimation of the total reflection coefficient 19 7.3.8 Calculation of the position of the reflection point 20 7.3.9 Optimum height difference 22

II

7.4 Precipitation 23 7.4.1 Types of precipitation 23 7.4.2 Precipitation: now 24 7.4.3 Precipitation: hail 24 7.4.4 Precipitation: fog and haze 25 7.4.5 Precipitation: rain 25 7.4.6 Cumulative distribution of rain 25 7.4.7 Obtaining Rain Intensity (the former ITU-R model) 25 7.4.8 Rain zones - diagram 26 7.4.9 Obtaining rain intensity (current ITU-R model) 26 7.4.10 The calculation of the specific rain attenuation 29 7.4.11 Calculating total rain attenuation 32 7.4.12 Calculating total rain attenuation for 0.01% 33 7.5 Obstruction - diffraction 33 7.5.1 Definition 33 7.5.2 Knife-edge obstructions 34 7.5.3 Knife-edge loss curve 35 7.5.4 Typical knife-edge losses 36 7.5.5 Single-peak method 36 7.5.6 Triple-peak method 37 7.5.7 Smoothly spherical earth 40 7.5.8 Typical losses resulting from smoothly spherical earth 41 7.5.9 Clearance and path geometry 41 7.5.9.1 The Earth bulge 41 7.5.9.2 Path geometry 42 7.5.9.3 The height of the line-of-sight 43 7.5.9.4 Clearance of the LOS 43 7.5.9.5 Antenna height 43 7.5.9.6 Obstacle penetration 44 7.5.10 Vegetation 44 7.6 The Link Budget 44 7.6.1 Path loss 45 7.6.2 Fade margin 45 7.6.3 Power diagram 46 7.6.4 Effective fade margin 46 8 The fading block 47 8.1 Definition 47 8.2 General cause 47 8.3 General classification 47 8.4 Classification based on source 48 8.5 The concept of outage 48 8.6 Rain fading (current ITU-R model) 48 8.6.1 Calculation of the fade margin based on a yearly basis 48 8.6.2 Outage due to rain fading - annual basis 49 8.6.3 Transformation between yearly and worst month basis 50 8.6.3.1 From yearly basis to worst month 50 8.6.3.2 From worst month to yearly 51 8.6.4 Presentation of the rain fading models in diagram form 51 8.7 Multipath fading 52 8.7.1 Flat and frequency selective fading 52 8.7.2 The effects of multipath propagation 53 8.7.3 Measures taken against multipath fading 54 8.8 Flat fading (former ITU-R model): small percentages of time 54 8.8.1 Introduction 54 8.8.2 Fade occurrence factor 55 8.8.3 Flat fading and quality (error performance) 55 8.8.4 Estimation of the geoclimatic factor 55 8.8.5 Inland Links 55 8.8.5.1 Antenna altitude coefficient 56 8.8.5.2 Latitude coefficient 57

III

8.8.5.3 Longitude coefficient 57 8.8.5.4 Climatic factor pL 57 8.8.6 Coastal Links 58 8.8.6.1 Coastal links over/near large bodies of water 58 8.8.6.2 Coastal links over/near medium-sized bodies of water 59 8.8.6.3 Links at other regions 59 8.8.7 Link and terrain parameters overview 60 8.8.7.1 Estimation of the path inclination 60 8.8.8 Outage due to flat fading 61 8.8.9 Range of values for the climatic factor pL 61 8.9 Flat fading (current ITU-R model): small percentages of time 62 8.9.1 Method for detailed link design 62 8.9.1.1 Geoclimatic factor 62 8.9.1.2 Parameters 62 8.9.1.3 Outage due to flat fading 64 8.9.2 Method for quick link design 64 8.9.2.1 Geoclimatic factor 64 8.9.2.2 Outage due to flat fading 65 8.9.3 Method for small percentage of time - conclusion 65 8.9.4 Method for all percentages of time 66 8.9.5 Range of validity for the flat fading method 68 8.10 Reduction of cross-polar discrimination 69 8.10.1 XPD outage due to multipath propagation 69 8.10.2 XPD outage due to precipitation 71 8.11 Outage due to frequency selective fading 72 8.11.1 General aspects 72 8.11.2 The prediction model 73 8.12 Refraction fading 75 9 Diversity 76 9.1 Basic concepts 76 9.2 The definition of the improvement factor 77 9.3 Improvement factor for space diversity 78 9.4 Improvement factor for frequency diversity 78 9.5 The calculation of outage when employing diversity 79 9.6 Prediction of outage using diversity 79 9.6.1 Space diversity 79 9.6.2 Frequency diversity 81 9.6.3 Space and frequency diversity with two receivers 81 9.6.4 Space and frequency diversity with four receivers 81 10 Prediction of total outage 82 11 Hardware failure 83 11.1 The calculation of the radio-link systems MTBF 83 11.2 Non-redundant systems 84 11.3 Redundant systems 85 11.4 Hardware failure per path 86 12 Passive repeaters 87 12.1 The basic concepts 87 12.2 Path calculation when using passive repeaters 88

RADIOWAVE PROPAGATION

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1 The decibel

1.1 A relative comparison It is usual in radio technique that two different values or entities are compared with one another. The comparison between two levels (expressed in power) by taking the ratio is a classical example. The decibel is a measure of the relationship between two power levels. Decibel is abbreviated as dB and is defined as follows

[ ]2

110log.10dB P

PA = (1)

where P1 and P2 are the power levels being compared.

Note that the decibel is a measure of a relationship and has no actual physical significance. The decibel is therefore not a measure of a physical entity.

One decibel corresponds approximately to the smallest variation in sound volume that can be discerned by the human ear.

1.2 Some motivations for using decibels Some of the motivations behind the widespread use of the decibel are:

The decibel is convenient to use since the direct relationship between radio-related power levels covers a wide range of numerical values. The logarithmic nature of the relationship between two power-levels results in values that is easy to handle.

Addition or subtraction operations can be easily performed on logarithmic values, simplifying the handling of amplification and attenuation.

The manner in which human sensory organs perceive differences in the sensory impressions of varying intensity that they receive is in fact logarithmic.

1.3 Absolute comparisons The decibel concept defined above is related to the quotient of two values, and provides no information as to the absolute value of these entities. An absolute comparison between two power levels can however be performed if a reference value is employed, for example the W (Watt) or mW (milliWatt), referred to respectively as dBW and dBm.

RADIO TRANSMISSION NETWORK AND FREQUENCY PLANNING

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[ ]Watt1

log.10dBW 10PA = (2)

where P is the power in Watt.

[ ]milliWatt1

log.10dBm 10PA = (3)

where P is the power in milliWatt.

Since,

10dBW

10 W1

=

P (4)

And

10dBm

10mW 1

=

P (5)

the result obtained following division is

=10

dBm-dBW

10 W1mW 1

(6)

Or

=10

dBm-dBW3

10 W1 W1

(7)

Giving

10dBm-dBW3 = (8)

Or

30dBWdBm += (9)

1.4 The comparison of field quantities The decibel concept can be generalized to also include the comparison between field magnitudes. The term field quantity refers to a quantity whose square is proportional to power. Examples of field quantities are electrical voltages, currents and field strengths.


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The application of the decibel concept results in

[ ] ( )( )

=

2

110 quantity Field

quantity Fieldlog20dBA (10)

1.5 Power and field quantity ratios Power and field quantities, lying between 103 and 10-3 are expressed in their equivalent decibel values in Table 1.

Power ratios

dB Field quantity ratios

dB

1 000=103

30

1 000=103

60

100=102

20

100=102

40

10=101

10

10=101

20

9

9.5

9

19

8

9

8

18

7

8.5

7

17

6

8

6

16

5

7

5

14

4

6

4

12

3

5

3

9.5

2

3

2

6

1

0 1 0

1/2 -3

1/2 -6

1/4 -6

1/4 -12

1/8 -9

1/8 -18

1/10=10-1 -10

1/10=10-1 -20

1/100=10-2 -20

1/100=10-2 -40

1/1000=10-3 -30

1/1000=10-3 -60

Table 1: Power and field ratios.

