performance and unavailabilty - principles and formulae

7/30/2019 Performance and Unavailabilty - Principles and Formulae

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Planning digital radio-relay networks

k&k engineering

erformance andunavailability

Principles & formulae

Version G.826


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2

k&k engineering01-07-2003 TECHNICAL PAPER KKE 5201/5 Rev. H

1998-2003Copying the contents of this booklet as well as translations to other languages, completely or partly, is not

allowed without the permission ofK&K Engineering HB. This includes any kind of copying by print, duplica-

tion, tape recording, electronic methods etc.

K&K Engineering HB, Box 2, S-610 54 NVEKVARN / Sweden

Phone & Fax: +46-155-535 77

or: +46-8-532 51 888

E-mail: [email protected]

Internet home page: http://www.KK-Engineering.a.se

030701


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k&k engineering TECHNICAL PAPER KKE 5201/5 Rev. H 01-07-2003

Introduction

K&K EngineeringsPC-based computer programs

FORMULAand

RLTool, are in-

tended for the prediction of performance and availability of radio-relay paths and circuits. This

paper, which is based on H. Karls booklets Planning and engineering of radio-relay networks

and Performance and availability as applied to digital radio-relay systems {1,2}, describes the

principles and formulae utilized in the program.

In version 1 of this TECHNICAL PAPER KKE 5201/1, the formulae were mainly derived from

CCIR Report 338. The ITU-R Recommendation P.530 has later on replaced this report.

In September 1997, the ITU-R published version 7 of its Rec. P.530. This recommendation con-

tains a complete new set of formulae for the prediction of both flat and selective multipath fad-

ing, as well as for the improvement due to diversity. Also the formulae for the prediction of at-tenuation by atmospheric gases have been modified - Rec. P.676-3. This new formulae have

been introduced in the above programs with effect from version 2.0 for FORMULA and version

2.20 for RLTool.

During 2001, ITU-R introduced version 9 of Rec. P.530, which contains a complete new set of

formulae for the prediction of multipath fading. This new formulae have been introduced in the

above programs with effect from version 2.0 for FORMULA and version 3.0 for RLTool.

This paper is based on the new versions of the above ITU-R recommendations.

Note:

In some of the formulae, a distance parameter may be included. Dependent on the subject of the

formula, this distance parameter may represent the geodetic distance, as read from a map, or the

real distance of the radio beam between two antennas. To distinguish between these two dis-

tances, two different symbols are used:

d... distance as read from a map in km, or: geodetic path length = plane projection of the radio

path

d*... real length of the radio beam between transmitter and receiver antenna in km = beam path

length

d*can be calculated applying the following formula:

( )622*

10

+= BA hhdd

d*

... real length of the radio beam between transmitter and receiver an-

tenna in km

d... geodetic path length in km = plane projection of the radio path

hA ... height above sea level for station A in m

hB ... height above sea level for station B in m


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.The revision concerns:

The note on page 3

d = Formlerna 1-6, 8, 10, 14, 15, 17, 21-29, 33, 49, 76, 79

d*

= Formlerna 31, 32, 38, 47, 48, 64, 85, 113

corr. of formulae [106]

corr av section 4.6.4.2

fr.o.m. formel 109: -1 siffra


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Table of contents

1 Path geometry........................................................................................................................91.1 Co-ordinates and bearing .................................................................... ........................... 9

1.1.1 Calculation of great-circle distance and bearing....................................................9

1.1.2 Determination of co-ordinates ................................................................. .............. 9

1.2 1st Fresnel zone radius...................................................................................................9

1.3 Calculation of antenna heights.....................................................................................10

1.4 Calculation of path clearance.......................................................................................11

1.5 Effective Earth radius factork.....................................................................................11

1.6 Ground reflection and its calculation...........................................................................11

1.6.1 Calculation of antenna heights.............................................................................11

1.6.2 Location of reflection point ................................................................ ................. 13

1.6.3 Difference in path length between direct and reflected ray..................................13

1.6.4 The distance between receiver input level minima or maxima ............................ 14

1.6.5 Optimum antenna spacing with space diversity protection..................................14

1.6.6 Efficiency of selected space diversity versus k-value variation...........................14

1.6.7 Antenna discrimination........................................................................................15

2 Path attenuation and receiver input level......................................................................... ....16

2.1 Total path attenuation during fading-free time ............................................................ 16

2.2 Free-space basic attenuation ................................................................... ..................... 16

2.3 Additional attenuation(s) ................................................................... .......................... 16

2.4 Gain or loss in a passive repeater, antenna back-to-back.............................................16

2.5 Gain or loss in a passive repeater, plane reflector........................................................17

2.5.1 Check of far-/near-field operation: ................................................ ...................... 17

2.5.2 Angle in space......................................................................................................17

2.5.3 Repeater gain in far field......................................................................................17

2.5.4

Half-power (3 dB) beam width............................................................................19

2.6 Losses due to atmospheric gases..................................................................................19

2.7 Receiver input level during fading-free time ............................................................... 20

3 Overall performance of a digital radio-relay link during fading-free time and time ofshallow fading..............................................................................................................................21

4 Overall performance of a digital radio-relay link during fading - Performance calculation21

4.1 General.........................................................................................................................21

4.2 The multipath occurrence factor ...................................................................... ............ 21

4.2.1 Prediction formula .......................................................... ..................................... 21

4.2.2 Path inclination .................................................................. .................................. 214.2.3 Geoclimatic factor K............................................................................................22

4.3 Performance prediction considering multipath fading and related mechanisms..........23


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4.3.1 Prediction formulae ............................................................... .............................. 23

4.3.2 Fading margin............................................................... ....................................... 24

4.3.3 Paths going via passive repeaters ................................................................... ..... 244.4 Performance prediction considering distortions due to propagation effects (selectivefading) 24

4.4.1 Prediction formulae ............................................................... .............................. 24

4.4.2 Prediction procedure for path going via a passive repeater ................................. 25

4.5 Small-time-percentage for exceeding the planning objectives due to attenuation causedby precipitation.................................... ................................................................ .................... 25

4.5.1 Attenuation caused by rain ........................................................... ....................... 25

4.5.2 Attenuation coefficient ................................................................... ..................... 25

4.5.3 Rainfall intensity .................................................................... ............................. 264.5.4 Effective path length................................................. ........................................... 26

4.5.5 Fading probability due to rain for one path ......................................................... 26

4.5.6 Prediction procedure for path going via a passive repeater ................................. 27

4.5.7 Worst-month concept and average annual probability ........................................ 27

4.6 Improvement of the performance by diversity reception.................... ........................ 28

4.6.1 Improvement by frequency diversity.......... ......................................................... 28

4.6.2 Improvement by space diversity.................................................................... ...... 29

4.6.3 Improvement by combined frequency and space diversity - 2 Rx....................... 31

4.6.4 Improvement by combined frequency and space diversity - 4Rx........................ 31

4.7 Total performance with respect to the G.826 objectives. ............................................ 32

4.7.1 Calculation of the block-based severely errored seconds ratio (SESR)............... 33

4.7.2 Fading exceeding the background block error ratio (BBER) objective............... 34

4.7.3 Fading exceeding the errored second ratio (ESR) objective ............................... 36

4.7.4 Total performance for the circuit........................................ ................................. 36

5 Unavailability calculations for radio-relay systems ............................................................ 38

5.1 Unavailability and reliability of hardware.................................... ............................... 38

5.1.1 Single (unprotected) structures.......... ............................................................ ...... 385.1.2 Duplicated (protected) structures......................................................................... 38

5.2 Unavailability due to propagation disturbances........................................................... 39

5.3 Total unavailability........................................................... ........................................... 39

6 Frequency planning .................................................... ......................................................... 41

