L29073 Prediction Method RevB

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L.nr. 29073 Rev. B 99.05.01 PT/InHe/Vba Page 1(28)

2.1 FREE SPACE LOSS........................................................ ............................................................ ............................................ 2

2.2 PROPAGATION LOSS ..................................................... ............................................................ ............................................ 2

2.3 NORMAL PATH ............................................................ ............................................................ ............................................ 3

2.4 PATH WITH PASSIVE REPEATER ....................................................... ............................................................ ........................ 4

2.5 FADING MARGIN.......................................................... ............................................................ ............................................ 5

3.1 MULTIPATH ....................................................... ............................................................ ...................................................... 5

4.1 SINGLE DIVERSITY....................................................... ............................................................ .......................................... 11

5.1 OUTAGE DUE TO CLEAR-AIR EFFECTS FOR CO-CHANNEL SYSTEMS .................................................... ................................. 16

5.2 OUTAGE DUE TO PRECIPITATION EFFECTS FOR CO-CHANNEL SYSTEMS........................................................ ....................... 17

6.1 SPECIFIC ATTENUATION ......................................................... ............................................................ ................................ 18

6.2 EFFECTIVE PATH LENGTH...................................................... ............................................................ ................................ 18

6.3 UNAVAILABILITY DUE TO RAIN ATTENUATION ..................................................... ........................................................... ... 19



Page 2(28) L.nr. 29073 Rev. B 99.05.01 PT/InHe/Vba

This document gives a description of the methods used by Nera Networks AS to predict the systemperformance of terrestrial digital line-of-sight radio relays. The prediction methods are based upon the

ITU-R Recommendation 530-7 [5.].

The system performance evaluation predicts the error performance due to multipath fading and related

mechanisms, as well as the unavailability due to rain.

The resulting sum error performance in percent for a system is presented and compared with the ITU-R

performance objectives.

For abbreviations and use of units in the formulas, please refer to Appendix 1.

During free-space conditions, the signal attenuation between two isotropic antennas is given by:

( ) . log ( )

= + ⋅ ⋅92 45 20

10

where is distance in km and is frequency in GHz.

The propagation loss relative to the free-space loss is the sum the following contributions:

attenuation due to atmospheric gases

multipath fading attenuation due to precipitation

In addition, diffraction loss due to obstructions and attenuation due to sand and dust storms may be

significant. These mechanisms are however not included in the prediction model.

At higher frequencies, above about 15GHz, the attenuation due to atmospheric gases will add to the

total propagation loss of a radio relay path. The attenuation on a path is given by:

= + ⋅( )




where

- path length in km

γ

- specific attenuation [dB/km] for dry air

γ W - specific attenuation [dB/km] for water vapour

The attenuation due to dry air and water vapour can be estimated using the simplified algorithms given

in ITU-R Rec. P.676 [3.] Section 2.1 are valid for frequencies below 57GHz.

( )

γ

=

+ +

− +

⋅ −7 27

0351

7 5

57 2 4410

2 2 2 2 2 5

2 2 2 3.

.

.

.

( )

( ) ( )

γ

ρ

ρ

= ⋅ + ⋅ + ⋅ + − +

+− +

+− +

⋅

− − −

−3 27 10 1 67 10 7 7 10

3 79

22 235 9 81

1173

183 31 1185

4 01

325153 10 44

10

2 3

7

4

2 2

2 2 2 2

2 4. . .

.

. .

.

. .

.

. .

where

- frequency in GHz

= p/1013

= 288/(273+t)

- pressure is set to 1013 hPa

- temperature in C°

ρ - water vapour density in g/m3 . The figure in APPENDIX 4 from ITU-R Rec. P. 836 [1.]

gives the annual surface water vapour density.