2 The main propagation mechanisms Most of the propagation mechanisms are affected by climactic conditions. When calculating the transmission quality and availability of radio networks, the significance of the various mechanisms varies as a function of the radio spectrum. The following propagation mechanisms may however be considered as the most notable:

Free-space

Diffraction


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Refraction

Absorption

Scattering

Reflection

2.1 Propagation along the earths surface An electromagnetic wave traveling close to and along the surface of the earth is affected by the following factors:

Electrical properties of the earths surface

Earths curvature

Atmosphere

Earths topography

Vegetation

3 The Fresnel zone and clearance Expressions for the calculation of the earth bulge, the height of the line-of-sight, the clearance of the line of sight, the antenna heights and obstacle penetration are given in section 7.5.9.

3.1 Definition Fresnel zones are specified employing an ordinal number that corresponds to the number of half-wavelength multiples that represents the difference in radio wave propagation path from the direct path. The first Fresnel zone is therefore an ellipsoid whose surface corresponds to one half-wavelength path difference and represents the smallest volume of all the other Fresnel zones.

The first Fresnel zone contains almost all the energy that is transmitted between the antennas and is therefore of great significance in the calculation of the attenuation caused by obstructing bodies.

3.2 The Fresnel ellipsoid The Fresnel zone is an ellipsoid having its focal points at the antenna points A and B as illustrated in Figure 1. The radius of the first Fresnel zone, R, is a function of the distance between A and B, the distance between any point M on the ellipsoid and the frequency. The radius of the first Fresnel zone is indirectly proportional to frequency and the higher the frequency the narrower the Fresnel zones.


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! dA= Distance from antenna A to point M, km

! dB= Distance from antenna B to point M, km

! R = Radius of the Fresnel zone at point M, m

! dA + dB = d = Distance between antennas A and B, km

MA BR

dBdA

! f = Frequency, MHz

( )df

dddR AA

= 547( )

dfdddR AA

= 3217 .

GHz

Figure 1: Fresnel zone between two stations located on an equivalent earth surface (the ray beam is straight).

3.3 Clearance The refractive properties of the atmosphere are not constant. The variations of the refraction index in the atmosphere (expressed by the earth-radius factor k) may force terrain irregularities to totally or partially intercept the Fresnel zone. Clearance can be described as any criterion to insure that the antenna heights are sufficient so that in the worst case of refraction (for which k is minimum!) the receiver antenna is not placed in the diffraction region.

hchc = LOS-clearance

Figure 2: The clearance of the line of sight.


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The direct path between the transmitter and the receiver needs a clearance above the ground or any obstruction of at least 60% of the radius of the Fresnel zone in order to insure free-space propagation. Clearance values have to fit the local climate conditions.

Clearance can be considered by applying clearance criteria that are climate dependent or by properly handling diffraction-diffraction fading (k-type fading).

Advices:

1) The higher the frequency the smaller the Fresnel zone and consequently more vulnerable to non-LOS effects (object attenuation).

2) Low k-values lower the LOS (demand higher antenna heights) but offer better protection against interference from other stations. Higher k-values give higher LOS (demand lower antenna heights) but expose the link to interference from other stations.

3) The most common discrepancy arises when the radius of the first Fresnel zone is not compensated for its vertical projection. The more inclined the path is the more correction is required.

4 Equivalent and true earth radii

4.1 Earth-radius factor In simple terms, one can describe the ray beam between two antennas by employing an imagined propagation path that directly links the two antennas. In free-space this path would describe a straight line, a so-called optical line-of-sight.

If instead, the antennas are placed on a spherical body surrounded by an atmosphere (as in the case for the earth), wave propagation will be affected by variations in atmospheric refractive index as the wave travels through the various atmospheric layers. The ray beam will now not follow the optical line-of-sight, but will describe a curved line between the two antennas. The form of the curve will vary as a function of variations in the refractive index of the atmosphere traversed by the wave.

To simplify the description of this curved ray beam, the concept of equivalent earth surface having an equivalent earth radius, Re, has been introduced. Defined as follows:

RkRe = (11)


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where

k = Earth-radius factor R = True earth radius (6.37106 m)

The earth-radius factor is a function of the refractive index gradient. For normal atmosphere (i.e., atmosphere in which the refractive index gradient decreases linearly with altitude), the k-value is 4/3 if the refractive index gradient is -39 N-units/km.

NOTE: k-values are determined by employing the diagram in Chapter 15-2 after selecting the appropriate value of the refractive gradient in Chapter 15-3.

4.2 Comparing the equivalent and true Earth surface The equivalent earth surface is that earth surface that would be required for the ray beam between the antennas to lie along a straight line, see Figure 3. A beam that travels outside of the optical line-of-sight must bend downwards in order to become a straight line, which is equivalent to enlarging the earths radius, i.e. reducing the curvature of the earth. The earth-radius factor, k, describes exactly the degree to which the earths radius would have to be changed in order that the ray beam describe a straight line.

True earth surface

Optical line-of-sightTrue ray beam

R

Equivalent ray beam

Equivalent earth surface

Optical line-of-sight

Re = k R

Figure 3: The equivalent and the true earth surface.

5 Prediction models Prediction models for the purpose of performing fading prognoses are almost always empirical (comes from the Greek word empeiria meaning experience), i.e., they are not founded on theoretical considerations but are only built upon observation and experience.


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Empirical models are arrived as the result of the application of mathematical regression techniques on measurement data and therefore result in a relationship that describes a variables dependency under certain given conditions.

Empirical prediction models often provide a fair description of the fading process for distances and frequencies that lie within the data-ranges for which measurements have actually been collected. Their application to other distances and frequency ranges may, on the other hand, result in significant error.

6 The prediction cycle Figure 4 of Chapter 2 (Radio-Relay Transmission Overview) illustrates the four blocks of the prediction cycle: loss/attenuation, fading, frequency planning and quality and availability. In this chapter, two blocks will be studied, namely the loss/attenuation and the fading blocks.

7 The loss/attenuation block The loss/attenuation block is composed of three main contributions: branching, propagation, and others.

The branching contribution comes from the hardware required to delivery the transmitter/receiver output to the antenna, for instance, wave-guides as well as splitters and attenuators.

The propagation contribution comes from the losses due to the Earth atmosphere and the terrain, for instance, free-space as well as gas, precipitation (mainly rain), ground reflection, and obstacle.

The others contribution has a somewhat unpredictable and sporadic character, for instance, sandstorm as well as fog, clouds, smoke, and moving objects crossing the path. In addition, poor equipment installation and unsuccessful antenna alignment may give rise to unpredictable losses. The others contribution is normally not calculated but it can be accounted in the planning process as an additional loss and then being part of the fade margin.

7.1 Free-space loss

7.1.1 Definition Free-space wave propagation implies that the effects caused by disturbing objects and other obstacles that are located at sufficiently long distances are assumed to be negligible.


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7.1.2 Free-space loss between two isotropic antennas Electromagnetic waves are attenuated when propagating between two points geometrically separated from each other. The attenuation is inversely proportional to the square of distance and gives the free-space loss that stands for most of the total attenuation caused by wave propagation effects. Free-space loss is always present and it is dependent on distance and frequency. The free-space loss between two isotropic antennas is currently derived from the relationship between the total output power from a transmitter and the received power at the receiver. Its value is illustrated in. The resulting expression is

dAbf

=

4log20 (12)

where

Abf = Free-space loss, dB d = Distance from the transmitting antenna, km

= Wavelength, m Following the transformation of wavelength into frequency (c=2.99792500108 m/s) and entering of the actual units, the following expression is attained

fdAbf log20log205.92 ++= (13) where

Abf = Free-space loss, dB d = Distance from the transmitting antenna, km f = Frequency, GHz

The free-space loss (dB) as a function of distance (km) is illustrated in Figure 4 in the frequency range 1 to 50 GHz.

1 GHz

15

5

203040

10

50

0 10 20 30 40 50

Distance, km

-170

-160

-150

-140

-130

-120

-110

-100

-90

-80

Free

-spa

ce lo

ss, d

B

Figure 4: The free-space loss as a function of distance for eight different frequencies.


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Advices:

1) If the distance is doubled while maintaining constant frequency, the free-space loss is increased by 20log 2= 6 dB. The same applies to a doubling of the frequency while maintaining a constant distance. In other words, an additional attenuation of 6 dB will be caused for every doubling of either the distance or the frequency.

