Formel KKE5201 5 Rev N A5 d

k&k engineering Planning digit al radio-relay radio-relay networks

erformance and unavailability Principles & formulae Version G.826

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TECHNICAL PAPER KKE 5201/5

© 1998-2005 Copying the contents of this booklet as well as translations to other languages, completely or partly, is not allowed without the permission of K&K Engineering HB . This includes any kind of copying by print, duplication, tape recording, electronic methods etc.

K&K Engineering HB,

Phone & Fax: or: E-mail: Internet home page: 050306

Box 2, S-610 54 NÄVEKVARN / Sweden +46-155-535 77 +46-8-532 51 888 [email protected] http://www.KK-Engineering.a.se

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© 1998-2005 Copying the contents of this booklet as well as translations to other languages, completely or partly, is not allowed without the permission of K&K Engineering HB . This includes any kind of copying by print, duplication, tape recording, electronic methods etc.

K&K Engineering HB,

Phone & Fax: or: E-mail: Internet home page: 050306

Box 2, S-610 54 NÄVEKVARN / Sweden +46-155-535 77 +46-8-532 51 888 [email protected] http://www.KK-Engineering.a.se

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ECHNICAL PAPER KKE 5201/5

Rev. N-A5

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Introduction K&K Engineering’s PC-based computer programs FORMULA and RLTool, are intended for the prediction of performance and availability of radio-relay paths and circuits. This paper, which is based on H. Karl’s 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 contains a complete new set of formulae for the prediction of both flat and selective multi path fading, as well as for the improvement due to diversity. Also the formulae for the prediction of attenuation 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 distances, 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:

*

d

=

2

d

+ (h A − h B )2 ⋅ 10 − 6

d* ... d ...

real length of the radio beam between transmitter and receiver antenna in km geodetic path length in km = plane projection of the radio path

h A ...

height above sea level for station A in m

h B ...

height above sea level for station B in m

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Table of contents 1

Path geometry.... ...................... ..................... ...................... ..................... ............ 7 1.1 Co-ordinates and bearing... ..................... ..................... ..................... .......... 7 1.1.1 Calculation of great-circle distance and bearing .................. .............. 7 1.1.2 Determination of co-ordinates........... ...................... ..................... ...... 7 1.2 1stFresnel zone radius........................ ...................... ..................... ............. 8 1.3 Calculation of antenna heights............. ..................... ..................... ............. 8 1.4 Calculation of path clearance...................... ..................... ..................... ...... 9 1.5 Effective Earth radius factor k ................... ..................... ..................... ..... 10 1.6 Ground reflection and its calculation... .................... ..................... ............ 10 1.6.1 Calculation of antenna heights.................. .................... ................... 10 1.6.2 Location of reflection point................... ..................... .................... .. 12 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......... 13 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 ..................... ..................... ..................... ..... 14

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......... ..................... ...................... .............. 18

2.5.4 2.6 2.7

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

Losses due to atmospheric gases....................... ..................... ................... 20 Receiver input level during fading-free time ............................... ............. 21

3

Overall performance of a digital radio-relay link during fading-free time and time of shallow fading ................... ..................... ..................... ................... 22

4

Overall performance of a digital radio-relay link during fading Performance calculation ................... ...................... ...................... ..................... 22 4.1 General.................................. ..................... ..................... ..................... ..... 22 4.2 The multipath occurrence factor ................... ..................... ..................... .. 22 4.2.1 Prediction formula..................................... ...................... ................. 22 4.2.2 Path inclination ................... ...................... ..................... .................. 23 4.2.3 Geoclimatic factor K.................... ...................... ..................... ......... 23