The net path loss ( ) level for a normal path is given by:

( ) = + + + + − − +1 2 1 2

and the received signal level is

( ) = −

where

- received power in dBm

- net path loss in dB




- transmitted power in dBm

- gain of antennas in dB over isotropic

- feeder loss in dB

- branching loss in dB (circulators, filters)

- attenuation due to atmospheric gases, equation

- other loss in dB (e.g. attenuators , degradation of threshold)

- free space loss in dB, equation

A path with a passive repeater is treated as two individual paths with one common passive site. The

receiver level at the active sites is thus given by:

( )

= − − − − + ⋅ − − − + + −1 2 1 2 1 2 1 22

When a plane reflector is used, the gain of the passive site is given by

( ) . log ( ) log cos= + + ⋅

2145 20 10

210 10

γ

where

- area (in square meters) of the reflector

γ - the angle between the incident and the reflected ray at the reflector

When a passive repeater with back-to-back antennas is used, the gain of the passive site is given by:

( ) = + −1 2

where

- gain of back-to-back antennas in dB

- coupling loss between antennas in dB




The difference between normal received signal level and the receiver threshold level is called the

fading margin:

( ) _= − −

where

- normal received signal level in dBm

- receiver threshold level in dBm

- receiver threshold degradation due in interference in dB

This fading margin is a critical parameter in prediction of system performance.

For small percentages of the time a path may experience that the signal level decreases or that the

signal gets distorted. This signal fading is mainly due to two mechanisms called multipath fading and

fading due to precipitation (rain).

Outages due to multipath are normally of short duration, less than 10 seconds. The sum of these

outages gives the error performance of the radio relay system and should be compared with the ITU-R

objectives given in ITU-R recommendations.

On the other hand, outages due to precipitation last longer than 10 consecutive seconds and are

therefore termed unavailability and are added to the total unavailability of the radio-relay system. This

total unavailability should be compared with the unavailability objectives given in ITU-R

recommendations.

Fading due to layering of the atmosphere is the dominating factor of degradation of radio-relays.

Meteorological conditions in the space separating the transmitter and the receiver, may sometimes

cause detrimental effects to the received signal. Rays that normally would have been lost in the

troposphere may be refracted into the receiving antenna where they are added to the wanted signal. The

phase- and amplitude relationship between signals thus received determines the resulting output from

the receiver.

This affects the transmission of digital signals in two ways. In some occasions, all components of the

useful signal spectrum will be equally reduced. This is called non-selective or "flat" fading.

Other times only some of the spectral components will be reduced, causing the spectrum to bedistorted. This is called frequency selective fading.




The cross-polarization discrimination (XPD) can deteriorate sufficiently to cause co-channel

interference. This outage due to clear-air cross-polarization will only contribute to the total outage

when the radio-relay system is utilising both polarizations on the same RF-channel to transmit two

traffic channels. The outage is negligible for other radio-relay system.These three effects will be treated separately.

The total outage due to multipath fading is calculated from:

( )

=

+ +

+ +

where

- non-selective (flat) outage

- non-selective outage with diversity

- selective outage

- selective outage with diversity

- outage due to clear-air cross-polarization for co-channel systems

The percentage of time that fade depth is exceeded in the average worst month can be calculated

from:

= ⋅ −

01010 %

When using equal to the fading margin found using formula gives us the percentage of time

when the receiver signal is fading below threshold.

The parameter 0, the fading occurrence factor, has been related to well-defined path parameters.

The methods are based on statistical analysis of paths in different parts of the world. The paths used

have path lengths ranging from 7 to 95 km, frequencies ranging from 2 to 37 GHz, path inclinations for

the range 0-24 mrad, and grazing angles in the range 1-12 mrad. Checks using several other sets of datafor paths up to 237 km in length and frequencies as low as 500 MHz suggest, however, that the method

is valid for larger ranges of path length and frequency

The fading occurrence factor for the average worst month:

0

3 6 0 89 1 41= ⋅ ⋅ ⋅ + −. . .( )ε

where

- Geoclimatic factor




- Path length (km)

- Frequency (GHz)

ε

= −1 2

- Path inclination (millirad)

- antenna heights (m)

The geoclimatic factor may be estimated for the average worst month from fading data. In absence of

such data the following empirical relations must be used

Inland links are those in which either the entire path profile is above 100 m altitude (with respect to

mean sea level) or beyond 50 km from the nearest coastline, or in which part or all of the path profile is

below 100 m altitude for a link entirely within 50 km of the coastline, but there is an intervening height

of land higher than 100 m between this part of the link and the coastline. Links passing over a river or a

small lake should normally be classed as passing over land.

( )

= ⋅ ⋅ ⋅− − ⋅ − −50 10 107 1 5 0 1 0. . .