6.1 The number of disturbing signals reaching a receiver................ ................................. 41

6.2 General formula for the calculation of interfering signal levels .................................. 41

6.3 Formulae for triangular network configuration ........................................................... 42

6.3.1 Nodal station disturbs outstation (TxA1_RxC)............. ..................................... 42

6.3.2 Outstation disturbs nodal point (TxC_RxA1) ..................................................... 43

6.4 Interference via passive repeater ................................................................... .............. 44


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6.4.1 Passive repeater as first-source transmitter..........................................................44

6.4.2 Passive repeater as receiver of interfering signals ............................................... 45

6.5 Total interference.........................................................................................................467 Bibliography ............................................................ ............................................................ 46

Appendix I ...................................................... ........................................................... ................. 50

Appendix II.................................................................................................................................52

Appendix III .................................................... ............................................................ ............... 53


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Principles and formulae

1 Path geometry

1.1 Co-ordinates and bearing

1.1.1 Calculation of great-circle distance and bearing

[1] [ ]( )122121 coscoscossinsincos12.111 xxyyyyad +=

d... great-circle distance in km

x1... longitude for site A in degrees negative values for

x2... longitude for site B in degrees W of Greenwich

y1... latitude for site A in degrees negative values for

y2... latitude for site B in degrees S of the equatorand the antenna bearing in A is:

[2]( )

( ) 1

22'1

cos0089992.0sin

0089992.0cossinsincos

yd

dyya

=

for sin (x2- x1) > 0: 1= '1for sin (x2 x1) < 0: 1= 360o - '11.1.2 Determination of co-ordinates

If the co-ordinates for one site, eg A, and the bearing and great-circle distance to the other site

are known, the co-ordinates of that site can be calculated accordingly:

[3] [ ] [ ]( )dyyday += 0089992.0cossincos0089992.0sincossin 1112

[4][ ]

21

2112

cos.cos

sinsin0089992.0coscos

yy

yydaxx

=

for 1180o: -acos1.2 1st Fresnel zone radius

[5]df

dd.r

= 211 317

r1... radius of the 1st Fresnel zone at a certain point in m


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d... radio beam length in kmd1... distance from one site to that point in kmd2= d d1, in km

f... radio frequency in GHz

1.3 Calculation of antenna heights

The below formula presumes the knowledge or the assumption of one antenna height. If the an-

tenna height at A is the known one, the antenna height at B can be calculated according to:

[6]

[ ]( ) ( )

B

GAAOBST

GB hd

hhdd.k

dddhrd

h +

++=

1

1211

7412

hGA... height above ground level for antenna at A in m

hGB... height above ground level for antenna at B in m

hA... height above sea level for station A in m

hB... height above sea level for station B in m

hOBST... height above sea level for highest obstacle (with respect to propagation) in m

d... distance A to B in km

d1... distance A to obstacle in km

k... effective earth radius factor

r1... required clearance above obstacle in m

where:

[7]100

11 rrrr =

r1... radius at the 1st Fresnel zone in m

rr... required clearance above obstacle in %


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If there is more than one obstacle which may influence the determination of antenna heights, thecalculation will have to be repeated and the highest value forhGB chosen.

For calculation ofhGA, ifhGB is known, replace the indices 1 by 2, A by B, and B by A.

1.4 Calculation of path clearance

Referring to the same parameters as in formula [6] and the associated figure, the clearance abovean obstacle is:

[8]( ) ( )( ) ( )

7412

11111

.k

dddh

d

hhddhhdr OBST

GAAGBB

+++

=

For r1> r1 the 1srFresnel zone is free from intrusions

For r1 > r1 > 0 the 1srFresnel zone is intruded, but there is still line-of-sight

For r1 < 0 no line-of-sight

1.5 Effective Earth radius factor k

The antenna heights according to the above sections have to be calculated for both the standard

atmosphere - k= 1.33 - and forkmin.

Ifkmin is not known, the below diagram may be used. Path lengths


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[10] ( ) += tan1032 ooBGB xdyhhh

h1... height of antenna above reflection area at site A in m

h2... height of antenna above reflection area at site B in m

tan ... inclination angle for sloping terrain ( = 0 for horizontal terrain) according toformula [11]

[11]

( )

3

12

12

10

tan

=

xx

yy

xo, yo... midpoint of the reflection area according to formulae [12] and [13]

[12]2

121

xxxxo

+=

[13]2

121

yyyyo

+=

x1... the distance from site A to the beginning of the reflection area in km

x2... the distance from site A to the end of the reflection area in km

y1... the altitude in m above sea level for point x1

y2... the altitude in m above sea level for point x2

Fig 2 Basic geometry for a reflective path


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1.6.2 Location of reflection point

[14] ( )Zd

d += 121

[15] ( ) 12 12

ddZd

d ==

d1 and d2 are the distances in km to the reflection point from either side of the path according to

Figure 2.

[16]

21

21

hh

hhq

+

=

q... parameter to be used in formula [18]

h1... height of antenna above reflection area at site A in m

h2... height of antenna above reflection area at site B in m

[17]( )

2

21

2

51

d

hhkQ

+=

Q... parameter to be used in formulae [18]-[20]

The other parameters have their previous significance.

[18]

Q

qV

1

1+

=

[19]

[ ] [ ] [ ]

+

++

++

++

++= ....

11111

4

8

3

6

2

42

Q

V

Q

V

Q

V

Q

VVZ

Since the series in the above formula converges quite rapidly, it can, with good approximation,

be terminated after the fourth term, and the formula can consequently be written as follows:

[20]

[ ] [ ]

++

++

++

3

6

2

42

1111

Q

V

Q

V

Q

VVZ

1.6.3 Difference in path length between direct and reflected ray

[21]3

22

2

21

1 1074.1274.12

2

=

k

dh

k

dh

d

... difference in path length between direct and reflected ray in mThe other parameters have their previous significance.

Expressed in terms of wavelengths, this difference will be:

[22]3.0

f=


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... difference in path length between direct and reflected ray in number of wavelengthsEach time the number of wavelengths, , is a positive integer (1, 2, etc), the receiver input level

passes through a minimum. The receiver input level will pass through more than one minimumwhen kis varying, as shown in Figure 1-5.

1.6.4 The distance between receiver input level minima or maxima

The pitch, 1 (or2), i.e. the distance between adjacent minima or maxima in the input level,can be calculated using the formulae below:

[23]3

22

2

1 10

74.12

115.0

=

k

dh

f

d

[24]3

21

1

2 10

74.12

115.0

=

k

dh

f

d

1.6.5 Optimum antenna spacing with space diversity protection

Optimum spacing between the antennas, for a certain kvalue, is obtained by dividing the pitch

1

and 2

respectively by a factor 2, i.e.:

[25] ( )( )

2

2121

=h

h1(2)... antenna spacing between diversity antennas in m at station A or B respectively

1(2)... as above1.6.6 Efficiency of selected space diversity versus k-value variation

[26]3

22

21

1 10

74.123,0

2

=

k

dh

d

hf

Fig 1 Receiver input level vs k value variation


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15


[27]3

21

12

2 1074.123,0

2

=k

dh

d

hf

1(2)... space diversity efficiency at station A or B respectively: = 0.5 corresponds tooptimum efficiency


1.6.7 Antenna discrimination

On steep paths or paths with large clearance it is sometimes possible to take advantage of the

radiation pattern of the antennas to discriminate the reflected signal. Then the angles 1 and 2in Figure 1-4 must be determined. With these values we can enter the radiation pattern for the

used antennas.

[28]3221

1

11 10

74.12

180

=

k

d

d

hh

d

h

[29]3112

2

22 10

74.12

180

=

k

d

d

hh

d

h

1(2)... angles between direct and reflected ray in degrees according to Figure 1-4All other parameters have their previous significance.