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4.3 Performance prediction considering multipath fading and related mechanisms.................................................................................................24 4.3.1 Prediction formulae ..................... ...................... ...................... ......... 24 4.3.2 Fading margin...................................................................................26 4.3.3 Paths going via passive repeaters......................................................26 4.4 Performance prediction considering distortions due to propagation effects (selective fading) ................... ...................... ..................... .......26 4.4.1 Prediction formulae ..................... ...................... ...................... ......... 26 4.4.2 Prediction procedure for path going via a passive repeater............ ...27 4.5 Small-time-percentage for exceeding the planning objectives due to attenuation caused by precipitation.........................................................................27 4.5.1 Attenuation caused by rain ..................... ..................... ..................... 27 4.5.2 Attenuation coefficient .................... ..................... ..................... .......28 4.5.3 Rainfall intensity...............................................................................28 4.5.4 Effective path length.........................................................................29 4.5.5 Fading probability due to rain for one path.......................................29 4.5.6 Prediction procedure for path going via a passive repeater............ ...29 4.5.7 Worst-month concept and average annual probability...................... 30 4.6 Improvement of the performance by diversity reception................ .......... 31 4.6.1 Improvement by frequency diversity .................... ...................... ......31 4.6.2 Improvement by space diversity ............................. .......................... 32 4.6.3 Improvement by combined frequency and space diversity - 2 Rx ....34 4.6.4 Improvement by combined frequency and space diversity - 4Rx.............35 4.7 Total performance with respect to the G.826 objectives........................................36 4.7.1 Calculation of the block-based severely errored seconds ratio (SESR)..............................................................................................37 4.7.2 Fading exceeding the background block error ratio (BBER) objective .................... ..................... ...................... .............. 39 4.7.3 Fading exceeding the errored second ratio (ESR) objective.............41 4.7.4 Total performance for the circuit ...................... ...................... .......... 41 5

Unavailability calculations for radio-relay systems........................................... .43 5.1 Unavailability and reliability of hardware..... ....................... ..................... 43 5.1.1 Single (unprotected) structures ...................... ...................... ............. 43 5.1.2 Duplicated (protected) structures......................................................44 5.2 Unavailability due to propagation disturbances....................... .................. 46 5.3 Total unavailability....................................................................................46

6

Frequency planning............................................................................................48 6.1 The number of disturbing signals reaching a receiver ............................... 48 6.2 General formula for the calculation of interfering signal levels ................ 48 6.3 Formulae for triangular network configuration .................... ..................... 49

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6.3.1

Nodal station disturbs outstation (Tx A1 _ RxC).............................. 50

6.3.2

Outstation disturbs nodal point (Tx C _Rx A1) ................................. 51

6.4 Interference via passive repeater................ ...................... ...................... ... 52 6.4.1 Passive repeater as first-source transmitter ....................... ............... 52 6.4.2 Passive repeater as receiver of interfering signals............................ 54 6.5 Total interference......................... ...................... ...................... ................. 54 7

Bibliography..................... ..................... ..................... ..................... .................. 56

Appendix I

59

Appendix II

61

Appendix III

62

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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 d = 111.12 ⋅ a cos(sin y1 ⋅ sin y 2

[1] d...

great-circle distance in km

x1... x2...

longitude for site A in degrees longitude for site B in degrees

y1... y2...

latitude for site A in degrees latitude for site B in degrees

+ cos y1 ⋅ cos y 2 ⋅ cos[ x2 − x1 ])    

 negative values for  W of Greenwich  negative values for of the equator S

and the antenna bearing in A is:

∠Θ'  =  cos sin

[2]

− sin  ⋅ cos(. ⋅ ) sin(. ⋅ ) ⋅ cos 



∠Θ1 = ∠Θ'1 ∠Θ1 = 360o - ∠Θ'1

for

sin (x2- x1) > 0:

for

sin (x 2 – x 1) < 0:

1.1.2

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]

y 2

= a sin (cos Θ1 ⋅ sin[0.0089992 ⋅ d ] ⋅ cos y1 + sin y1 ⋅ cos[0.0089992 ⋅ d ]) [4]

for for

x2

= x1 ± a cos

∠Θ1 < 180o: ∠Θ1 > 180o:

cos[0.0089992 ⋅ d ] − sin y1 ⋅ sin y 2 cos y1. cos y 2 +acos - acos

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1st Fresnel zone radius

1.2

[5]

r 1

= 17.3

d 1 ⋅ d 2 f ⋅ d

r 1... d ... d 1... d 2 = f...