The coefficient C Lat of latitude ξ is given by

[ ]

= 0 dB 53oS ≥ ξ ≤ 53

oN

[ ]

= − +53 ξ dB 53oN or

oS < ξ < 60

oN or

oS

[ ]

= 7 dB ξ ≥ 60oN or

oS

The longitude coefficient C Lon is given by

[ ]

= 3 dB Longitudes of Europe and Africa

[ ]

= −3 dB Longitudes of North and South America

[ ]

= 0 dB All other longitudes

The value of the coefficient 0 is given in Table 1 for three ranges of altitude of the lower of the

transmitting and receiving antennas and three types of terrain (plains, hills, or mountains). In cases of

uncertainty as to whether a link should be classified as being in a plain or hilly area, the mean value of

the coefficients 0 for these two types of area should be employed. Similarly, in cases of uncertainty as

to whether a link should be classified as being in a hilly or mountainous area, the mean value of the

coefficients 0 for these two types of area should be employed. Links traversing plains at one end andmountains at the other should be classified as being in hilly areas. For the purposes of deciding whether




a partially overwater path is in a largely plain, hilly, or mountainous area, the water surface should be

considered as a plain.

For planning purposes where the type of terrain is not known, the following values of the coefficient 0should be employed:

0 = 1.7 for lower-altitude antenna in the range 0-400 m above mean sea level;

0 = 4.2 for lower-altitude antenna in the range 400-700 m above mean sea level;

0 = 8 for lower-altitude antenna more than 700 m above mean sea level.

Table 1 Values of C0 for various types of inland links

is the percentage of time that the average refractivity gradient in the lowest 100 metre of the

atmosphere is less than -100 Nunits/km.

The figures in APPENDIX 2 from ITU-R Rec. P.453 [4.] give for four different months. The month

that has the highest value should be chosen. An exception to this is that only the maps for May and

August should be used for latitudes greater than 60oN or 60

oS. These figures are given in Appendix 2.

The size of a body of water can be chosen on the basis of several known examples: Large bodies of

water include the English Channel, the North Sea, the larger reaches of the Baltic and Mediterranean

Seas, Hudson Strait, and other bodies of water of similar size or larger.

Altitude of lower antenna and type of link terrain 0

(dB)

Overland or partially overland links, with lower-antenna altitude less than 400 m above mean sea level,located in largely plains areas

0

Overland or partially overland links, with lower-antenna altitude less than 400 m above mean sea level,located in largely hilly areas

3.5

Overland or partially overland links, with lower-antenna altitude in the range 400-700 m above mean sealevel, located in largely plains areas

2.5

Overland or partially overland links, with lower-antenna altitude in the range 400-700 m above mean sealevel, located in largely hilly areas

6

>

Overland or partially overland links, with lower-antenna altitude more than 700 m above mean sea level,located in largely plains areas

5.5

>

Overland or partially overland links, with lower-antenna altitude more than 700 m above mean sea level,located in largely hilly areas

8

>

Overland or partially overland links, with lower-antenna altitude more than 700 m above mean sea level,located in largely mountainous areas

10.5




=

( )( – ) log log= ≥

<

+10

1for

for

where

is the fraction of the path profile below 100 m altitude above the mean level of the body of

water in question and within 50 km of the coastline, but without an intervening height of land above100 m altitude,

is given by the expression for for inland links in equation 14), and:

= ⋅ ⋅− − ⋅ − ⋅2 3 10 104 0 1 0 0110.

. . ξ

where ξ is the latitude in degrees.

The size of a body of water can be chosen on the basis of several known examples: Medium-sized

bodies of water include the Bay of Fundy (east coast of Canada) and the Strait of Georgia (west coast of

Canada), the Gulf of Finland, and other bodies of water of similar size.

=

( ) ( – ) log log= ≥<

+10 1 for

for

where

is the fraction of the path profile below 100 m altitude above the mean level of the body of

water in question and within 50 km of the coastline, but without an intervening height of land above

100 m altitude,

is given by the expression for for inland links in equation 14), and:

= ⋅ +

100 5. (log log )

with

given by equation Note that the condition

<

occurs in a few regions at low and mid

latitudes.

Regions (not otherwise in coastal areas) in which there are many lakes over a fairly large area are

believed to behave somewhat like coastal areas. The region of lakes in southern Finland provides the

best known example. Until such regions can be better defined, should be calculated from:

= − +100 5 2. [( ) log log ]

with

given by equation ,

given by equation and where

is the fraction of the path profile

below 100 m altitude above the mean level of the body of water in question and within 50 km of the

coastline, but without an intervening height of land above 100 m altitude.