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2 Path attenuation and receiver input level

2.1 Total path attenuation during fading-free time

[30] RBWWgAoL GGGAAAAAAA +++++= 2121

AL .... total (or net) path attenuation in dB

Ao .... free-space basic attenuation in dB

AA ... additional attenuation(s) in dB

Ag ... attenuation due to atmospheric gases in dB

AW1,2 ... antenna feeder attenuation at the transmitting (1) and receiving (2) end, in dB

AB ... attenuation in the RF-branching assembly of the radio-relay equipment in dB

G1,2 ... antenna gain at the transmitting (1) and receiving (2) end, in dB

GR ... gain in a passive repeater in dB

2.2 Free-space basic attenuation

[31] fdAo lg20lg204.92* ++=

d*... length of the radio beam between transmitter and receiver antenna in km

f ... radio frequency in GHz

2.3 Additional attenuation(s)

The additional attenuation can be caused by:

- RF attenuators- obstacles,

- partial clearance,

- periscopic antennas,

- passive repeaters in the near-field of the closest antenna.

The first four values have to be given as fixed input data, the computer program is not designed

to determine one of these values. Passive repeaters, however, are dealt with by the program - seenext section.

2.4 Gain or loss in a passive repeater, antenna back-to-back

In formula [30] the free-space basic attenuationAo is replaced by:

oBoA AA + where:

AoA... free-space basic attenuation between station A and the repeater site

AoB... free-space basic attenuation between station B and the repeater site

and GR by:

BA GG + where:

GA... antenna gain in the passive repeater for the antenna directed towards site A

GB... antenna gain in the passive repeater for the antenna directed towards site B


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2.5 Gain or loss in a passive repeater, plane reflector

2.5.1 Check of far-/near-field operation:

[32]

2cos

75 *

=

Yf

ds sZ

d*s ... the shorter one of the two partial paths (legs) in km

f... radio frequency in GHz

Y... reflector area in m2

... angle in space at repeater in degrees

For sZ>2.5 far-field condition

For sZ


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[35]

=2

cos5.139lg20 2 YfGR

2.5.3.1 Repeater loss in near field

In formula [30] the free-space basic attenuationAo is replaced by:

olA

where:

Aol... free-space basic attenuation for the longer of the two legs

The repeater loss is obtained from the below, computerized diagram. The help parameters are as

per formulae [32] and [36]

[36]

2cos4

=

YDas

ReadAA from the above diagram and insert it in formula [30].


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2.5.4 Half-power (3 dB) beam width

[37]

2cos

3.15

2max

3 bfdB

23dB ... half-power or 3 dB beam width in degreesbmax... largest side of reflector in m


2.6 Losses due to atmospheric gases

[38]*dA gg =

Ag... attenuation in dB due to absorption by oxygen and water vapour

g... specific attenuation in dB/km


and:

[39] wog +=

o... specific attenuation in dB/km for dry air

w... specific attenuation in dB/km for water vapour

Forf= radio frequency < 57 GHz:

[40]

[ ]

3222

5222225710

44.257

5.7

351.0

27.7

++

+

= tp

tptp

to rrf

rrfrrf

r

For 57


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[44]1013

prp =

t... average lowest temperature in C

p... air pressure in hPa

where:

... water vapour density in g/m3. (If no measured data are available for the watervapour density, approximate values can be obtained from the charts in Appendix I.)

2.7 Receiver input level during fading-free time

[46] LTxRx ALL =

LRx... receiver input level in dBm during fading-free time

LTx... transmitter output level in dBm

AL... total path attenuation in dB during fading-free time acc. to formula [30]

[ ]

[ ] [ ]

42

2222

22

5.047

10

44.10153.325

01.4

85.1131.183

73.11

81.9235.22

79.3107.7

00167.00327.0

++

++

+++

+

= tp

tp

t

tp

t

tpp

tt

rrf

rrf

r

rrf

r

rrff

r

rr


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3 Overall performance of a digital radio-relay link

during fading-free time and time of shallow fadingDuring fading-free time, the performance is determined by the background bit-error ratio,

BBER. This is also valid for the time of shallow fading.

4 Overall performance of a digital radio-relay link

during fading - Performance calculation

4.1 General

The calculation with respect to the small-time-percentage objective is carried out indi-vidually for each path.

The small-time-percentage objectives only take account of multipath fading through thetroposphere, of precipitation and of the influence of interfering signals. Other fading

types, such as two-way propagation by ground-reflected waves, ducting etc are assumed

to be compensated for by appropriate engineering, such as the selection of suitable an-

tenna heights and/or sites, diversity reception, etc.

For the SESR objective - rain attenuation is assumed to exceed the available fadingmargin for at least 10consecutive seconds. It is thus considered as unavailability. For

theESR andBBER performance objective, however, all rain fading, irrespective its du-

ration, has to be treated as a performance influencing parameter.

Multipath propagation and precipitation appear uncorrelated. The total time percentageduring which the planning objectives are not met is the sum of two independent contri-

butions.

4.2 The multipath occurrence factor

4.2.1 Prediction formula

For detailed planning:

[47] ( ) Lhfoi dKP+ += 00085.0032.0297.02.3* 101

For approximate planning:

[48] ( ) Lhfoi dKP+ += 001.0033.022.10.3* 101

Poi... multipath occurrence factor for the individual radio hop

hL ... the lower of the two antenna altitudes in m above sea level, i.e. hA+hGAor

hB+hGB

K... geoclimatic factor

f... frequency in GHz


... hop inclination in milliradiansi... serial number of the individual hop (i = 1...n)

4.2.2 Path inclination

The path inclination, , is the angle between the line-of-sight and the horizontal. Its absolutevalue, calculated according to equation [49], is used in formulae [47] and [48].


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[49]( ) ( )

d

hhhh GBBGAA +

... inclination in milliradiansd... path length in km

hA... elevation in m above sea level for the left-hand site

hB... elevation in m above sea level for the right-hand site

hGA... antenna height in m above the ground for the left-hand site

hGB... antenna height in m above the ground for the right-hand site

4.2.3 Geoclimatic factor K

If no fading data are available for the area concerned, the factorKcan be estimated following

the below procedure:For detailed planning (formula [47]):

[50] 1003.09.342.0 10

dNaK

=

For approximate planning (formula [48]):

[51] 10029.02.4

10dN

K=

The parameters have the following significance:

dN1... The point refractivity gradient in the lowest 65 m of the atmosphere not exceeded

for 1% of an average year. The figure can be obtained on a 1.5o

grid resolution in

latitude and longitude from a database2

available from ITU-R (see also ITU-R

Rec. 453-8).a... The area terrain roughness, defined as the standard deviation in m of the terrain

heights (in m) within a 110 km x 110 km area with a 30 resolution. The area

should be aligned with the longitude, such that two equal halves of the area are on

each side of the longitude going through the hops midpoint. Terrain data are

available from Internet, eg the Globe gtopo30 data.

The standard deviation can be calculated applying the following formula:

[52]

( )1

2

11

2

=

=

= jj

j

j

a

hh

Fora < 1, set a = 1.hj... altitude a.s.l. in m for the individual height sample

... total number of samplesj... ordinal number of the individual sample (j = 1...)

For the calculation of a hops midpoint, and for the bilinear interpolation in order to obtain the

correct figure fordN1, reference should be made to the Annex of this booklet, page 48.

2The corresponding data files, DNDZ_01.txt, DNDZ_LAT.txt and DNDZ_LON.txt can be downloadedfrom ITU-Rs website. A table - dN_1.xls - showing dN1 versus longitude and latitude can be downloaded

from K&K Engineerings website (see page 2).