radius of the 1stF resnel zone at a certain point in m radio beam length in km distance from one site to that point in km d – d 1, in km 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 antenna height at A is the known one, the antenna height at B can be calculated according to:



d ⋅  ∆r 1 [6]

hGB

=



+ hOBST +

d 1 [d − d 2 ] 

 − (d − d 1 ) ⋅ (h A

k ⋅ 12.74  d 1

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

h B... hOBST ...

height above sea level for station B in m

d ... d 1...

distance A to B in km distance A to obstacle in km

k ... ∆r 1...

effective earth radius factor required clearance above obstacle in m

where:

+ hGA )

− h B

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

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[7]

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∆r = 1

2005-03-06

r 1 ⋅ ∆r r

100

r 1...

radius at the 1st Fresnel zone in m

∆r r ...

required clearance above obstacle in %

If there is more than one obstacle which may influence the determination of antenna heights, the calculation will have to be repeated and the highest value for hGB chosen. For calculation of hGA, if hGBi s known, replace the indices 1 by 2, and 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 above an obstacle is:

[8] For For For

∆r 1 =

∆r 1> r 1 r 1 > ∆r 1> 0 ∆r 1< 0

d 1 (h B

+ hGB ) + (d − d 1 )(h A + hGA ) d

− hOBST −

d 1 (d − d 1 ) k ⋅ 12.74

the 1 st Fresnel zone is free from intrusions the 1 stF resnel zone is intruded, but there is still line-of-sight no line-of-sight

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1.5

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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 for k min.

If k min is not known, the below diagram may be used. Path lengths <20 km should be set to 20 km.

1.6

Ground reflection and its calculation

1.6.1

Calculation of antenna heights

The below formulae require the antenna height above the reflection area. Reference should hereby be made to the figure, which shows the basic path geometry for a reflective path. Parameters not stated below are according to section 1.3.

[9] [10] h1... h2... tan υ...

h h2

1

= hGA + h A − yo + xo ⋅ 10 3 ⋅ tan υ

= hGB + h B − y o − (d − xo ) ⋅ 103 ⋅ tan υ

height of antenna above reflection area at site A in m height of antenna above reflection area at site B in m inclination angle for sloping terrain ( υ = 0 for horizontal terrain) according to formula [11]

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Basic geometry for a reflective path

[11]

xo , yo...

tan υ =

− y1 ( x 2 − x1 ) ⋅ 10 3 y 2

midpoint of the reflection area according to formulae [12] and [13]

[12]

xo

= x1 +

[13]

y o

= y1 +

x 2 − x1

2 y 2

− y1 2

x1... x2...

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

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1.6.2

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Location of reflection point [14]

d 1

[15]

= d (1 + Z ) 2

d = (1 − Z ) = d − d 1

d 2

2

d 1 and d 2 are the distances in km to the reflection point from either side of the path according to Figure 2.

[16]

q

=

h1 − h2

h1 + h2

q... h1...

parameter to be used in formula [18] height of antenna above reflection area a t site A in m

h2...

height of antenna above reflection area at site B in m

Q=

[17] Q...

51 ⋅ k ⋅ (h1 + h2 ) 2 ⋅ d 2

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

The other parameters have their previous significance.

[18]

q

V =

1+

  

[19] Z = V 1 +

V 2

1+ Q

+

V 4

[1 + Q]2

+

1 Q

V 6

+ 3

[1 + Q ]

V 8

[1 + Q]4



+ .... 

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] Z ≈ V 1 +

V 2

1+ Q

+

V 4

[1 + Q]2

+

  3 [1 + Q]  V 6

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1.6.3

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Difference in path length between direct and reflected ray [21]

δ=

2   2   h − d 1   h 1 2 12.74 ⋅ k   d 



δ ...

2005-03-06

−

 

 − 3  ⋅ 10 12.74 ⋅ k   d 22

difference in path length between direct and reflected ray in m

The other parameters have their previous significance. Expressed in terms of wavelengths, this difference will be:

[22]

τ ...