In cases of uncertainty as to whether the size of body of water should be classed as medium or large,

should be calculated from:




= − + +

10 1 0 5( ) log . (log log )

with

given by equation ,

given by equation Kcl given by equation ) and where

is the

fraction of the path profile below 100 m altitude above the mean level of the body of water in question

and within 50 km of the coastline, but without an intervening height of land above 100 m altitude.

There are a number of different methods for predicting outages due to frequency selective fading. The

method using the signature curve is described in ITU-R Rec. P.530 [5] .This method agrees reasonably

well with measured results and clearly shows the radio’s ability to withstand the selective fading.

= ⋅ ⋅ ⋅430

2

0

η τ

τ in %

where η is related to the fading occurrence factor 0. η is often called the fading activity factor:

η = − − ⋅

1

0 2100

00 75

.

.

where P0 is the multipath occurrence factor corresponding in %, given in equation 13).

τ

is the typical path echo delay given by :

τ

= ⋅ 0 750

1 3

.

.

is the path length in km and is called the equipment signature factor.

τ

is the echo delay time used during measurement of the signature curves. A much used value (also

used by Nera) is:

τ 0 = 6.3 ns

The signature factor is derived from the signature curve of the equipment, using the formula:

( )

= ⋅ × + ×− −1

210 1020 20 / /

where:

: minimum phase signature width (GHz)

: minimum phase signature depth (dB)

: non-minimum phase signature width (GHz)

: non-minimum phase signature depth (dB)




The performance of a radio-relay system can be improved substantially by applying diversity reception

or transmission techniques such as space, frequency or hybrid diversity.

By switching or combining the different channels carrying the same signal, it is possible to attain animprovement relative to a single channel given by the factor:

= Single channel

Diversity

The degree of improvement afforded by all of the diversity techniques depends on the extent to which

the signals in the diversity branches of the system are uncorrected. For narrow-band analogue systems,

it is sufficient to determine the improvement in the statistics of fade depth at a single frequency. Forwideband digital systems, the diversity improvement also depends on the statistics of in-band

distortion.

The vertical space diversity improvement factor on overland paths can be estimated from:

( )

= − − ⋅ ⋅ ⋅ ⋅ ⋅

⋅− −−

−1 334 10

100104 0 87 012 0 48 0

10410

exp . . . ..

where

- path length (km)

- fade depth (dB) for the unprotected path

- frequency (GHz)

- gains of the two space diversity antennas (dB)

0 fading occurrence factor in %

vertical separation (centre-to-centre) of receiving antennas (m)

= −1 2

The relation for applies only when the following conditions are met:

2 GHz < < 11 GHz




43 km < < 240 km

3 m < < 23 m

ITU-R Rec. P.530 [5.] indicates that can be used with reasonable accuracy for path lengths down to

25 km. In cases where any of these boundaries have been exceeded (within reasonable limits), theparameters have been set equal to the boundary value in the program. E.g. for 13 or 15 GHz links, the

improvement factor for 11 GHz will be calculated.

The following procedure is used to calculate the selective and non-selective outages:

Calculate the square of the non-selective correlation coefficient,

, from:

21 100= −

⋅

η

where in % is the outage due to the non-selective component of the fading that is given by equation and η is the fading activity factor that is given by equation

Calculate the square of the selective correlation coefficient,

, from:

( )

( )

2 0109 013 1

0 5136

0 8238 05

1 0195 1 05 0 9628

1 0 3957 1 0 9628

=

≤

− − < ≤

− − >

− −

. .

. . .

. .

. . log ( )

.

for

for

for

where the correlation coefficient,

, of the relative amplitudes is given by:

( )( )

=− − ≤

− − >

1 0 9746 1 0 26

1 0 6921 1 0 26

2 2 170 2

21034

2

. .

. .

.

.

for

for

Calculate the non-selective outage,

, from:

= in %

where

in % is the outage due to the non-selective component of the fading given by equation

Calculate the selective outage,

, from:

( )

=⋅ −

2

2100 1η

in %

where

in % is the non-protected selective outage given by equation





Calculate the improvement factor for frequency diversity from:

{ }

=

⋅

⋅ ⋅ ≥80

10 510∆

∆ - frequency spacing between rf-channels in GHz

- carrier frequency in GHz

- distance in km

- fading margin in dB

[ ]

The equation is considered valid only for values of ≥ 5. The relation for applies only when the

following conditions are met :

1.7 GHz < < 13 GHz

20 km < < 75 km

∆ / < 0.05

In cases where these boundaries are exceeded (within reasonable limits), the is calculated with

boundary values. E.g. if the distance is 15 km, then is calculated with = 30 km.