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23


4.3 Performance prediction considering multipath fading and re-

lated mechanisms

4.3.1 Prediction formulaeFrom the multipath occurrence factor, Po, calculated according to either formula [47] or[48], a

fading depthM (dB) is calculated:

[53] oPM lg2.14.27 +=

IfMis less or equal than the available fading margin,MF, i.e.

[54] FMM

the probability, that the available fading margin is exceeded is calculated according to the below

formula

[55]1010 F

MoFi PP

=

PFi... probability rate for exceeding the planning objective, defined by the available fad-

ing margin,MF, for one radio hop during the average worst month

Po... multipath occurrence factor for the respective radio hop as per

formula [47] or[48]

MF... fading margin in dB

i... serial number of the individual hop (i = 1...n)

For fade depths, M, larger than the available fading margin, MF, the following method is rec-

ommended:(i) Use formula [55] above, calculate PFiM for the fade margin M as obtained by

formula [53].

(ii) Calculate parameterqa for the same fade margin, M, and the associated value for

PFiMfrom:

[56] ( )[ ]FiMa PM

q

= 1lnlg20

(iii) IfPFi is very small, your calculator may round:

1 - PFiM

to become ln 1 = 0. To avoid that, set the quotient to the highest value for 0.999..., which still isconsidered by your calculator as an

ln 0.999... 0(iv) Calculate parameterqtfor the same fade margin,M, from:

[57]

( )

++

=

800103.4

10103.01

2 2016.020

Mqq

M

MM

at

(v) Finally, calculate the probability, PFi, that the plannedfading margin,MF, is ex-

ceeded:

[58] SFi eP = 1

where:


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24


[59]2010 F

MqS

=

and:

[60] [ ]

++++= 800

103.410103.01220016.020 FM

tMM M

qq FFF

The parameters PFi and MFhave their previous significance.

4.3.2 Fading margin

[61] DLLLLM TeRxTeIRxF ==

MF... flat-fading margin in dB

LRx... receiver input level in dBm during fading-free time

LTr... receiver threshold level in dBm for the planning criterion and for an undisturbed

receiver (CIR = )LTrI... receiver threshold level in dBm for the planning criterion and for a disturbed re-

ceiver (CIR)D... receiver threshold degradation in dB due to interfering signals

4.3.3 Paths going via passive repeaters

The total probability rate for exceeding the fading margin, MF, is the sum of the percentage of

time that the fading margin, MF, is exceeded for each leg:

[62] 21 legFilegFiFi PPP +=

4.4 Performance prediction considering distortions due to propaga-

tion effects (selective fading)

4.4.1 Prediction formulae

[63]3

220 10103.4

=

ref

mBSi WP

with:

[64]

3.1

507.0

=

dm

and:

[65]75.02.0

1 oP

e=

PSi... probability that one radio hop exceeds the planning criterion due to distortions

during the average worst month

... multipath activity factorPo. multipath occurrence factor acc. to formula [47] or[48]

W... mean value of the width of the signature inMHz

B... mean value of the signature (or notch) depth in dB

ref... reference delay in ns used to obtain the signature (WandB)


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25


d*... beam path length in km

In case the manufacturer submits its equipment data separately for minimum phase (MPh) and

non-minimum phase (NMPh) fading, the mean value can be calculated as

[66]2

NMPhMPh WWW+

=

for the signature width, and

[67]

+=2

1010lg20

2020 NMPhMPh BB

B

for the notch depth, and

[68]2

,, NMPhrefMPhrefref

+=

for the reference delay.

4.4.2 Prediction procedure for path going via a passive repeater

The statement given in section 4.3.3 is also valid here, i.e. the fading contribution due to selec-

tive multipath propagation will be calculated individually for each leg, applying formulae [63] to

[65]. The fading margin, MF, is, again, that for the total path length, and will thus be the same

for both legs.

The total percentage of time for selective fading is thus:

[69] 21 legSilegSiSi PPP +=

4.5 Small-time-percentage for exceeding the planning objectives due

to attenuation caused by precipitation

The influence of rain is predicted by calculating the rain attenuation for 0.01% of the time. Re-

lating the rain attenuation to the available flat-fading margin, the percentage of time duringwhich the fading margin is exceeded is calculated.

4.5.1 Attenuation caused by rain

The attenuation caused by rain is:

[70]effRR

dA =01.0

AR0.01... attenuation due to rainfall in dB during 0.01% of time

R... rain attenuation coefficient in dB/km

deff... the path length in km influenced by rain - the effective path length

4.5.2 Attenuation coefficient

The attenuation coefficient, R, versus radio frequency,f, for various clock-minute rainfall ratesduring 0.01% of time, J0.01, is calculated from formula [71]:

[71]=

01.0JR

J0.01... clock-minute average annual rainfall rate (or rainfall intensity) in mm/h exceeded

for 0.01% of the time, see section 4.5.3


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26


and are frequency- and polarization-dependent parameters, which are to be obtained fromthe table in Appendix III

4.5.3 Rainfall intensity

If no measured data are available, the rainfall intensity can be estimated from 3 parameters, Pr6,

Ms and Mc. Their data can be found in the corresponding data files esarainPR6.txt,

esarain_Mc.txtand esarain_Ms.txt3. The data are extracted the following way:

For each of the 3 parameters, Pr6,Ms andMc, the figures for the 4 grid points surrounding the

hops midpoint are used in order to calculate the corresponding figures for the midpoint applyingbilinear calculation - see formula [169] on page 49.

The midpoints rainfall intensity,J0,01, is then calculated with the help of the midpoint figures

forPr6,Ms andMc:

[72]( )

++

+=

A

MMCBB

MM

AJ cs

cs

42

4

01.010936.110033.1

[73] ( 60117.06 1 rs PMr ePA =

[74] CA

MMB cs

++= 3103736.111.1

[75]

=A

C01.0

ln

Appendix II at the end of this handbook shows rainfall intensity charts based on the above data.

4.5.4 Effective path length

[76]

oeff

dd

dd

+=

1

[77] 01.0015.0

35J

o ed=

d... geodetic path length in km

deff... effective path length in km

Note: ForJ0.01 > 100 mm/h, useJ0.01 = 100 mm/h in formula [77].

4.5.5 Fading probability due to rain for one path

The percentage of time during which the rain attenuation exceeds the available flat-fading mar-

gin,MF, is estimated to be:

responding data files,ESARAINPR6.txt, ESARAIN_Mc.txtandESARAIN_Ms.txtcan be downloaded from

s website. Tables - P-Pr6.xls, P-MC.xls and P-MS.xls - showing the csorresponding parameters versus longitude andcan be downloaded from K&K Engineerings website (see page 2).


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[78][ ]( )

= ++ 154023.010 01.012.0lg172.029812.0546.0628.11 01.0

F

RMARi M

Ap FR

pRi... fading probability in % of time for a radio hop due to rain

MF... fading margin in dB

Equation [78] converges quickly to % as the factor decreases and approaches 0.154. For values


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28


UP... portion in percentage of the average annual probability rate, which lasts longerthan 10 consecutive seconds and, thus, has to be treated as unavailability

4.5.7.2 Worst month probability

[83] ( ) 87.033.301.0 RiRwmi pP =

PRwmi... average worst month probability, during which the rain attenuation exceeds the

available fading margin

Consequently, that part, UP, of the average annual probability rate, which lasts shorter than 10

consecutive seconds, has also to be converted to an average worst month probability rate, ap-plying formula [83]:

[84]

87.0

100

10033.301.0

= UP

pP SESRaiUPRwmi

PRwmi-UP... average worst month probability, during which the portion (100-UP) of the rain

attenuation exceeds the available fading margin to the BERSESthreshold level of

the receiver

pRai-SESand UP as above

4.6 Improvement of the performance by diversity reception

4.6.1 Improvement by frequency diversity

4.6.1.1 For flat fading

[85] 102

1080 FMfidffI =

Ifi... improvement factor due to frequency diversity for the individual hop

f... band centre frequency in GHz

f... frequency separation between the two diversity paths, r.f.1 r.f.2, in GHzd

*... beam path length in km

MF... flat fading margin according to section 4.3.2. In case the main and the diversity

path have different fading margins (due to different Tx output levels, etc.), thelower of the two fading margins has to be used.