τ = δ ⋅ f 0.3

difference in path length between direct and reflected ray in number of wavelengths

τ

Each 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 minimum when k is varying.

Receiver input level vs k value variation

1.6.4 The pitch,

The distance between receiver input level minima or maxima

ϑ1 (or ϑ2), i.e. the distance between adjacent minima or maxima in the input

level, can be calculated using the formulae below:

[23]

ϑ1 =

0.15 ⋅ d f

1

⋅ h2

−

d 22

12.74 ⋅ k

⋅ 103

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1.6.5

ϑ2 =


0.15 ⋅ d f

1

⋅ h1 −

d 12

⋅10 3

12.74 ⋅ k

Optimum antenna spacing with space diversity protection

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

ϑ1 and ϑ2 respectively by a factor 2, i.e.: [25]

∆h1(2) =

ϑ1(2) 2

∆h1(2)... ϑ1(2) ...

as above

1.6.6

Efficiency of selected space diversity versus k-value variation

antenna spacing between diversity antennas in ma t station A or B respectively

[26]

[27]

∆τ1(2)...

∆τ1 =

2 ⋅ f ⋅ ∆h1  h 2 0,3 ⋅ d 

∆τ 2 =

2  2 ⋅ f ⋅ ∆h2   h − d 1  ⋅ 10 − 3 1 0,3 ⋅ d  12.74 ⋅ k 

−

 − 3  ⋅ 10 12.74 ⋅ k  d 22





space diversity efficiency at station A or B respectively: = 0.5 corresponds to optimum efficiency

∆τ


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 and

α1

α2 in the figure on page 11 must be determined. With these values we can enter the

radiation pattern for the used antennas.

[28]

 h

α1 = 180  1 − π  d 1

h1 − h2 d

−

 − 3  ⋅ 10 12.74 ⋅ k  d 2

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[29]

α1(2) ...

 h

α 2 = 180  2 − π  d 2

Rev. N-A5 h2

− h1 d

−

2005-03-06

 − 3  ⋅ 10 12.74 ⋅ k  d 1

angles between direct and reflected ray in degrees according to the figure in

section 1.6.1 All 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]

A L

= Ao + A A + Ag + AW 1 + AW 2 + A B − G1 − G2 − G R

A L .... Ao .... A A ... Ag ... AW 1,2 ... A B ... G1,2 ... G R ...

total (or net) path attenuation in dB free-space basic attenuation in dB additional attenuation(s) in dB attenuation due to atmospheric gases in dB antenna feeder attenuation at the transmitting (1) and receiving (2) end, in dB attenuation in the RF-branching assembly of the radio-relay equipment in dB antenna gain at the transmitting (1) and receiving (2) end, in dB gain in a passive repeater in dB

2.2

Free-space basic attenuation [31] Ao

*

= 92.4 + 20 ⋅ lg d * + 20 ⋅ lg f

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. The program, however, deals with passive repeaters, - see next section.

2.4

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

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

AoA + AoB where: AoA...

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

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ECHNICAL PAPER KKE 5201/5 AoB... and G R by:

Rev. N-A5

2005-03-06

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

G A

+ G B

where: G A...

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

G B...

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

2.5

Gain or loss in a passive repeater, plane reflector

2.5.1

Check of far-/near-field operation: [32]

s Z =

75 ⋅ π ⋅ d s* f ⋅ Y ⋅ cos

ψ 2

d *s ... f... Y... ψ ...

the shorter one of the two partial paths (legs) in km radio frequency in GHz reflector area in m2 angle in space at repeater in degrees

For For

s Z > 2.5 ⇒ s Z < 2.5 ⇒

2.5.2

Angle in space

[33]

cosψ =

h R

far-field condition near-field condition

− h A' 2 + d A ⋅ d B ⋅10 6 cos ψ 1 − h R − h A' h B' − h A' (d A2 ⋅106 + [h R − h A' ]2 ) (d B2 ⋅106 + [h R − h B' ]2 ) [34]

∠ψ = a cos ψ

h’ A...

height above sea level for the antenna at station A in m (= h A+hGA)

h’ B...

height above sea level for the antenna at station B in m ( = h B+hGB)

h R... d A...

height above sea level for passive repeater 1 in m distance station A to passive repeater in km (in plane projection)

d B...

distance station B to passive repeater in km (in plane projection)

1This height is the sum of ground level and

eight reflector h

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ψ 1... ψ ...