Calculate the square of the non-selective correlation coefficient,

, from:

21 100= −

⋅

η

where

in % is the outage due to the non-selective component of the fading that is given in formula

and η is the fading activity factor that is given in formula


, from:

( )

( )

2 0 109 013 1

0 5136

0 8238 05

1 0195 1 0 5 0 9628

1 0 3957 1 0 9628

=

≤

− − < ≤

− − >

− −

. .

. . .

. .

. . log ( )

.

for

for

for



( )

( )

=− − ≤

− − >

1 0 9746 1 0 26

1 0 6921 1 0 26

22 170

2

21034

2

. .

. .

.

.

for

for





, from:

= in %

where



, from:

( )

=⋅ −

2

2100 1η

in %

where


If frequency diversity is used in n+1 operation, n>1, the diversity improvement factor will be reduced

since there are more than one channel sharing the same diversity channel.

If it is assumed that no more than two of the rf-channels are simultaneously afflicted by equal fading,

and both have the same priority, the reduced diversity improvement factors are given by:

) { } 2 1 0 67+ = ⋅. { } 5 1 0 49+ = ⋅.

{ }

3 1057

+ = ⋅.

{ }

6 10 47

+ = ⋅.

{ } 4 1 052+ = ⋅. { } 7 1 0 45+ = ⋅.

Hybrid diversity is an arrangement where a 1+1 system has two antennas at one of the radio sites only.


The non-selective correlation coefficient,

, is found from:

= ⋅, ,

where

,

and

,

are the non-selective correlation coefficients computed for space diversity equation

and frequency diversity equation , respectively.


, from:

( )

( )

2 0109 013 1

0 5136

0 8238 05

1 0195 1 05 0 9628

1 0 3957 1 0 9628

=

≤

− − < ≤

− − >

− −

. .

. . .

. .

. . log ( )

.

for

for

for






( )

( )

=− − ≤

− − >

1 0 9746 1 0 26

1 0 6921 1 0 26

22 170

2

21034

2

. .

. .

.

.

for

for


, from:

= in %

where



, from:

( )

=⋅ −

2

2100 1η in %

where


Combined diversity is an arrangement where both frequency and space diversity are used.


, from:

= + in %

where


is the improvement factor for frequency diversity given by equation and

is the vertical space

diversity improvement factor given by equation 32).


, from:

=+

in %

where


[ ]

Co-channel operation of radio relay systems will double the capacity compared to conventional radio

relay systems. In co-channel systems transmission of two separate traffic channels is performed on the

same radio frequency but on orthogonal polarisation. This works well as long as the discrimination




between the two polarisations called Cross Polar Discrimination (XPD), is sufficient to ensure

interference-free operation. The nominal value of XPD is termed XPD0 and is governed by the cross-

polarisation patterns of the antennas.

Both multipath- and rainfading can result in severe degradation of the XPD level. As the XPD

decreases, the interference level in the channel will rise and may cause threshold degradation and errorsin the data traffic. Procedures for predicting both the outage due to clear-air effects and due to

precipitation conditions is given ITU-R Rec. P.530 [5.].

The following procedure is used to calculate the outage due reduction of XPD in clear-air:

0

5 35

40 35=

+ ≤

>

for

for

is the manufacturer’s guaranteed minimum XPD at boresight for both the transmitting and

receiving antennas, i.e., the minimum of the transmitting and receiving antenna boresight XPDs.

= − ⋅

10

100

0

logη

whereη is the fading activity factor given by equation and P0 in % is the fading occurrence factor

given by equation and:

= − − ×

−0 7

1 0 3 4 106

2.

. exp

one transmit antenna

two transmit antennasλ

In the case where two orthogonally polarized transmissions are from different antennas, the vertical

separation is

(m) and the carrier wavelength is λ (m).