2) Comparing to other kind of loss, free-space loss gives the major contribution. Expressed in the GHz range, the free-space loss has a minimum of approximately 92 dB. If it is expressed in the MHz range the minimum is 92 dB 60 dB = 32 dB (1 GHz = 1000 MHz 20log 1000 = 60 dB).

3) This relatively small increase of free-space attenuation by only 6 dB with increased distance might give the impression that long paths can easily be obtained by simply increasing the transmitter output power, or the receiver sensitivity or the antenna gain. This is not so easy to accomplish because the total path attenuation is also determined by other negative contributions, for example gas attenuation.

4) Cell-planners commonly refer to half-wave dipole antenna gains. Comparing to the above presentation for which the gain of an ideal isotropic antenna is 1 (0 dB), the gain of a half-wave dipole antenna is 1.64 (2.15 dB). Considering both stations of a radio link, the difference between free-space loss comparison using isotropic and half-wave dipole antennas is about 4.30 dB.

7.2 Atmospheric gases

7.2.1 Definition The atmosphere, up to an altitude of 30-40 km, consists of two layers:

Troposphere

Stratosphere

An often sharply demarcated transition layer referred to as the tropopause separates the troposphere and stratosphere.

It is within this troposphere in which all weather-related processes (precipitation, cloud formation, electrical storms, etc.) arise.

The troposphere lies at an altitude of 10 km over the earths medium latitudes and somewhat less over its poles. At the equator, the troposphere lies at an altitude varying between 16 and 18 km above the earths surface.


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7.2.2 The troposphere The troposphere consists of approximately 9/10 of the earths atmospheric mass, and aside from variations in moisture content, density and temperature, its constitution is more or less constant throughout its volume. This layer contains just a few notable elements and their compounds, which are of significance in the propagation of radio waves.

7.2.3 Chemical composition Nitrogen and oxygen molecules account for approximately 99% of the total volume. From the propagation point of view, it is suitable to consider the atmosphere as being a mixture of two gases, dry air and water vapor.

The chemical composition of the earths atmosphere is illustrated in Table 2.

Chemical Composition of the Earths Atmosphere, % N2 O2 Ar CO2 Ne He Kr Xe H2

78.09 20.93 0.93 0.03 0.00018 5.210-4 1.010-4 8.00-6


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7.2.5.1 Oxygen (dry air) Two atmospheric parameters are involved in the calculation of the specific attenuation of oxygen: the atmospheric pressure and the temperature.

The atmospheric pressure is normalized to the value at see level (1013 hPa) by

1013prp = (14)

where rp is the normalization factor and p (hPa) the pressure of the atmosphere at a certain altitude. A normal atmosphere is the atmosphere where the pressure at the see level is 760 mmHg, which corresponds to 1 atm or 1013.25 hPa. The non-SI unity is bar (100 kPa).

The temperature is normalized to a mean value of 15 C by

( )trt += 273288

(15)

where rt is the normalization factor and t is the temperature (C).

The following parameters are determined:

( )[ ]115663.15106.05050.01 e7665.6

=tr

tp rr (16)

( )[ ]115496.08491.04908.02 e8843.27

=tr

tp rr (17)

( )5.3lnln

1

2

=

a (18)

1

4

a

b = (19)

( ) ( )[ ]trtpO rr = 15280.26032.14954.1' e128.254 (20) Finally, the specific attenuation due to oxygen for frequencies equal or lower than 54 GHz is given by


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( )( )

32222

32

1054

54'3429.036.0

34.7

+

++

= fbf

brrf

rra

O

tp

tpO

(21)

where f is the frequency and the other parameters are defined earlier.

7.2.5.2 Water vapor In the calculation of the specific attenuation due to water vapor, one more atmospheric parameter is required: water vapor content (g/m3).

NOTE: Water vapor content can be selected from the charts included in Chapter 15-6.

However, in combination with a given temperature, the water-vapor content selected from the charts might not be physically consistent with the appropriate value correspondent to the vapor saturation pressure. In other words, the water-vapor pressure cannot exceed the vapor saturation pressure at the temperature considered. To avoid this common mistake, one more atmospheric parameter has been introduced in the step-by-step calculation: relative humidity (%).

The vapor saturation pressure, ps, is solely dependent on the temperature and is given by

+

=97.240

502.17

e1121.6 tt

sp (22)

The relative humidity of the atmosphere, RH, is given as the ratio between the water vapor pressure in the atmosphere, pH2O, and the vapor saturation pressure, ps.

1002 =s

OH

ppRH (23)

Solving the above expression for the vapor pressure it is obtained

sOH pRHp =1002

(24)

The water vapor content (water-vapor density) can be derived from the general gas equation. It is given by


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15.2737.216 2

+=

t

p OH (25)

The following parameters are determined

+= 0061.09544.0 69.01 tpw rr (26)

+= 0067.095.0 64.02 tpw rr (27)

+= 0059.09561.0 67.03 tpw rr (28)

+= 0061.09543.0 68.04 tpw rr (29)

+= 006.0955.0 68.05 tpw rr (30)

( )( )2

2

22 235.22235.221

+

+=ffg (31)

( )( )2

2

557 5575571

+

+=ffg (32)

( )( )2

2

557 5575571

+

+=ffg (33)

( )( )2

2

752 7527521

+

+=ffg (34)

Finally, the specific attenuation of water vapor for frequencies equal or lower than 50 GHz is given by

[ ]{ } 425.25.8322 101076.11013.3 ++++++= fEDCBArrrr tttpw (35) where

( )( )

( ) 212123.2

221

42.9235.22e84.3

w

rw

fgA

t

+

=

(36)


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( )( )

( )( )( )

( ) 23214385.6

32

22

17.02

29.6226.321e078.0

48.931.183e48.10

w

rw

w

rw

ffB

tt

+

++

=

(37)

( )( )

( )( )( )

( )2109.1

52

42

16.14

380e36.26

22.9153.325e76.3

++

=

ffC

tt rw

w

rw

(38)

( )( )

( )( )( )

( )2117.0

55752

146.15

557e7.883

448e87.17

+

=

fg

fD

tt rw

rw (39)

( )( )

( )2141.0

7525

752e6.302

=

fgE

trw (40)

7.2.5.3 Total gas attenuation Specific attenuation (dB/km) for water vapor and oxygen (dry air) are separately calculated and then added together to give the total specific attenuation.

( ) dA wOG += (41) where

AG = Total gas attenuation, dB

w = Specific absorption due to the effects of water vapor, dB/km o = Specific absorption due to the effects of oxygen (dry air), dB/km

d = Path length, km The specific attenuation is strongly dependent of frequency, temperature and absolute or relative humidity of the atmosphere as is illustrated in Figure 5.

Figure 5: The total specific atmospheric attenuation.


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Advices:

1) If gas absorption is calculated as a function of relative humidity and temperature, be aware both parameters are reciprocally consistent.

2) If local values of temperature are available, select the average summer temperature.

3) For tropic climate nearby large bodies of water, annual temperature charts can be employed for the selection of temperature.

4) Frequency bands located close to the strong features of water vapor (23 GHz) and oxygen (50-60 GHz) are strongly affected by attenuation. Depending on the values of temperature and humidity, the specific attenuation can be as much as 1 or 2 dB/km. This gives a large negative contribution to the fade margin, then making the quality and availability objectives harder to be accomplished. On the other hand, such high values of specific attenuation are also of benefit because it provides valuable shielding to co-channel interference.

5) Considering the atmospheric isolation described above as a positive contribution, the use of high frequency systems will improve the efficiency of spectrum utilization through the enhanced opportunity for multiple frequency re-use for short-distance communication systems operating within the same part of the frequency band.

7.3 Reflection Reflection on the earth surface may give rise to multipath propagation. Depending on the path geometry, the direct ray at the receiver may be interfered with the ground-reflected ray and the reflection loss can be significant. Since the refraction properties of the atmosphere are constantly changing (k-value changes), the reflection loss varies (fading).

Due to its fading characteristics, reflection loss is normally not included in the link-budget because it may lead to heavy over or under dimensioning. Some rough estimations of reflection loss as a function of the total reflection coefficient is described below.

7.3.1 Ground reflection interference The respective field strength components of the direct and reflected waves interfere with one another at the receiver. Receiver interference due to ground reflection is the result of the reception of the resultant field strength, i.e., the vector addition of the field components.


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Signal strength is dependent on the total reflection coefficient (resulting from dielectric constant, conductivity and polarization) and the total phase shift (resulting from antenna height, path length, earth-radius factor, frequency and the phase angle of the reflection coefficient).