Rev. N-A5


angle at repeater point in plane projection in degrees

Y...

angle in space at repeater point in degrees reflector area (physical area) in m2

bmax...

largest side dimension (width or height) of the reflector in m

f...

radio frequency in GHz

2.5.3

Repeater gain in far field


AoA + AoB 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 G R is calculated according to:

[35]

2.5.3.1

G R

= 20 ⋅ lg  139.5 ⋅ f 2 ⋅ Y ⋅ cos ψ  

2 

Repeater loss in near field


Aol 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]

η s = Da

π 4 ⋅ Y ⋅ cos

ψ 2

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

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2.5.4

Rev. N-A5

Half-power (3 dB) beam width [37]

2 Θ 3dB

≈

15.3 f ⋅ bmax ⋅ cos

ψ 2

2005-03-06

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2Θ3dB... bmax...


half-power or 3 dB beam width in degrees largest side of reflector in m


2.6

Losses due to atmospheric gases [38] Ag

= γ g ⋅ d *

Ag... γ g...

attenuation in dB due to absorption by oxygen and water vapour

d*... and:


specific attenuation in dB/km

[39]

γ o... γ w...

∗ [40]

∗ [41]

specific attenuation in dB/km for dry air specific attenuation in dB/km for water vapour

For f = radio frequency < 57 GHz:

γ o − 57

 =  2  f

  ⋅ f 2 ⋅ r 2 ⋅ r 2 ⋅ 10 − 3 + p t + 0.351 ⋅ r p2 ⋅ r t 2 [ f − 57]2 + 2.44 ⋅ r p2 ⋅ r t 5  7.27 ⋅ r t

γ o − 60 =

( f − 60) ⋅ ( f − 63) 18

( f − 60)( f − 63)

γ o − 57 − 1.66 ⋅ r p2 ⋅ r t 8.5 ⋅ ( f − 57 ) ⋅ ( f − 63) +

γ o − 63

For 63 < f < 350 GHz

 − 4 1.5 − 5 1.5  2 ⋅ 10 ⋅ r t 1 − 1.2 ⋅ 10 ⋅ f  =  0.28 ⋅ r t 2   [ f − 118.75]2 + 2.84 ⋅ r p2 ⋅ r t 2 

[

[42]

7.5

For 57 < f < 63 GHz:

18

∗

γ g = γ o + γ w

γ o − 63

]+

4 2

[ f − 63] + 1.5 ⋅

⋅

r p2 r t 5

+ 

  ⋅ f 2 ⋅ r p2 ⋅ r t 2 ⋅ 10 − 3    

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ECHNICAL PAPER KKE 5201/5 r t =

[43]

[44] t ... p...

Rev. N-A5

r p

2005-03-06

288 273 + t

=

p

1013

average lowest temperature in °C air pressure in hPa

7   3.79  0.0327 r t + 0.00167 ρ r t + 7.7 ⋅10 − 4 f 0.5 +  2 2   r p [ f − 22.235] + 9.81 r p r t 2  f ρ r p r t ⋅10 − 4 γ w =    11.73 r t 4.01 r t +  +  2 2 2 2 − + − + f r r f r r [ ] [ ] 183 . 31 11 . 85 325 . 153 10 . 44 p t p t   [45]

ρ ...

2.7

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

Receiver input level during fading-free time [46] L Rx

= LTx − A L − ATPC

L Rx... LTx...

receiver input level in dBm during fading-free time

A L... ATPC …

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

transmitter output level in dBm control range of the adaptive transmitter power control in dB

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3

Rev. N-A5


Overall performance of a digital radio-relay link during fading-free time and time of shallow fading

During 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 individually for each path.