Derive the parameter from:

= +0

Calculate the outage

due to clear-air cross-polarization from:

= × −

01010 in %

where P0 in % is the fading occurrence factor given by equation and

(dB) is the equivalent

XPD margin for a reference BER given by:




=−

− +

0

0

without XPIC

with XPIC

Here, C0 / is the carrier-to-interference ratio for a reference BER, which is measurements.

XPIF is a laboratory-measured cross-polarization improvement factor that gives the difference in cross-

polar isolation XPI at sufficiently large carrier-to-noise ratio and at a specific BER for systems with and

without cross polar interference canceller (XPIC).

In addition to the usual attenuation of microwave signals due to rain, there will also be a depolarisation

effect. This depolarisation may be substantial even at frequencies where the attenuation is insignificant

(below 10 GHz). The following procedure is used to calculate the outage:

Calculate the coefficients U and V.

58) = 0 + 30 log

where 0 is set to equal 15 dB and is the frequency in GHz.

59)

( )

.

.

.

.=

<

≤ ≤

< ≤

19 002 8

12 8 8 20

22 6 20 35

0 19

[ ]

Determine the path attenuation, 0,01 (dB), exceeded for 0.01% of the time from :

60)

0 01. = ⋅

where ψ is the effective path length given by equation and γ r is the specific attenuation given by

equation

Determine the equivalent path attenuation,

(dB):

= − +10 0(( / ) / )

in dB

where 0

(dB) is the carrier-to-interference ratio defined for the reference BER without XPIC, and

XPIF (dB) is the cross-polarized improvement factor for the reference BER. If an XPIC device is not

used, set XPIF = 0.

Determine the following parameters:




[ ]

=

≤2326 012

40

400 01. log . .

if

otherwise

and:

( ) = − + −12 7 16123 4 2. . /

Determine the outage due to precipitation effects for co-channel systems from:

= ⋅ −100 10 2( ) in %

The total outage probability due to rain is calculated from taking the largest value of

and

.

On any path there is a possibility of additional attenuation of the radio signal due to absorption and

scattering by rain and sleet. This can be ignored at frequencies below 5 GHz. At higher frequencies, in

particular above 10 GHz, it can be quite significant.

The model described in ITU-R Rec. P.530 [5.] is used to calculate the unavailability due to rain. The

rainfall contour maps in appendix 3 may be used if specific rainfall data for the region of interest is not

available.

The specific attenuation γ (dB/km) for the frequency, polarization and rain rate is given by

γ α

= ⋅

- the rain intensity in mm/h not exceeded for more than 0.01% of the worst month. Appendix 3

and α are regression coefficients that have been calculated for oblate spheroid raindrops for a range of frequencies. These parameters are appropriate to the polarization. These regression coefficients are

given in ITU-R Rec. 838 [2.]. It should be noted that the specific attenuation is lowest for the vertical

polarization.

Since the rain cells have a tendency to cluster, only parts of the path will be affected by rain. The

effective path length containing rain cells is given by

Ψ =+

⋅

− ⋅

1

35 0 015.




- path length (km)

For rain rates > 100 mm/h, the value 100 mm/h is used in place of .

The unavailability (in percent) due to rain is given by:

( )

= ⋅ ⋅ ⋅ − + ⋅0120 546 0 0 43 10.

( . . log )Ψ γ

- unavailability in percent

- fading margin in dB

The unavailability may be found by solving equation with respect to

( )( )

= ⋅ − + + ⋅ ⋅ ⋅

1011 628 0 546 0 29812 0 172 0 12. . . . log . / ψ γ

in %

To avoid imaginary values, use ψ ⋅ γ

in case where ψ ⋅ γ

The prediction procedure outlined above is considered to be valid in all parts of the world at least for

frequencies up to 40 GHz and path lengths up to 60 km.

The total outage probability due to rain is calculated from taking the largest value of

and

.

, = >

<

if

ifin %

The outage due to precipitation effects for co-channel systems is set to zero,

= 0, for radio relay

systems without a co-channel arrangement.




Water vapour: Surface density and total columnar content.ITU-R Recommendation P.836-1 1997

Specific attenuation model for rain for use in prediction methods.

ITU-R Recommendation 838 1992

Attenuation by atmospheric gases.

ITU-R Recommendation P.676-3 1997

[] The radio refraction index: Its formula and refractivity data..

ITU-R Recommendations P.453-6 1997

[] Propagation data and prediction methods required for the design of terrestrial line-of-sight

systems.