Generally, Figure 6 illustrates two extreme cases:

1) How the highest value of signal strength, AMAX, varies with the total reflection coefficient. This case illustrates amplification, i.e., the field strength components have the exact same direction, a phase angle of 0.

2) How the lowest value of signal strength, AMIN, varies with the total reflection coefficient. This case illustrates a loss, i.e., the field strength components are directed opposite to one another, a phase angle of 180.

Figure 6: The signal strength as a function of the total reflection coefficient. The highest value of signal strength is obtained for a phase angle of 0 and the lowest value for a phase angle of 180.

7.3.2 The problems of handling reflection The handling of reflection is difficult and complicated, particularly due to the uncertainties and measurements of the following parameters:

High frequencies mean short wavelengths (at 23 GHz, the wavelength 1.3 cm)

Terrain data accuracy can affect the total reflection coefficient which in effect, consists of three factors, of which one is directly coupled to the degree of irregularity of the terrain

Antenna height cannot be determined with sufficient accuracy since the height database has its limitations

Earth-radius factor


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7.3.3 Reflection coefficient The total reflection coefficient for a smooth spherical surface consists of three elements: Fresnel reflection coefficient, divergence factor and correction factor.

7.3.4 The Fresnel reflection coefficient The Fresnel reflection coefficient for a smooth flat surface is dependent on frequency, grazing angle, polarization and ground characteristics (from the dielectric and conductivity constant). Figure 7 shows the Fresnel reflection coefficients absolute value for sea water as a function of grazing angle, two different frequencies and both horizontal and vertical polarization.

Figure 7: The Fresnel reflection coefficient as a function of the grazing angle for seawater.

7.3.5 Divergence factor The divergence factor is applied to the Fresnel reflection coefficient when approximating the earths surface as being spherical. Its value is a function of antenna height, earth radius factor and the path length.

The divergence factor increases as both the difference in antenna heights, transmitter-receiver, and the value of the earth radius factor increase - it decreases with hop length (longer distances along the earths surface must be considered as being an arc).


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7.3.6 Correction factor The correction factor accounts for the surface irregularities (roughness) in different types of ground formations. Table 3 illustrates the approximate values of the correction factor for different ground surfaces at two different frequencies, 1 and 10 GHz.

Ground-surface types s 1 GHz s

10 GHz Sea, lake, mirror-face ice field 0.95-1 0.90-1 Snow & ice field, frozen soil, naked damp ground 0.85-0.95 0.80-0.90

Damp field, flat and large scale agricultural and cattle breeding land 0.75-0.85 0.65-0.80

Flat grass land, flat field with thin bush, desert 0.55-0.75 0.45-0.65

Gently rolling terrain, savanna, partitioned plowed fields and pasture 0.35-0.55 0.25-0.45

Rolling terrain, forest, thick forest against sandy wind, wind break, medium or small city area, area where a bank or a high way transverses the radio path near the reflection point

0.18-0.35 0.09-0.25

Terrain with outstanding undulation, undulated forest, medium or small city with high rise buildings, area with large factories, stadiums located to transverses the radio path near the reflection point

0.08-0.18 0.04-0.09

Mountainous area, area with a deep ridge to shield the reflected area 0.04-0.18


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The value of the divergence factor may also lie around 0.90. For example the divergence factor is 0.91, for a 30 kilometer hop and a height difference of 30 m between the antennas and k=1.33. If the height difference is increased to 330 m, the divergence factor increases to 0.97 for the same k value. If the hop length is decreased to 15 km, the divergence factor increases to 0.99 for a height difference of 30 m and a k value of 1.33.

The value of the correction factor varies with frequency and ground surface type in accordance with the Table 3. For very smooth surfaces, e.g., the surface of a body of water, the correction factor is approximately 0.90.

The total reflection coefficient for a spherical and very smooth surface can be approximated to 0.900.900.90 0.73. From the diagram in Figure 6, the reflection loss is approximately 12 dB.

Estimations can be easily performed if one assumes that the values of both the Fresnel reflection coefficient and divergence factor lie close to 0.90 and then apply the correction factor value given in the Table 3 for the different ground surface types.

7.3.8 Calculation of the position of the reflection point The calculation of the position of the reflection point is primarily a geometric problem and the result is therefore presented in connection with the presentation of the path profile. The ground-reflected beam path and the reflection points position are clarified.

There are two different methods available for the calculation of the reflection points position. The simplest algorithm avoids the numerical solution of third-degree equation and is therefore employed in here. The following intermediate parameters are calculated initially:

Intermediate parameter c

BA

BA

hhhh

c''''

+

= (42)

where

c = Intermediate parameter m

hA = Antenna height at station A, m

hB = Antenna height at station B, m Intermediate parameter m


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( ) 32

10''4 +=

BAe hhRdm (43)

where

m = Intermediate parameter d = Distance between stations A and B, km Re = Equivalent earth radius, km

hA = Antenna height at station A, m

hB = Antenna height at station B, m Intermediate parameter b

( )

+

+

+= 31

32

3acos31

3cos

312

mmc

mmb (44)

The position of the reflection point is calculated from

( )bdd A += 12 (45) and

AB ddd = (46) where

dA = The distance between station A and the reflection point, km dB = The distance between station B and the reflection point, km d = The distance between stations A and B, km b = The intermediate parameter as above

Advices:

1) The grazing angle of radio-relay paths is normally very small, currently lower than 1 degree.

2) It is strongly recommended to avoid ground reflection. This can be achieved by shielding the path against the indirect ray.

3) Vertical polarization gives less loss. For large grazing angles the difference between vertical and horizontal polarization is substantial.


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4) Changing the antenna heights can move the location of the reflection point. This approach, usually known as the Hi-Lo technique, force the reflection point to move closer to the lowest antenna by affecting the height of the higher antenna. The grazing angle increases and the path becomes less sensitive to k-value variations.

5) Space diversity normally provides good protection against reflection. It is currently applied for paths over open water surfaces.

6) The contribution due to reflection loss is NOT automatically included in the link budget, but in the case reflection cannot be avoided the fade margin may be adjusted by including this contribution as additional loss in the link budget.

7.3.9 Optimum height difference To calculate the optimum height difference between the diversity antennas, one first calculates the height difference between two adjacent points along the mast, at which signal strength is a minimum (or a maximum). This calculation is naturally performed for both stations, A and B. For example, assume that an antenna is mounted on a mast at a given position, i.e., at a given height. As the antenna is moved from this starting position, the resultant signal strength (the sum of the signal strengths of the direct and the phase-shifted reflected waves) will either increase to a maximum or decrease to a minimum depending on the direction of movement. The distance between the points in which minimum (or maximum) signal strength is measured is the distance referred to above.

32

'

' 10

74.12

123.0

=

kdh

fdh

BB

A (47)

32

'

' 10

74.12

123.0

=

kdh

fdh

AA

B (48)

where

hA = Height difference between the two maximum/minimums at station A, m


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hB = Height difference between the two maximums/ minimums at station B, m

hA = Antenna height above the point of reflection at station A, m hB = Antenna height above the point of reflection at station B, m dA = Distance between station A and the point of reflection, km dB = Distance between station B and the point of reflection, km d = Distance between station A and B, km f = Frequency, GHz k = Earth-radius factor

The distance between the stations and the point of reflection is calculated as described in accordance to section 7.3.8.

The distance required between the diversity antennas is then calculated as follows:

2

'A

Ahh = (49)

2

'B

Bhh = (50)

where

hA = Height difference between the antennas at station A, m hB = Height difference between the antennas at station B, m

7.4 Precipitation

7.4.1 Types of precipitation Precipitation can take the form of:

Rain

Snow

Hail

Fog and haze

In common for all of the above forms of precipitation is the fact that they all consist of water particles (haze can also consist of small solid particles). Their distinctions lie in the distribution of the size and form of their water drops. Rain attenuation is, however, the main contributor in the frequency range used by commercial radio links.


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Sharp demarcations between these forms of precipitation is however not always apparent. Intermediate states can very well occur.

7.4.2 Precipitation: now Attenuation is only caused by wet snow.

The attenuation caused by dry snow can be considered as negligible for frequencies below 50 GHz.