∗

The small-time-percentage objectives only take account of multipath fading through the troposphere, 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 antenna heights and/or sites, diversity reception, etc.

∗

For the SESR objective - rain attenuation is assumed to exceed the available fading margin for at least 10 consecutive seconds . It is thus considered as unavailability. For the ESR and BBER performance objective, however, all rain fading, irrespective its duration, has to be treated as a performance influencing parameter.

∗

Multipath propagation and precipitation appear uncorrelated. The total time percentage during which the planning objectives are not met is the sum of two independent contributions.

4.2

The multipath occurrence factor

4.2.1

Prediction formula

For detailed planning: planning:

[47]

Poi

= K ⋅ d * 3.2 (1 + ε )−0.97 ⋅ 10 − 2 + 0.032 ⋅ f − 0.00085⋅ h L

For approximate planning:

[48] Poi...

Poi

= K ⋅ d * 3.0 (1 + ε )−1.2 ⋅ 10 − 2 + 0.033⋅ f − 0.001⋅ h L

multipath occurrence factor for the individual radio hop

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h L...

the lower of the two antenna altitudes in m above sea level , i.e. h A+hGA or

... K ... ... f ...

h B+hGB geoclimatic factor frequency in GHz

*

d ...


ε... i...

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

4.2.2

Path inclination

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

[49]

(h A + hGA ) − (h B − hGB )

ε≈

d

ε... d... h A...

inclination in milliradians milliradians path length in km elevation in m above sea level for the left-hand site

h B... hGA...

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

hGB...

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

4.2.3

Geoclimatic factor K

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

If no fading data are available for the area concerned, the factor K can be estimated following the below procedure: For detailed planning (formula [47]):

[50]

0.42 ⋅ 10 −3.9 − 0.003⋅ dN 1 K = σ − a

For approximate planning (formula [48]):

[51]

K = 10

−4.2 − 0.0029 ⋅ dN 1

The parameters have the following significance: dN1... The point refractivit y gradient in the lowest 65 m of the atmosphere not exceeded for 1% of an average year. The figure can be obtained on a 1.5 o

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2005-03-06

σa...

Rev. N-A5


grid resolution in latitude and longitude from a database 2 available from ITU-R (see also ITU-R Rec. 453-8). 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 hop’s midpoint. Terrain data are available from Internet, eg the Globe gtopo30d ata. The standard deviation can be calculated applying the following formula:

 κ  κ ⋅ ∑ h j2 −  ∑ h j  j =1  j =1 

κ

σa =

[52]

2

κ ⋅ (κ − 1)

For σa< 1, set σa = 1. h j... altitude a.s.l. in m for the individual height sample ... κ ... j...

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

For the calculation of a hop’s midpoint, and for the bilinear interpolation interpo lation in order to obtain the correct figure for dN 1, reference should be made to the Annex of this booklet, page 57.

4.3

Performance prediction considering multipath fading and related mechanisms

4.3.1

Prediction formulae

From the multipath occurrence factor, Po, calculated according to either formula [47] or [48], a fading depth M (dB) is calculated:

[53] M = 27.4 + 1.2 ⋅ lg Po If M is less or equal than the available fading margin, M F , i.e.

[54]

≤ M F M ≤

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

2 The corresponding data files, DNDZ_01.txt, DNDZ_LAT.txt and DNDZ_LON.txt can be downloaded from ITU-R’s website. A table - dN_1.xls - showing dN 1 versus longitude and latitude can be downloaded from K&K Engineering’s website (see page 2).

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ECHNICAL PAPER KKE 5201/5 [55] PFi...

PFi

Rev. N-A5

2005-03-06

= Po ⋅ 10 − M F 10

probability rate for exceeding the planning objective, defined by the available fading margin, M F , for one radio hop during the average worst month

Po...

multipath occurrence factor for the respective radio hop as per formula [47] or [48] fading margin in dB

M F ... i...