ITU-R Recommendation P.530-7 1997




: area of reflector (passive repeater) in square meters

Aa : attenuation due to atmospheric gases in dBAp : equivalent path attenuation in dB

: critical notch depth in dB

: minimum phase signature depth (dB)

: non-minimum phase signature depth (dB)

C0 /I : carrier-to-interference ratio in dB

Clat : latitude in deg

Clon : longitude in deg

: path length in km

: fading margin

: frequency in GHz

: gain of antennas in dB over isotropic

: gain of passive repeater in dB

: gain of back-to-back antennas (passive repeater) in dB

: gain of space diversity antennas in dB

: antenna heights in m (above sea level)

: diversity improvement figure

: frequency diversity improvement figure

: space diversity improvement figure

: geoclimatic factor

: coefficient used in computing rain attenuation

k ns : non-selective correlation coefficient

k s : selective correlation coefficient

: branching loss in dB (circulators, filters etc.)

: feeder loss in dB

: free space loss in dB : free space loss of one part (passive repeater)

: free space loss of second part (passive repeater)

: other loss in dB (attenuators, degradation of threshold)

L.O.S. : line of sight

LThr_Deg : receiver threshold degradation due in interference in dB

MXPD : equivalent XPD margin in dB

: radio refractivity

: net path loss in dB

p : pressure in hPa




: fading occurrence factor in %

: probability of flat fading in %

: percentage of time that the average refractivity gradient in the lowest 100 metre

of the atmosphere is less than -100 Nunits/km : received signal power in dBm

: outage due to non-selective fading in % for system with diversity

: outage due to selective fading in % for system with diversity

: outage due to non-selective fading in %

: total outage probability due to rain in %

: outage due to selective fading in %

: power output from transmitter in dBm

: threshold power of receiver in dBm (referred to BER)

: total outage due to multipath fading in %

: outage due to clear-air cross-polarization

: outage due to precipitation cross-polarization

: rain intensity in mm/h not exceeded for more than 0.01% of worst month

rc : fraction of the path profile below 100 m altitude above the mean level of the body of water

rw : correlation coefficient

: space diversity distance in m (vertical distance between

antennas in a space diversity arrangement)

St : different in vertical separation between two antennas transmitting on orthogonally

polarization.

: signature factor

: temperature in C°

: minimum phase signature width (GHz)

: non-minimum phase signature width (GHz)

XPIF : cross-polarized improvement factor in dB

XPD0 : equivalent XPD for the antennas

XPDg : minimum XPD at boresight for the antennas

ε : path inclination in millirad

α : regression coeffisient used in computing rain attenuation

∆ : frequency spacing between RF channels in GHz

γ : the angle between the incident and the reflected ray at the reflector

γ : specific rain attenuation in dB/km

η : fading activity factor

τ

: typical path echo in nsτ

: median echo delay in ns(used during measurements)

Ψ : effective path length in km




γ : specific attenuation [dB/km] for dry air

γ : specific attenuation [dB/km] for water vapour

ρ : water vapour density in g/m3

λ : wave length in m




Figure A1 Percentage of time gradient ≤ -100 (N/km) : February

Figure A2 Percentage of time gradient ≤ -100 (N/km) : May




Figure A3 Percentage of time gradient ≤ -100 (N/km) : August

Figure A4 Percentage of time gradient ≤ -100 (N/km) : November




(Reference to Figs. A5 to A7)

Figure A5 Europe and Africa

Percentageof time

(%)A B C D E F G H J K L M N P Q

1.001 < 0.1 20.5 20.7 12.1 10.6 01.7 13 12 18 101.5 102 114 115 112 124

0.301 <0.8 22. 22.8 14.5 12.4 04.5 17 14 13 104.2 107 111 115 134 149

0.101 <2.8 23.5 25.5 18.5 16.5 08.5 12 10 20 012.5 115 122 135 165 172

0.031 <5.8 26.5 29.5 13.5 12.5 15.5 20 18 28 023.5 133 140 165 105 196

0.003 14.8 21. 26. 29. 415 545 45 55 45 070. 105 195 140 200 142

0.001 22.8 32. 425 425 705 785 65 83 55 1005 150 120 180 250 170




Figure A6 America

Figure A7 Asia and Australia



Figure A8 Annual surface water vapour density (g/m3)

Documents

L29073 Prediction Method RevB