Snow cover on antennas and radomes, so-called ice coatings, can result in two problems:

Increased attenuation

Deformation of the antennas field radiation diagram

Both cases result in the reduction of the input signal strength at the receiving station.

Antenna ice coating can of course be alleviated by electrically heating the antennas, however the disadvantages are unfortunately greater than the advantages. Some of the disadvantages are:

Antennas must be held warm constantly, there is otherwise the risk that melted snow forms to ice

Electrical heating may be interrupted in the event of an electrical power loss

There is no knowledge as to the impact, or its degree, on an antennas field radiation diagram due to electrical heating

7.4.3 Precipitation: hail The effects of hail on radio connections are first apparent when hail particle sizes approach the size of radio waves, for example, 150 mm (2 GHz), 9.6 mm (31 GHz) and 6 mm (50 GHz). Hail particle sizes greater than 10 mm are however quite rare.

Measurements made in Sweden show that the deepest fading lasted for just under 5 minutes and was less than 10 dB.

Hailstorms can therefore not be considered as availability limiting factor, since they occur quite infrequently together with other forms of precipitation.


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7.4.4 Precipitation: fog and haze Measurements performed in Sweden show that the deepest fading that can be related to heavy fog and haze amounted to between 4 and 7 dB.

Fog and haze can therefore not be considered as availability limiting factor, since both fog and haze occur quite infrequently together with other forms of precipitation.

7.4.5 Precipitation: rain Attenuation due to rain is the generally responsible for two principal attenuation mechanisms: absorption and scattering caused by the raindrops.

The extent of the attenuation due to rain is primarily a function of

Form of the rain drops

Size distribution of the rain drops

The most common form of falling raindrops under the influence of air resistance is the oblate form (not exactly ellipsoidal). This causes horizontally polarized waves to attenuate more than vertically polarized waves.

7.4.6 Cumulative distribution of rain Due to the rapid time-variation of rain, the measured cumulative distribution of rain intensity is heavily dependent of the integration time selected for the measuring process. The rain intensity statistical distributions used in ITU-R reports are assumed to be the results of measurements or transformations corresponding to an integration time of 1 minute. The instantaneous rain intensity (which is extremely difficult to measure) is however more suitable from a network-planning standpoint.

For the purpose of availability calculations, one is however interested in the cumulative distribution of rain intensity (rainfall rate), i.e., that percentage of time during which a given level of rain intensity is attained or exceeded.

Normally, the reference level applied to rain intensity is the rain intensity that is exceeded during 0.01% of the time, which is often designated as R0.01.

7.4.7 Obtaining Rain Intensity (the former ITU-R model) NOTE: The former ITU-R procedure for obtaining rain intensity values employed worldwide charts of rain zones in which the world is subdivided into 15 different rain zones, see Chapter 15- 10.


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NOTE: Once the proper rain zone is geographically found, then its correspondent rain intensity expressed in mm/h for different fractions of time (%) is obtained from the table in Chapter 14-11.

For instance, three rain zones cover Sweden, C, E and G and three rain zones, K, N and P, cover Brazil.

7.4.8 Rain zones - diagram The cumulative distributions listed in the previous table are illustrated in diagram form in Figure 8. The curves represent ITU-Rs 15 different rain zones covering the entire earth. The distribution of rain intensity (mm/h) represents a percentage of time that is equivalent to the attainment or exceeding of a given rain intensity. The Y-axis to the right shows the time percentage expressed in minutes per year.

0 50 100 150 200 250Rain intensity, mm/h

0.001

0.010

0.100

1.000

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

2

3

4

5

6

7

8

9

Perc

enta

ge o

f tim

e ra

in in

tens

ityis

exc

eede

d, %

5.26

52.56

525.60

5256.00

Min

utes

/yr

P

N Q

LMKHFG

E

J

A B

CD

Perc

enta

ge o

f tim

e ra

inin

tens

ity is

exc

eede

d, %

Figure 8: The rain zones represented as cumulative distributions.

7.4.9 Obtaining rain intensity (current ITU-R model) The new ITU-R rain intensity procedure, also known as Baptista- Salonen model, is conditioned to the following aspects:

1. High quality, long integration-time (few hours) and high spatial resolution (about one grid point per 100 km)

2. Models for transforming long integration-time rain data to short integration-time rain data


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The new procedure does not demand any rain zone chart and rain intensity (rainfall rates) is directly calculated as a function of the geographical location of the site. Rain intensity values are not any longer representative for a certain major rain region but represent local values.

The basic of the new ITU-rainfall model is the rain intensity data that is now available from two different rain-data programs: 1) Global Precipitation Climate Project (GPCP-data) and 2) European Center for Medium-Range Weather Forecast (ECMWF-data).

The new model is derived in two steps. First, suitable functions describing properly the rainfall rate distributions in tropical and mid-latitude climates are derived. This function is expressed as follows:

( )( )Rc

RbRaePp +

+

=11

0 (51)

where p is the annual probability that the rain intensity R (mm/h) is exceeded, P0 is the rain probability obtained from statistical data and a, b and c are parameters.

The next step is to optimize the above parameters by employing empirical functions. The difference between predicted and measured rainfall rates is minimized. The rain intensity data used in the optimization is from ITU-R databases covering a large amount of sites all over the world at different climates.

The probability of rain P0 is approximated by the following expression:

=

60.0117-

60 e1 rS

PM

rPP (52)

where Ms (mm) is the annual rainfall amount of stratiform-type rains and Pr6 (%) is the probability of rainy 6 hours periods.

The annual probability that the rain intensity R (mm/h) is obtained from the previous expression

ACABBR

+=

242

(53)

where

baA = (54)


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+=

0

lnPpcaB (55)

=

0

lnPpC (56)

For p>P0, R(p)=0

The parameters a, b and c are empirically optimized and finally given by the expressions:

1.1=a (57)

( )022932 P

MMb sc

+= (58)

where Mc (mm) is the annual rainfall amount of convective-type rains.

bc = 5.31 (59) The users of the new ITU rainfall rate model are, however, not forced to calculate the parameters Ms, Mc and Prg6 since they are calculated and stored in data files at the ITU-R. The files are as follows:

ESARAINPR6.TEXT ! contains the numerical values of the parameter Pr6.

ESARAIN_MC.TXT ! contains the numerical values of the parameter Mc.

ESARAIN_MS.TXT ! contains the numerical values of the parameter Ms.

The values of the parameters Ms, Mc and Pr6 are stored as 121-rows and 241-columns matrix (121x241) corresponding to each point in a grid system.

It is assumed that the Earth surface is divided in a grid having a 1.5-degree resolution, that is, every square has a side of 1.5 degrees and for interpolation purposes each square can be considered as a plane (flat) square. The longitude and latitude of the Earth determine every point forming the grid. The values of the parameters Ms, Mc and Pr6 are given from the above databases for every grid point.


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The values of the longitude and latitude for all grid points are also stored as 121-rows and 241-columns matrix (121x241) and can be obtained from data files at the ITU-R. The files are as follows:

ESARAINLON.TXT ! contains the longitude values for each grid point.

ESARAINLAT.TXT ! contains the latitude values for each grid point.

For each specific grid point (LONi, LATj) there will be Msij, Mcij and Pr6ij corresponding values.

Parameter values for other geographical locations than the grid points given in the above matrices are obtained by two-dimensional interpolation technique.

NOTE: Rain intensity values all over the world are displayed in the charts presented in Chapter 15-12.

Figure 9 gives an overview of the geographical distribution of rain intensity for 0.01% of time, R0.01.

Figure 9: Distribution of rain intensity R0.01 all over the world. High rain intensity regions are encountered in the dark regions.

7.4.10 The calculation of the specific rain attenuation The calculation of specific rain attenuation is performed in two steps:

First, a calculation is performed of the values of the coefficients corresponding to certain assumptions concerning the distribution of rain-drop size, form, temperature and type of polarization (horizontal/vertical)

Then, a calculation is performed of the specific rain attenuation for a given instantaneous rain intensity

Calculate the coefficients as follows


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( ) ( )2

2coscos2 ++=

VHVHf

kkkkk (60)

( ) ( )f

VVHHVVHHf k

kkkk

++=

22coscos2

(61)

where

kH, H, kV, V = Frequency dependent coefficients.

= The paths elevation angle = The polarization tilt angle relative to the horizontal plane

NOTE: Frequency dependent coefficients are provided in Chapter 15-9.