The above formula is verified by measurements for the following data ranges:

2 0.5 GHz, use f= 0.5

The validity of formula [85] outside these ranges is not yet sufficiently proved.

Calculate the improved fading probability by applying:

[86]

fi

FidfFi

I

PP =

PdfFi... probability for the worst month for exceeding the planning criterion due to fading

for a 1+1 frequency-diversity configuration for the individual hop


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29


PF... probability in for the worst month for exceeding the planning criterion due to fad-

ing for an unprotected configuration according to equations [55] or[58] for the in-dividual hop

4.6.1.2 For distortions

[87]

( )22

1fSi

SidfSi

k

PP

=

PdfSi... probability for the worst month for exceeding the planning criterion due to distor-

tions for a 1+1 frequency-diversity configuration for the individual hop

PSi... probability for the worst month for exceeding the planning criterion due to distor-

tions fading for an unprotected configuration according to equation [63] for theindividual hop

... multipath activity factor, see equation [65] for the individual hop

[88] 8238.02 =fSi

k for rwi < 0.5

[89] ( ) ( )wirwifSi rk= 1lg13.0109.02 1195.01 for 0.5 < rwi < 0.9628

[90] ( ) 5136.02 13957.01 wifSi rk = for rwi > 0.9628

[91] ( ) 17.2219746.01fFi

wi kr = for k2

fFi < 0.26

[92] ( ) 034.1216921.01fFiwi

kr = for k2fFi > 0.26

[93]

= Fifi

fFi

PIk 12

4.6.2 Improvement by space diversity

4.6.2.1 For flat fading:

Withfand d* having their previous significance, the equation for the space-diversity improve-

ment factor can be written as follows:

[94]101034.3

10104.148.012.087.04

Fo MPdfhsi eI

=

Isi... improvement factor due to space diversity for the individual hop

h... vertical spacing of receiving antennas, centre-to-centre, in mMF... flat fading margin in dB according to section 4.3.2. In case the main and the diver-

sity path have different fading margins (due to different antenna sizes, waveguide

length, etc.), the fading margin has to be corrected accordingly:

[95] GMM mFF =


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30


[96] dWmWdm AAGGG +=

If G < 0 G = 0MF-m... flat fading margin in dB for the main-antenna path

Po... multipath occurrence factor according to formula [47] or[48]

Gm... gain in dB for the main antenna

Gd... gain in dB for the diversity antenna

AW-m... waveguide attenuation dB for the main-antenna path

AW-d... waveguide attenuation dB for the diversity-antenna path

The above formula is verified by measurements for the following data ranges:

2 < f < 11 GHz

43 < d< 240 km

3 < h < 23 m

The validity of the formula outside these ranges is not yet sufficiently proved.

Calculate the improved flat-fading probability by applying:

[97]

si

FidsFi

I

PP =

PdsFi... probability rate for the worst month for exceeding the planning criterion due to

fading for a space-diversity configuration for the individual hop

PFi... probability rate for the worst month for exceeding the planning criterion due to

fading for an unprotected configuration according to equations [55] or[58] for the

individual hop

4.6.2.2 For distortions

[98]

( )22

1 sSi

SidsSi

k

PP

=

PdsSi... probability for the worst month for exceeding the planning criterion due to distor-

tions for a frequency-diversity configuration for the individual hop

PSi... probability for the worst month for exceeding the planning criterion due to distor-

tions for an unprotected configuration according to equation [63] for the individ-

ual hop

... multipath activity factor, see equation [65] for the individual hop

[99] 8238.02 =sSik for rwi < 0.5

[100] ( ) ( )wirwisSi rk= 1lg13.0109.02 1195.01 for 0.5 < rwi < 0.9628

[101] ( ) 5136.02 13957.01 wisSi rk = for rwi > 0.9628

[102] ( ) 17.2219746.01 sFiwi kr = for k2sFi < 0.26

[103] ( )034.1

216921.01 sFiwi kr = for k2sFi > 0.26


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31


[104]

= FisisFiPI

k 12

4.6.3 Improvement by combined frequency and space diversity - 2 Rx


The flat fading improvement,Is,f-2, and the improved probability,pds,fF-2, is obtained by using

the same formulae [94]-[97] as for space diversity.

The limitations apply also here

4.6.3.2 For selective fading:

Also here, the same formulae as for space diversity are valid, i.e. formulae [98]-[104]. The flat-

fading correlation coefficient, k

sFi

, in formulae [102] and [104], however, has to be replaced by:

[105] sFifFisFif kkk =,

with ksFi according to formula [104], and kfFi according to formula [93].

4.6.4 Improvement by combined frequency and space diversity - 4Rx


[106]

D

FiisFdf

m

PP

4

4, =

[107]223 11 sFifFiD kkm =

Pdf,sFi... probability rate for the worst month for exceeding the planning criterion due to

fading for a combined frequency/space-diversity configuration with 4 Rx

PFi... probability rate for the worst month for exceeding the planning criterion due to

fading for an unprotected configuration according to equations [55] or[56]

... multipath activity factor acc. to equation [65]ksFi... flat fading correlation coefficient for space diversity configuration according to

formula [104]

k

fFi

...

flat fading correlation coefficient for frequency diversity configuration according

to formula [93]

4.6.4.2 For distortions:

[108]

( )[ ]224

4,

1 sSi

SiisSdf

k

PP

=

Pdf,sS-4i... probability rate for the worst month for exceeding the planning criterion due to

distortions for a combined frequency/space-diversity configuration with 4 Rx

PSi... probability rate for the worst month for exceeding the planning criterion due to

distortions for an unprotected configuration according to equation [63]

ksS... selective fading correlation coefficient for space diversity configuration according

to formulae [99] to [104]


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4.7 Total performance with respect to the G.826 objectives.

Table 1 BERSESand block sizes...

Path type Bit rate

(Mbit/s)

BERSES

(Note ii)

Blocks/s

(Note ii)

n

Bits/block

(Note ii)

NB

...for various PDH systemsNote i

E1 2 4x10-4

2 000 1 120

2xE1 2x2 2x10-4

2 000 2 000

E2 8 1.1x10-4

2 000 4 224

8xE1 8x2 8.8x10-5

4 000 5 170

E3 34 6.5x10-5

8 000 6 120

...for various SDH paths and sections

VC-11 1.5 5.4x10-4

2 000 832

VC-12 2 4.0x10-4

2 000 1 120

VC-26 1.3x10

-4

2 000 3 424

VC-3 34 6.5x10-5

8 000 6 120

VC-4 140 2.1x10-5

8 000 18 792

STM-1 1552.3x10

-5

2.33x10-4

8 000

192 000

19 940

801

i No figures are stated so far for PDH systems. P.530 advises to select the BERSESclosest to the SDH

transmission rate. This applies for 2 and 34 Mbit/s systems. For the other PDH capacities, the author

proposes the above figures.

ii The BERSES is the bit-error ratio for which the number of errored blocks within 1 second exceeds

30%. The figures stated assume a Poisson distribution of errors.


