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
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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:
Page 6(28) L.nr. 29073 Rev. B 99.05.01 PT/InHe/Vba
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:
L.nr. 29073 Rev. B 99.05.01 PT/InHe/Vba Page 7(28)
- 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
L.nr. 29073 Rev. B 99.05.01 PT/InHe/Vba Page 11(28)
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:
Page 12(28) L.nr. 29073 Rev. B 99.05.01 PT/InHe/Vba
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
The following procedure is used to calculate the selective and non-selective outages:
Page 16(28) L.nr. 29073 Rev. B 99.05.01 PT/InHe/Vba
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
Page 18(28) L.nr. 29073 Rev. B 99.05.01 PT/InHe/Vba
[ ]
=
≤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