The calculation of specific rain attenuation (dB/km) is performed as follows

fRk fR = (62)

where

kf, f = Frequency dependent coefficients R = Rain intensity, mm/h

The specific rain attenuation that is exceeded during 0.01% of the time, can be calculated by relating the rain intensity to the reference level 0.01%, i.e.,

fRk fR 01.001.0 = (63)

Figure 10 illustrates specific rain attenuation (dB/km) that are exceeded during 0.01% of the time as a function of frequency (GHz) for three different values of rain intensity, R0.01, for both horizontal and vertical polarization.


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Figure 10: Specific rain attenuation exceeded during 0.01% of the time as a function of frequency.

Figure 11 illustrates the specific rain attenuation (dB/km) that are exceeded during 0.01% of the time as a function of rain intensity for four different values of frequency (GHz), for both horizontal and vertical polarization.

Figure 11: Specific rain attenuation exceeded during 0.01% of the time as a function of rain intensity.


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Figure 12 illustrates the specific rain attenuation (dB/km) that is exceeded during 0.01% of the time as a function of rain intensity for horizontal (H) and vertical (V) polarization at 23 GHz.

At 23 GHz and horizontal polarization, the specific rain attenuation at R0.01=30 mm/h is almost twice the value at R0.01=12 mm/h.

Figure 12: Specific rain attenuation exceeded during 0.01% of the time as a function of rain intensity for a frequency of 23 GHz.

7.4.11 Calculating total rain attenuation The total rain attenuation for a radio link path can be calculated as follows, if the statistical distribution of the rain cells along the path is known

effRR dA = (64) where

AR = Total rain attenuation, dB

R = Specific rain attenuation, dB/km deff = Effective path length, km

The effective path length is calculated as follows

rddeff = (65) where


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d = Actual path length, km r = Reduction factor

The reduction factor is arrived at as follows

0

1

1

dd

r+

= (66)

The factor 1/d0 is coupled to rain intensity for the 0.01% reference level. d0 is then

01.0015.00 e35

Rd = (67) The reduction factor accounts for the extensions of rain cells and transforms actual path lengths to equivalent path lengths along which the rain can be regarded as having a uniform distribution.

7.4.12 Calculating total rain attenuation for 0.01% The total rain attenuation that is exceeded 0.01% of the time can be calculated if the rain intensity is related to the 0.01% reference level, as follows

effRR dA = 01.001.0 (68) where

AR 0.01 = Total rain attenuation that is exceeded during 0.01% of the time, dB

R0.01 = Specific rain attenuation that is exceeded during 0.01% of the time, dB/km

deff = Effective path length, km The total rain attenuation that is exceeded during 0.01% of the time is used later in the calculation of unavailability caused by rain.

7.5 Obstruction - diffraction

7.5.1 Definition Diffraction is the responsible mechanism for obstacle loss/attenuation. In fact, obstacle loss is also known in the literature as diffraction loss or diffraction attenuation.


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Depending on the shape, size and electrical properties of the obstacle, diffraction calculations can be cumbersome and time-consuming. Since radio-relay paths normally require LOS, relatively simple methods for calculating the obstacle loss are currently employed. One powerful, although simple method for calculation of obstacle loss, is the single-peak method that is based on the knife-edge approximation. This method can easily be extended to comprise the three most significant peaks inside the Fresnel zones.

Obstruction loss is calculated based on the paths geometry and on the actual frequency used.

The geometry is a function of:

Topography

The antennas height above ground level

The earth-radius factor, k Different k-values result in different obstruction loss values. Small k-values result in the greatest obstruction loss due to the fact that the beam tends to bend more towards the ground surface, or expresses in another manner, the obstruction penetrates deeper into the Fresnel zone.

7.5.2 Knife-edge obstructions A knife-edge obstruction is one that consists of an individual obstruction having negligible length in the direction of the radio waves propagation path as illustrated in Figure 13. The loss contributed by such an obstruction is derived from the knife-edge loss curve, which is a physically derived function.

A B

Equivalent earth surface

r1F

hLOS

v < 0

v > 0

Figure 13: Knife-edge obstruction showing the obstructions height relative the free line-of-sight.


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In the case of knife-edge obstructions, the obstruction loss value, AH is only dependent on the parameter , which is defined as the obstructions relative penetration of the Fresnel zone:

F

LOS

rh

1

= (69)

where

hLOS = The obstructions height above the free line-of-sight r1F = The Fresnel zones radius at the point of the obstruction

The parameter , as defined above, differs by a factor of 2 1.41 from the definition in Rep. 715-3, vol. 5, which means a difference of approximately 1-3 dB in obstruction loss for the particular value of .

The height of the obstruction over the free line-of-sight may be defined as

hLOS = (ground elevation + height of the tree line or building height) - the height of the free line-of-sight

7.5.3 Knife-edge loss curve The loss caused by an obstruction is arrived at from the knife-edge loss curve, which is a physically derived function. Knife-edge loss AH as a function of the relative penetration , is shown in Figure 14.

Figure 14: Knife-edge loss as a function of the relative penetration parameter.


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When performing path calculations, realistic degrees of Fresnel zone penetration are often considered as lying in the interval from -0.5 to 2, which means calculation of obstruction losses based on the diagram insertion above.

For 10, obstruction losses are calculated as follows:

( ) 10 log2016 += HA (70) where

AH = Obstruction loss, dB

= The obstructions relative penetration of the Fresnel zone

7.5.4 Typical knife-edge losses Figure 15 illustrates a few typical examples of loss values (dB) for the knife-edge function.

0 0 6 12 16 20

Figure 15: Typical loss values (dB) resulting from the knife-edge function.

7.5.5 Single-peak method The single-peak method calculates the value of the obstruction loss as the greatest knife-edge obstruction loss attained as a result of an individual obstruction lying along the path as illustrated in Figure 16.

The algorithm defines those peaks in the path profile between station A and station B that penetrate the Fresnel zone. The penetration, , of every peak is calculated relative to the Fresnel zone along the free line-of-sight, AB. The corresponding knife-edge loss, AH, is calculated as if only one peak existed along the path. The greatest loss value that is found along the path is returned as the sought obstruction loss value.


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A B

Figure 16: In the single-peak method the obstruction loss is taken as the greatest knife-edge obstruction loss lying along the path.

The single-peak method is, as is obvious, a pure application of the knife-edge model. It works best for paths that have one dominant peak. The results of the model are less reliable for more realistic paths having a number of significant peaks.

7.5.6 Triple-peak method Simply stated, the triple-peak method may be described as a calculation of the obstruction loss value along the propagation path, based on the sum of the three largest knife-edge losses.

The algorithm involves an initial calculation of the obstruction loss based on the single-peak method, as described earlier. This first calculation of the single knife-edge loss represents the first contribution, A1, to the total obstruction loss.

The path profile is then split at that the point, M, which resulted in the largest knife-edge loss, see Figure 17. The peak of point M is regarded as being a common antenna or termination point along the partial paths AM and MB. If the peak consists of trees, then the mast height of the fictitious antenna is set to the height of the trees, otherwise the mast height is set to zero. In the event that the fictitious antenna attains a height beneath the original free line-of-sight, AB, then the mast height is instead set so that the antenna exactly reaches the free line-of-sight.


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A B

M

Figure 17: The path profile after the first split.

The partial paths, AM and MB to the left and right of the located peak, M, are each searched for two new paths in the same manner as was the original path. Note that the partial paths, as illustrated in the figure above, generally have other free lines-of-sight and Fresnel zones than does the original path. Each partial path results in a separate knife-edge loss value. The higher of the two values will represent the second contribution, A2, to the total obstruction loss.

The particular partial path is then subdivided at the peak, N, that resulted in the highest knife-edge loss, see Figure 18. The resultant partial paths are then each searched in the same manner as was the original partial paths. The third and final contribution, A3, to the total obstruction loss is the largest knife-edge loss resulting from one of the partial paths AN, NM, and MB.

The total obstruction loss, AH, is obtained by summing the three contributions described above, A1, A2 and A3.

321 AAAAObst ++= (71)


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A B

N M

Figure 18: The path profile after the second split.

The triple-peak method is entirely empirical, but it has proven to work well in actual applications. It works better than the single-peak method in many path profile scenarios, since it accounts for more than only the highest peak along the path.