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33


The Block/s is defined in Rec. G.826 for SDH paths, and in G.829 for SDH sections. Some STM-1 equipment might be

designed with 8000 blocks/s (19 940 bits/block), but Rec. G.829 defines the block rate and size to be192 000 block/s and 801 bits/block respectively.

4.7.1 Calculation of the block-based severely errored seconds ratio (SESR)...

4.7.1.1 ... for an unprotected hop

The total fading probability rate for the individual, unprotectedhop is:

[109] SESSiSESFiSESMi PPP +=

PMi-SES... probability rate for the worst month for exceedingBERSESon an unprotected hop

due to multipath propagation

PFi-SES... probability rate for the worst month for exceedingBERSESon an unprotected hop

due to multipath fading; calculated acc. to formulae [55] or [58], applying the

relevant fading margin toBERSESBERSES... the bit-error ratio for which the number of errored blocks within one second ex-

ceeds 30% (Table 1)

PSi-SES... probability rate for the worst month for exceedingBERSESon an unprotected hop

due to distortions; calculated acc. to formula [63], applying the relevant signature

data forBERSES

i... ordinal No for the individual hop

4.7.1.2 ...for a diversity-protected hop

The total fading probability for the individual, protected hop is:

[110] 3475.075.0 SESsSiSESdFiSESMi PPP +=

PMi-SES... probability rate for the worst month for exceeding BERSES on a diversity-

protected hopdue to multipath propagation

PdFi-SES... probability rate for the worst month for exceeding BERSES on a diversity-

protected hop due to multipath fading; calculated acc. to formulae [55] or [58],

applying the relevant fading margin toBERSES

BERSES... the bit-error ratio for which the number of errored blocks within one second ex-

ceeds 30% (Table 1)

PSi-SES... probability rate for the worst month for exceeding BERSES on a diversity-

protected hop due to distortions; calculated acc. to formula [63], applying the rele-

vant signature data forBERSES


4.7.1.3 Distribution between performance and unavailability

Performance part

A part of the above excess probability - UM% - (formulae [109] and [110]) may last longer than

10 consecutive seconds and have to be treated as unavailability. The above figure forPMi-SES

has, thus, to be reduced to:

[111]

100

100'

UMPP SESMiSESMi

=

PMi-SES-1... resulting probability rate for the worst month for exceedingBERSESon a hopdue

to multipath propagation


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34


PMi-SES... probability rate for the worst month for exceeding BERSESon a hopdue to mul-

tipath propagation as per formulae [109] or[110]

UM... part in percentage of the probability rate, which has to be treated as unavailability

Unavailability part

[112]1010

100

GSESMiuMi

UMPP

=

[113] ( )++= 1lg7.1lg7.22cos1.1lg6.55.10 7.0 dG

ForG > 10,8: use 10,8

PMi-u... average annual unavailability rate on a hopdue to multipath propagation

PMi-SESand UMas above

... latitude in degrees + 1 decimal... + for45 for >45o N or S of the Equatord

*... hop length in km

... path inclination in mrad(formula [49])

4.7.1.4 Resulting block-based severely errored seconds ratio (SESR)

[114] UPRwmiSESMiSESMi PPP += '"

PMi-SES ... final probability rate for the worst month for exceeding BERSESon a hopdue tomultipath propagation

PMi-SES .. resulting probability rate for the worst month for exceedingBERSESon a hopdue

to multipath propagation acc to formula [111] above

PRwmi-UP... probability rate for the worst month for exceeding BERSESon a hopdue rain fad-

ing acc to formula [84]

4.7.2 Fading exceeding the background block error ratio (BBER) objective

This fading event is caused both by multipath propagation and rain

4.7.2.1 Prediction of BBER due to multipath propagation

The following prediction model is recommended:

[115]( )18.2 12

1

= m

PP SESMiBBEMi

[116]

SESMiRBERMi

SES

PP

BERRBERm

=lglg

lglg1

PMi-BBE... BBER probability rate for the worst month due to multipath propagation

PMi-SES

... probability rate for the worst month for exceeding BERSES

due to multipath

propagation acc. to formula [109],[110] or[111]

RBER... residual bit-error ratio


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35



ceeds 30% (Table 1)

PMi-RBER

... from the next formula:

[117] RBERSiRBERFiRBERMi PPP +=

PFi-RBER... probability rate for the worst month for exceedingRBER on a hop due to fading;

calculated acc. to formulae [55] or [58], applying the relevant fading margin to

RBER

PSi-RBER... probability rate for the worst month for exceedingRBER on a hop due to distor-

tions; calculated acc. to formula [63], applying the relevant signature data for

RBER

1... number of error/burst for theBER in the range betweenBER = 10-3 andBERSES;normally between 10 and 30

2... number of error/burst for theBER in the range betweenBERSES; andRBER; nor-mally between 1 and 10


4.7.2.2 Prediction of BBER due to rain fading

Use again formula [115] to obtain PRwmi-BBER, but written as:

[118]( )18.2 22

1

= m

PP SESRwmiBBERwmi

PRwmi-BBE...BBER probability rate for the worst month due to rain

PRwmi-SES... probability rate for the worst month for exceedingBERSESdue to rain, calculated

acc. to formula [78], applying the relevant fading margin to BERSES, and trans-

ferred to the worst-month value by formula [83]



ceeds 30% (Table 1)

1... number of error/burst for theBER in the range betweenBER = 10-3 andBERSES;normally between 10and 30

2... number of error/burst for theBER in the range betweenBERSES; andRBER; nor-mally between 1and 20

whereby:

[119] 22

1

and:

[120]

SESRwmiRBERRwmi

SES

PP

BERRBERm

=lglg

lglg2

PRwmi-RBER...probability rate for the worst month for exceeding RBER due to rain, calculated

acc. to formula [78], applying the relevant fading margin toBERRBER, and trans-

ferred to the worst-month value by formula [83]



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36


4.7.2.3 Prediction of BBER due to equipment contribution

[121] RBERNP BBBEEi =

PEi-BBE... BBER probability rate due to equipment contribution


NB... number of bits/block - see Table 1

4.7.3 Fading exceeding the errored second ratio (ESR) objective

This fading event is caused both by multipath propagation and rain.

4.7.3.1 Prediction of ESR due to multipath propagation

[122]1m

SESMiESMinPP

=

PMi-ES... ESR probability rate for the worst month due to multipath fading

n... number of block/s - see Table 1

m1... according to formula [116]

The other parameters have their previous significance

4.7.3.2 Prediction of ESR due to rain fading

[123]2m

SESRwmiESRwmi nPP =

PRwmi-ES

... ESR probability for the worst month due to rain

m2... according to formula [120]

The other parameters have their previous significance

4.7.3.3 Prediction of ESR due to equipment contribution

[124] RBERNnP BESEi =

PMi-ES... ESR probability rate due to equipment contribution

NB... number of bits/block - see Table 1

n... number of block/s - see Table 1

4.7.4 Total performance for the circuit

The total rate of time, Pc, during which the planning objectives are not met for the circuitis the

sum of the cumulated rates, i.e.:

[125] ( )

= ++=

10

1

i

i

xEixRwmixMixc PPPP

Pc-x... fading probability rate for exceeding SESR, ESR orBBER respectively for the ra-

dio circuit

PMi-x... fading probability rates for exceeding SESR, ESR orBBER respectively for the

individual hop due to multipath propagation

PRwmi-x... fading probability rates for exceedingESR orBBER respectively for the individual

hop due to rain fading


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PEi-x... fading probability rates for exceedingESR orBBER respectively for the individual

hop due equipment contribution

Remember: Concerning the SESR, it should be observed, that:

PRwmi-SES =PEi-SES = 0

x... eitherSESR, ESR orBBER

The values forPc-x should not exceed the planning objectives, i.e.:

[126] xplxc PP

Pc-x... predicted total probability rate during which the planning objective is not met for a

radio-relay circuit

Pp-xl... allowed probability rate for exceeding the planning objective for a radio-relay cir-

cuit, i.e. the planning objectivex... eitherSESR, ESR orBBER

Formula [125] can be expressed in time:

[127] xcUNx Phs

=12

360010628.2 6

sx... total time for exceeding the corresponding planning objective in sec / average

month

hUN... from formula [135]


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38


5 Unavailability calculations for radio-relay systems

5.1 Unavailability and reliability of hardware5.1.1 Single (unprotected) structures

[128]

SrS

SrSuS

M

MP

+=

1

PuS... unavailability rate for the single structure

S... failure rate (failures per time unit) - the sum of the failure rates for the individual

units, i, connected in tandem:

[129] ==

n

i

iS

1

MrS... mean-time-to-repair(MTTR) for the single structure, in same time unit as the fail-ure rate.