The difference between the triple-peak method and a hypothetical repetition (three times) of the single-peak method, lies in the fact that secondary peaks in the triple-peak method will contribute less than the primary peak considering the peaks penetration of the original Fresnel zone. This is a function of two factors:

The partial paths are always shorter than the full path

The partial paths free lines-of sight always lies higher than (or at the same level as) the original full path

A shorter path results in a smaller Fresnel zone radius. Higher free line-of-sight results in a relatively lower peak free line-of-sight. Together, these factors result in a smaller relative penetration. The result is that the secondary peaks cause lower obstruction losses.

The triple-peak method, as it is applied here, is a further development of the original multiple-peak method introduced by Deygout, Multiple Knife-Edge Diffraction of Microwaves, IEEE Trans. Ant. Prop. vol. AP-14, 1966.


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7.5.7 Smoothly spherical earth In the case of smoothly spherical earth (flat-earth), the obstruction is represented by an smooth surface, such as a sea or lake, penetrating the Fresnel zone. Losses are calculated using a simple function that may be derived from empirical considerations. The geometry of the smoothly spherical earth is illustrated in Figure 19.

drd

dBdA

hB

hA B

A

Figure 19: The geometry of the smoothly spherical earth.

The loss calculation is performed in accordance with the Cheriex method. First the distances to the radio horizon from both antennas are calculated as follows

AA hRkd 3102 (72)

BB hRkd 3102 (73)

where

dA = Distance from station A to the radio horizon, km dB = Distance from station B to the radio horizon, km hA = Antenna height at station A, m hB = Antenna height at station B, m k = Earth-radius factor

R = True earth radius (6370 km) The distance between both radio horizons may be easily calculated as

( )BAr dddd + (74) where

d = Distance between station A and B, km


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The obstruction loss for evenly curved earth is calculated as

rObst dkfA +

32

3112.020 (75)

where

AObst = Obstruction loss, dB f = Frequency, MHz

7.5.8 Typical losses resulting from smoothly spherical earth Figure 20 illustrates typical loss values (dB) for smoothly spherical earth for a path of 50 kilometers and a frequency of 2.2 GHz.

40

10

20

Figure 20: Typical loss values (dB) resulting from a smoothly spherical earth.

For grazing lines-of-sight, i.e., the antennas have the same horizon (dA + dB = d), the loss is 20 dB, which applies regardless of frequency and path length.

7.5.9 Clearance and path geometry

7.5.9.1 The Earth bulge The local height of the Earth bulge (h) is dependent on the k-value. The parameter h is very important for clearance purposes. The shadow region in Figure 21 covers its local value.


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x

hmax

d2d1y

y=d/2y=-d/2

kRkR kR-hmax

h

O

A B

M

N

Figure 21: The local height of Earth bulge.

The local height of the Earth bulge is given by

kddh

=

74.1221 (76)

where the distances d1 and d2 are normally expressed in km and h in meters.

The local height of the Earth bulge is inversely proportional to the earth-radius factor. For high k-values, the Earth surface is close to a plane surface while for low k-values the Earth surface becomes more curved and may penetrate the radio path.

7.5.9.2 Path geometry In what follows, clearance, obstacle penetration and antenna height will be discussed. Figure 22 displays the path geometry for which the path parameter clearance c is depicted. The height of the line-of-sight is x, the bulge of the Earth is h and the height of the obstacle above the earth surface is h3. The other parameters have their current designation. The antenna heights are represented as total heights, that is, both the terrain and the actual antenna heights are included.


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h1

d2

x

d1

h2

h2-x

x-h1

d

h3

h

c

Figure 22: Path geometry (the path is drawn on a equivalent earth).

7.5.9.3 The height of the line-of-sight The height of the line-of-sight with respect to the antenna heights is given by the following expression

1112 hd

dhhx += (77)

where h1and h2 are given in m and d and d1 in km.

7.5.9.4 Clearance of the LOS The clearance of the LOS (the height above the obstacle) is given as follows

121

112

1 74.12h

kddd

dhhhc

+= (78)

where d, d1 and d2 are expressed in km and c, h1, h2 and h3 are expressed in m.

7.5.9.5 Antenna height The antenna height as a function of the obstacle height and the Earth radius factor for a given clearance is easily obtained from the above expression by setting h2 = H,


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+++= 121

31

1 74.12h

kddhc

ddhH (79)

7.5.9.6 Obstacle penetration Now, assume the height of the line-of-sight is lower than the height of the obstacle and gives an obstacle penetration expressed by b meters above the line-of-sight. Thus, the height of the line-of-sight x is properly expressed as

bhhx += 3 (80) Employing the above expressions, the obstacle penetration is obtained according to

dd

hhhk

ddhb

+= 12121

3 74.12 (81)

with the parameters expressed as before.

7.5.10 Vegetation For unexpected obstacle intercepting the Fresnel zone, for instance growing vegetation, the additional loss can be calculated using the method recommended by the ITU-R.

Advices:

1) High-resolution path profiles and careful site (and path) surveys are important tasks in the planning process to avoid unexpected obstacle attenuation.

2) Vegetation is continuously growing. What seems to be LOS today might not be LOS tomorrow!

7.6 The Link Budget The Link budget is the process of adding and subtracting gain and losses of a radio-relay path, see Figure 23. The main output of link budget calculations is the signal level at the receiver (dBm), the path loss and the fade margin. In most applications, the same duplex radio set-up is applied to both stations forming the radio-relay path. Thus, the calculation of the received signal level is independent of direction.


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7.6.1 Path loss The path loss is the sum of all losses and gains between the transmitters and the receivers antenna contacts and is calculated as follows:

ARxATxFLObstGbfS GGAAAAAA ++++= (82) where

AS = Path loss, dB Abf = Free-space loss, dB AG = Gas attenuation, dB AObst = Obstruction loss, dB AL = Additional loss, dB AF = Antenna feeder loss, dB GAtx = Transmitter antenna gain, dBi GArx = Receiver antenna gain, dBi

7.6.2 Fade margin Under interference-free conditions, the fade margin is defined as the difference between the received signal level under normal wave propagation conditions (fade-free time) and the receivers threshold level at a given bit-error level, i.e.,

TrR PPM = (83) where

M = Fade margin, dB PR = Receiver signal level, dBm PTr = Receiver threshold level, dBm

Receiver signal level is calculated as the difference between the transmitters output power and the path loss, i.e.,

STrR APP = (84) where

PR = Receiver signal level, dB PTr = Transmitter output power, dBm AS = Path loss, dB


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7.6.3 Power diagram A power diagram is a schematic approach to the illustration of the effects on a transmitters radiated power as it propagates towards a receiving station as shown in Figure 23. Concepts such as fade margin and receiver threshold value are also included in the definition.

AntennaSplitter

Transmitter /Receiver


Wave guide

Wave guide

WaveguideAntenna Splitter



Wave guide

Wave guide

Waveguide

OutputPower

Branching Losses Anten

na G

ain

Propagation Losses

Anten

na G

ainBranching Losses

Receiver Thresh.Value

Received Power

UnfadedFade

Margin

Tran

smitt

ed P

ower

Figure 23: The power diagram showing possible losses from the transmitter to the receiver. The fade margin is indicated as the difference between the received power and the receivers threshold value.

7.6.4 Effective fade margin The receivers threshold value as defined earlier only applies under negligible or interference-free conditions. In reality, this is however not the case. A certain interference contribution is almost always present when performing path calculations, which usually affects availability results.

The interference contribution can be interpreted as degradation in the receivers threshold value, i.e., threshold degradation. The effective fade margin is therefore defined as the difference between the fade margin and the threshold degradation. The effective fade margin is used later in availability calculations.

Interference calculations provide the value of the threshold degradation.


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Advices:

1) The main purpose of the link budget is to calculate the fade margin and delivery its value to the fading block.

2) The fade margin is calculated with respect to the receiver threshold level for a given bit-error ratio (BER). The threshold level for BER=10-6 for MINI LINK equipment is about 4 dB higher than the threshold level for BER= 10-3. Consequently, the fade margin is 4 dB larger for BER=10-6 than for BER=10-3. For other equipment than MINI LINK, it is generally common to have one dB of threshold level for each decade of BER.

3) The fade margin is NOT an input parameter for tuning path proprieties in the design of microwave links. Appropriate planning of microwave networks relies on the values of quality and availability objectives.

8 The fading block

8.1 Definition Fading is often defined as a variation in signal strength over time, phase or polarization. Fading is normally the result of changes in the physical properties of the atmosphere or due to ground or water reflections.

8.2 General cause Fading can be caused by the occurrence of an isolated phenomenon, one that is solely responsible for its appearance. It is however more common that fading appears in one and the same hop as the result of a combination of various phenomenon that interact with one another, leading to the degradation of signal quality and availability. Climate, topography and surroundings can vary to such great degrees that fading often depends on the aggregate effects of numerous phenomenon.

8.3 General classification Fading can be classed as follows:

Source

Propagation attributes

Time variation

Statistical distribution


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8.4 Classification based on source The phenomenon of fading is often classified based on the source of the phenomenon. Source can be divided into four primary groups:

Atmospheric fading: absorption, refraction and turbulence.

Ground-based fading: geology, the roughness of the surrounding terrain, propagation path differences due to tides or variations in snow depth, obstructions due to variations in vegetation

Man-made fading: obstruction or reflection caused by boats, aircraft and temporary constructions sites, antenna vibration.

Mixed fading: due to the occurrence of atmospheric inversion layers and the reflection they cause.

8.5 The concept of outage Outage is generally defined as the probability that a pre-defined bit-error ratio is exceeded during a certain measured period. The concept of outage comprises quality (error performance) and availability events that are referred to bit-error ratio.

8.6 Rain fading (current ITU-R model)

8.6.1 Calculation of the fade margin based on a yearly basis The fade margin that is exceeded during different periods of time based on a yearly basis is calculated as follows

( )PRP PAM

log043.0546.001.0

12.0 += (85) where

AR0.01= Total rain attenuation that is exceeded 0.01% of the time, dB

MP = Fade margin that is exceeded p% of the time, dB P = Percentage of the time during which 0.001 < P < 1%

The total attenuation for 0.01% of time, A0.01, is calculated as a function of the rain intensity (rainfall rate) for 0.01% of time, R0.01, and the effective path length by equation (68).

The attenuation exceeded for a certain percentage of time can be referred to as the fade depth. If we adapt the fade margin, M, to be as much as the fade depth, then Ap can be replaced by M in both expressions above.


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In the previous ITU-model, the above expression was valid for all values of latitude and longitude. In the new revision of the ITU-R recommendation, however, the above expression is modified to fit different values of the latitude. Thus, for radio links located at latitudes equal or greater than 30 (North and South) the above expression is still applied. On the other side, for latitudes lower than 30N and 30S (60 belt along the equator), the current model is expressed as

( )pp pAA log139.0855.0

01.0

07.0 += (86)

with the parameters defined as previously.

Compared to the previous model, the new model presented does not provide any remarkable improvement. In addition, it seems to be statistically inconsistent since it gives higher p values than the model used for latitudes equal to or greater than 30N and 30S.

When discussing both models for calculating the probability (percentage of time) that the fade margin will be exceeded, transmission network planners are encouraged to stress the inconsistency of the new model to be used in the 60 belt along the equator. Particularly, the fact the model does not provide any remarkable improvement.

8.6.2 Outage due to rain fading - annual basis The prediction model for the rain fading across a particular area is a cumulative distribution over fade margin. It calculates the probability that a given fade margin will be exceeded.

The probability that a given fade margin M is exceeded, on an annual basis, can be attained from the previous mathematical expression by solving the equation for the fraction of time, P. The empirical prediction model for rain fading becomes

++

=

MAR

p01.012.0log172.029812.0546.0628.11

10 (87)

where

p = Percentage of time that a given fade depth M (fade margin) is exceeded in the average year, %

AR0.01 = Total rain attenuation that is exceeded 0.01% of the time, dB

M = Fade margin, dB The outage is finally obtained by transforming the annual value given by the above expression from percentage to ratio as follows:


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100pP =rain (88)

Where Prain is the probability (expressed in ratio) of exceeding the fade margin M in the average year and p (expressed in %) as given by expression (87).

8.6.3 Transformation between yearly and worst month basis

8.6.3.1 From yearly basis to worst month The transformation from an annual probability to one based on a worst month is obtained as follows

rainPQp =w (89) where

pw = Probability (expressed in ratio) of exceeding the fade margin M during the average worst month Prain = Probability (expressed in ratio) of exceeding the fade margin M in the average year Q = Conversion factor (climatic constant), 12> Q >1

The probability pw and Prain are referred to the same threshold level. The conversion factor Q is expressed as a function of Prain and the climatic parameters Q1 and . In the range of interest for microwave planning, Q is given by following expression

% 3 12

for 1

11


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Q1 = 2.85

= 0.13 8.6.3.2 From worst month to yearly

The transformation from a yearly probability to worst-month probability is obtained from expression (91)

= 11

11

1 wrain pQP (92)

The selection of the climatic parameters when transforming annual worst-month time percentage to average annual time percentages may in some applications of microwave design have an important effect.

The range of validity of the conversion model is strongly dependent on the climate and should be known by microwave designers.

8.6.4 Presentation of the rain fading models in diagram form Figure 24 illustrates the rain fading models (worst month and on a yearly basis) for different values of the quotient between total rain attenuation exceeding 0.01% of the time (AR0.01) and the fade margin, M. When the quotient is equal to 0.155, outage is set to 810-7.

0 1 102 3 4 5 6 7 8 9 2 3 4 5 6 7 8

AR0.01/M

10-8

10-7

10-6

10-5

10-4

10-3

10-2

10-1

100

Perc

enta

ge o

f tim

e th

efa

de m

argi

n is

exc

eede

d, %

Rain fading modelannual basis

Rain fading modelworst month

1

Figure 24: The rain fading models for worst month and on a yearly basis.


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8.7 Multipath fading Figure 25 illustrates a multipath scenario.

Atmospheric layer

Figure 25: Multipath propagation illustrated by three radio beams:

Beams that are reflected by the atmosphere or the ground travel a longer distance than do direct beams. Dependent on the size of the time delays and the employed channel bandwidth, fading can either be

Flat or

Frequency selective

In general:

Fading due to rain, for frequencies below 10 GHz, may be considered as negligible in comparison with fading due to multipath propagation, which is often dominant below 10 GHz.

Fading due to multipath propagation, for frequencies above 10 GHz, may be considered as negligible in comparison with fading due to rain, which is often dominant above 10 GHz.

A good rule of thumb is however, that there exists a cross-over region between the frequencies of 10 and 18 GHz, and a point at which fading due to rain and multipath propagation are of about the same order of magnitude.

8.7.1 Flat and frequency selective fading Flat fading implies that there does not exist any noticeable local variation within the transmitted frequency band, see Figure 26, i.e., fading has the same degree throughout the band.

Frequency selective fading implies that there does exist a noticeable variation within the transmitted frequency band (see the figure below).


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fB

A

fB

A Flat Frequency selective

Figure 26: Flat and frequency selective fading.

The extent of the influence of multipath propagation on a radio link system depends on whether the system is analog or digital and whether the fading is flat or frequency selective.

8.7.2 The effects of multipath propagation The effect of flat fading for digital and analog connections is similar. Signal level decreases and quality degrades. Continued quality degradation will eventually lead to the breakdown of the connection. Digital systems usually exhibit a somewhat higher tolerance to flat fading than do analog systems.

In the case of base band, analog link connections utilize frequency multiplexing in which each channel of N channels contains a small (B/N) frequency band.

For frequency selective fading, signal levels vary locally within the frequency band, both in amplitude and phase. The result, in the case of analog connections, is that a number of channels may attain signal levels that are so low that connection within these channels is virtually impossible. The connection can, however, be maintained at a lower capacity.

In the case of base band, digital link connections utilize the entire frequency band, B, of all channels in a time-multiplexed manner. This means that every channel has a time slot and synchronism is therefore required for system management purposes.

In-band variations in the case of a time-duplexed digital connection represents a loss of information, the connection loses synchronization, resulting in the fact that the connection can no longer be maintained. The disturbance affects all channels and is abated, only after synchronization is once again established.


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8.7.3 Measures taken against multipath fading Measures

radiowave propagation

Documents

total rain attenuation

specific rain attenuation

total reflection coefficient

fresnel reflection coefficient

spherical earth

total gas attenuation

true earth radii

earth bulge