The mean-time-to-repair figures do no include any waiting time for spare parts. It is thus as-

sumed that there is always access to spare parts when a fault occurs.

The failure rate, , can also be expressed in terms ofmean-time-between-failure (MTBF):

[130]

=1

MTBF

MTBF... mean-time-between-failure for the single structure, in same time unit as the failure

rate

5.1.2 Duplicated (protected) structures

The unavailabilityof a this type of duplicated structure, including the protection switching facili-

ties, is calculated according to the following formula:


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39


[131]

+

+=rND

rS

NDrND

SrSSrSuD

M

M

MMMP

1

PuD... unavailability rate for the duplicated structure as per above figure

S... failure rate (failures per time unit) for one of the duplicated equipment (= singlestructure as per above figure

ND... failure rate (failures per time unit) for the (non-duplicated) splitting and switchingdevice proper - see also below

MrS... mean-time-to-repair for one of the duplicated equipment, in same time unit as the

failure rate

MrND... mean-time-to-repair for the (non-duplicated) splitting and switching deviceproper, in same time unit as the failure rate

Formula [131] is only valid for systems using optional switching. This type of switching means

that a failure in the switch element will not cause system failure unless switching is required.

Consequently, the failure rate, ND, includes only the values for the splitting and switching ele-ments themselves, together with those for the switchs logic and control unit (L in the above

figure), while the level and impedance interfacing elements of the splitting and switching units

are a part of the failure rate of the duplicated equipment, S, and of the single (i.e. non-protected) interface units (I), respectively, as they cause interruption of the traffic. The MTTR

figures for these traffic-interrupting parts are the same as for the duplicated equipment, or = MrS.

For the complete path, including the non-protected interface units (I), equation [132] is extended

to:

[132] 21 uIuIuDuP PPPP ++=

where PuI(1,2) are calculated according to equation [128], using the same value forMrSas in for-

mula [131], and the failure rate, I(1,2), instead ofS.

5.2 Unavailability due to propagation disturbances

The unavailability due to propagation disturbances, PRa, consists of contributions from rain and

from multipath fading:

[133]uMiSESaiRai

PRP

+=

PRai... probability rate for a radio hop due to rain for the average annual year

PRi-SES... average annual probability rate, during which the rain attenuation exceeds the

available fading margin acc to formula [82]

PMi-u... average annual unavailability rate on a hopdue to fading and distortions acc to

formula [112]

i... ordinal No for the radio hop

5.3 Total unavailability

The total unavailability of a radio circuit, URt, is the sum of the contributions from the hardware

and the rain. It should be observed, however, that the unavailability of the hardware has to beconsidered for both the go and the return direction of transmission, i.e. twice, while that for rain

is counted only once:


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40


[134] =

+=n

i

Raiut PPUR

1

2

URt... total unavailability rate of a radio circuit

Pu... unavailability rate of the total hardware, according to section 5.1

PRai... unavailability due to precipitations, see above

n... number of radio hops included in the circuit

Formula [135] expressed in time:

[135] 8760= tUN URh

hUN... total unavailability in hours / average year


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41


6 Frequency planning

6.1 The number of disturbing signals reaching a receiver

[136] yxNn

=

1

N... number of disturbing signals at each receiver

n... number of hops in the area concerned

x... number of parallel r.f. channels on the individual hop

y... number of parallel r.f. channels on the own hop

and the number of total interferences possible is

[137] nNK =

K... number of interference connections

6.2 General formula for the calculation of interfering signal levels

[138] GARxTxBRxBTxWRxWTxoTxIi GAAAAAAAALI +=

LIi ... level of a single interfering signal in dBm

LTx ... output level of the disturbing transmitter in dBm

Ao ... free-space attenuation in dB between disturbing transmitter and disturbed receiver

AWTx,Rx.. waveguide attenuation in dB in the transmitting alt. receiving stationABTx,Rx branching attenuation in dB in the transmitting alt. receiving station

AWTx,Rx r.f. attenuators in dB in the transmitting alt. receiving station

AA... additional attenuation in dB due to non-clearance of the interference path and/or

other attenuations in the interference path

GG ... total antenna gain in dB(i) for angles 1and2, according to the following for-mula [139]:

[139] ( ) ( )GRxGTxRxTxGRxGTxG AAGGGGG ++=+=

Note: In case the transmitter and the receiver antenna operate at different polarization planes, the

two possible H/V combinations have to be considered. In this case, the next equations apply instead:

[140] ( )

+++=

+= 10101010

10lg101010lg10AA

RxTxGG

G AGGG

[141] += RxTx GGG

[142] RxTx GGG +=

[143]

+= RxTx

AAA

[144] RxTx AAA +=


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GTx... antenna gain for the main direction in dB(i) of the transmitting antenna,referred toan isotropic radiator

GRx

... ditto for the receiving antenna

GTx||... antenna gain in dB(i) of the transmitting antenna for angle 2 and parallel polari-sation,referred to an isotropic radiator

GRx... ditto for the receiving antenna for angle 1 and cross polarisation

GTx... ditto for the transmitting antenna cross polarisation,GRx||... ditto for the receiving antenna and parallel polarisation

ATx|| ... antenna discrimination in dB of the transmitting antenna for angle 2and parallelpolarisation,referred to the antenna gain in the direction of transmission

ARx ... ditto for the receiving antenna for angle 1 and cross polarisation

ATx... ditto for the transmitting antenna cross polarisationARx||... ditto for the receiving antenna and parallel polarisation

6.3 Formulae for triangular network configuration

6.3.1 Nodal station disturbs outstation

(TxA1_RxC)

[145] WTxBTxTxTxAGCRxCIi AAALGALL ++= 1

[146] 21 AA GGG =

[147] 21 ATxATxTx LLL = [148] 21 ATxATxTx AAA =

[149] 21 ABTxABTxBTx AAA =

[150] 21 AWTxAWTxWTx AAA =

LIi ... level of a single interfering signal in dBm

i ... ordinal number of the interfering signal

LRx-C... received level of the wanted carrier signal in dBm during fading-free time at dis-

turbed receiver C

G .. antenna discrimination or side- and back lobe attenuation for angle

in dB, for an-

tenna A1 in the nodal station, considering the polarisation for the disturbed anddisturbing signal

GA1... antenna gain in dB for the disturbing transmitter A1 in the nodal station


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GA2 ... antenna gain in dB for the transmitter A2 in the nodal station

LTx-A1... output level in dBm for the disturbing transmitter A1

LTx-A2... output level in dBm for the transmitter A2ATx-A1... RF attenuator in dB in the disturbing transmitter A1

ATx-A2... RF attenuator in dB in the transmitter A2

ABTx-A1.. branching attenuator in dB in the disturbing transmitter A1

ABTx-A2.. branching attenuator in dB in the transmitter A2

AWTx-A1..waveguide attenuation in dB in the disturbing transmitter A1

AWTx-A2.. waveguide attenuation in dB in the transmitter A2

If there is only one interference path to receiver C, equation [145] can be used to select the an-

tenna A1 by writing:

[151] WTxBTxTxTxFiITrIG AAALGMLLA +++= 1

Applying the definition ofCIR, this equation can be expressed as:

[152] WTxBTxTxTxFiG AAALGMCIRA +++=

This equation shows, that the higher theCIR, and the higher the flat fading margin, MFi, the

higher the antenna discrimination necessary.

6.3.2 Outstation disturbs nodal point

(TxC_RxA1)

[153] WRxBRxRxRxAGARxAIi AAALGALL ++= 111

[154] 12 ARxARxRx LLL =

[155] 21 ARxARxRx AAA =

[156] 21 ABRxABRxBRx AAA =

[157] 21 AWRxAWRxWRx AAA =

LRx-A1

... receiver input level of the wanted signal in dBm during fading-free time at dis-

turbed receiver A1

LRx-A2... receiver input level of the wanted signal in dBm during fading-free time at re-

ceiverA2


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ARx-A1... RF attenuator in dB in the disturbed receiver A1

ARx-A2... RF attenuator in dB in the receiver A2

ABRx-A1.. branching attenuation in dB in the disturbed receiver A1ABRx-A2.. branching attenuation in dB in the receiver A2

AWRx-A1.. waveguide attenuation in dB in the disturbed receiver A1

AWRx-A2.. waveguide attenuation in dB in the receiver A2


Also equation [153] can be expressed with the antenna discrimination as the unknown param-

eter:

[158] WRxBRxRxRxFiG AAALGMCIRA +++=

6.4 Interference via passive repeater

6.4.1 Passive repeater as first-source transmitter

[159] SGAWRxWTxooTxIi GGAAAAALL ++= 221

ForGG, equation [139] is valid.

Ao1

... free-space attenuation in dB between PR and its associated transmitter, Tx

Ao2... free-space attenuation in dB for the interference path between PR and the dis-

turbed receiver, Rx

AA2... (eventual) additional attenuation in dB due to obstacle in the interference path to

Rx

GS... passive repeater gain in dB for the interfering signal at angle S- for antenna back-to-back:

[160] 221 GSSS AGGG +=

- for plane reflector:

[161]

SS

bfYG += sin

lg205.22


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[162] If : RSRS GGYfGG =

=2

cos5.139lg20 2

GR.... gain in passive repeater, plane reflector type, in dB for the wanted signal, and an-

gle GS1... passive repeater - antenna back-to-back type - gain in dB for the parabolic antenna

towards Tx (main direction)

GS2... ditto for the parabolic antenna towards Rx'

AG2... antenna discrimination in dB for angle S for the passive repeater antenna to-wards Rx'

f..... radio frequency in GHz

Y..... physical area of the plane reflector in m2

b..... largest side dimension of the reflector in m

Rx... angle in degrees between the wanted and the interfering signal paths for receiverRx

S.... angle in degrees between the reflected ray and the interfering signal path

..... angle in space, in degrees, between the incident and reflected ray

The significance of the remaining parameters is according to formula [138].

Formula [161] is valid for:

290


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6.5 Total interference

If more than one interfering signal has to be considered at a receivers input, the various con-

tributions are added together on a power law basis:

[164]( )

=

=n

i

ALI

jIiL

1

1010lg10

LI. combined level in dBm of all interfering signals

LIi... level in dBm of an individual interfering signal

Aj... adjacent-channel attenuation in dB of the interfering signal in the receiver, see

above. For co-channel interference (f= 0):Aj = 0.

7 Bibliography

{1} Heinz Karl, Performance and availability as applied to digital radio-relay sys-

tems, K&K Engineering

{2} Heinz Karl, Planning and engineering of radio-relay networks, K&K Engineering


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@ Heinz Karl, 2003


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Annex

1. The co-ordinates for the hops midpoint are calculated as follows:

- for the longitude:

[165]2

21 xxxo+

=

- for the latitude:

[166]2

21 yyyo+

=

xo... longitude for the midpoint in degrees

x1... longitude for site A in degrees negative figures forx2... longitude for site B in degrees W of Greenwichyo... latitude for the midpoint in degrees

y1... latitude for site A in degrees negative figures fory2... latitude for site B in degrees S of the equator

2. The co-ordinates for the corners of the 110x110 kmareaaround a hops midpoint:

[167] ( )oC yyay sin999925.0cos0122165.0cossin 11 +=

[168]

Co

CooC

yy

yyaxx

coscos

sinsin999925.0cos

+=

xo andyo are the co-ordinates in degree of the hops midpoint as calculated above.

NE corner: 1 = 45o cos 1 = 0.707107 acos = +

SE corner: 1 = 135o cos 1 = - 0.707107 acos = +

SW corner 1 = 225o cos 1 = - 0.707107 acos = -

NW corner 1 = 315o cos 1 = 0.707107 acos = -


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3. Bilinear interpolation

The co-ordinates of a hops midpoint, xo and yo, have been calculated according to section 1above. This midpoint is located between 4 grid points of a digital map, points I, II, III and IV, eg

those with a mutual distance of 1.5o - see the below figure.

x andy are the longitudes and latitudes in degree,z11-22 are the co-ordinated third parameters, eg

the refractivity gradient, dN1 - section 4.2.3 - or the rainfall intensity, J0.01 - section 4.5.1. The

unknown parameter,zo, is obtained by the following calculation:

[169] ( )( ) ( )( ) ( )1121122211121121

11 zzzzyy

yy

xx

xx

yy

zzyy

xx

zzxxzz

bb

ao

ab

ao

ab

ao

ab

aoo +

+

+

+=

1.5o

1.5o


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Appendix I

Water vapour density - a World atlasThe data below are an extract from ITU-R Rec. P.836 and show the water vapour density in

g/m3 for two months of the year for the various regions of the world. These charts should beused the following way:

for the small time-percentage calculation, use the higher of the two values for the loca-tion concerned,

for the fading-free time calculation, use the lower of the two values.


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Appendix II

Rain intensity data - a World atlas

The data below are an extract from ITU-R Rec.P.837-3 and refer to the annual average clock-

minute rainfall rates in mm/h for 0.01% of the time. The figures in the below chart have been

derived from the data and equations shown in chapter4.5.3. For the charts of other regions of the

World, reference should be made to bibliography {1} or to ITU-R Rec.P.837-3.


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Appendix III

Rain attenuation coefficient, parameters and

Regression coefficients for estimating specific attenuations in equation [71]

Frequency

(GHz)H H V V

7

8

10

12

15

20

25

30

35

40

35

50

0.00301

0.00454

0.0101

0.0188

0.0367

0.0751

0.124

0.187

0.263

0.350

0.442

0.536

1.332

1.327

1.276

1.217

1.154

1.099

1.061

1.021

0.979

0.939

0.903

0.873

0.00265

0.00395

0.00887

0.0168

0.0335

0.0691

0.113

0.167

0.233

0.310

0.393

0.479

0.00265

0.00395

0.00887

0.0168

0.0335

0.0691

0.113

0.167

0.233

0.310

0.393

0.479

Raindrop size distribution according to Laws and Parsons, [1943]

Terminal velocity of raindrops according to Gunn and Kinzer, [1949]

Index of refraction of water at 20C, seeRay, [1972]

Values ofH, V,H and V for spheroidal drops [Fedi, 1979;Maggiori, 1981] based on re-gression for the range 1 to 150 mm/h.

performance and unavailabilty - principles and formulae

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