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

, the following method is For fade depths, M , larger than the available fading margin, M F

recommended: (i) Use formula [55] above, calculate PFiM for the fade margin M as obtained by formula [53]. (ii) Calculate parameter qa for the same fade margin, M , and the associated value for PFiM from:

[56] (iii)

qa

=−

20

M

⋅ lg[− ln(1 − PFiM )]

If PFi 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 is considered by your calculator as an

ln 0.999... ≠ 0 (iv)

Calculate parameter qt for the same fade margin, M , from:

[57]

(v)

qt =

qa

−2

(1 + 0.3 ⋅10 − M 20 )⋅10

M   − 4.3 ⋅ 10 − M 20 +  − 0.16 ⋅ M



800 

Finally, calculate the probability, PFi, that the planned fading margin, M F , is exceeded: [58] PFi 1 e − S where: − q ⋅ M F 20

=( −

[59]

)

S = 10

and:

[60]

q

= 2 + [1 + 0.3 ⋅ 10 − M F

20

]⋅10 − 0.016⋅ M

F

  − M F qt + 4.3 10  

20

+

M F  



800  

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The parameters PFi and M F have their previous significance.

4.3.2

Fading margin [61] M F = L Rx

+ ATPC − LTeI = L Rx + ATPC − LTe − D

M F...

flat-fading margin in dB

L Rx...

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 ...

ATPC …

receiver threshold level in dBm for the planning criterion and for a disturbed receiver (CIR ≠ ∞) receiver threshold degradation in dB due to interfering signals selected control range of the adaptive transmitter power control in dB

4.3.3

Paths going via passive repeaters

D...

The total probability rate for exceeding the fading margin, M F , is the sum of the percentage , is exceeded for each leg: of time that the fading margin, M F

[62]

PFi

= PFi − leg 1 + PFi − leg 2

4.4

Performance prediction considering distortions due to propagation effects (selective fading)

4.4.1

Prediction formulae [63]

PSi = 4.3 ⋅ η ⋅ W ⋅ 10 − B

20

τ 2m ⋅ ⋅ 10 − 3 τ ref

with: 1.3  d ∗  = 0.7    50 

[64]

τm

[65]

η = 1 − e − 0.2⋅ Po

and: 0.75

PSi...

probability that one radio hop exceeds the planning criterion due to distor-

η...

tions during the average worst month multipath activity factor

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Po. W ... B... τref ...

multipath occurrence factor acc. to formula [47] or [48] mean valueo f the width of the signature in MHz mean value of the signature (or notch) depth in dB reference delay in nsu sed to obtain the signature ( W and B)

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]

W W = MPh

+ W NMPh 2

for the signature width, and

[67] B



B MPh 20

= 20 ⋅ lg  10

+ 10 B NMPh 2



20 

  

for the notch depth, and

[68]

τ ref =

τ ref , MPh + τ ref , NMPh 2

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 selective multipath propagation will be calculated individually for each leg, applying formulae [63] to [65]. The fading margin, M F , is, again, that for t he total path length, and will thus be the same for both legs. The total percentage of time for selective fading is thus:

[69]

4.5

PSi

= PSi − leg 1 + PSi − leg 2

Small-time-percentage for exceeding the planning ob jectives due to attenuation caused by precipitation

The influence of rain is predicted by calculating the rain attenuation for 0.01% of the time. Relating the rain attenuation to the available flat-fading margin, the percentage of time during which the fading margin is exceeded is calculated.

4.5.1

Attenuation caused by rain

The attenuation caused by rain is:

[70] A R0.01

= γ R ⋅ d eff

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A R0.01... γ R...

attenuation due to rainfall in dB during 0.01% of time

d eff ...

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

4.5.2

Attenuation coefficient

rain attenuation coefficient in dB/km

The attenuation coefficient, γ R, versus radio frequency, f, for various clock-minute rainfall rates during 0.01% of time, J 0.01, is calculated from formula [71]:

[71] J 0.01...

γ R = Τ ⋅ J 0α.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

Τ and α are

frequency- and polarization-dependent parameters, which are to be obtained from the 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 , M s and M c. Their data can be found in the corresponding data files esarainPR6.txt, esarain_Mc.txt and esarain_Ms.txt 3. The data are extracted the following way:

For each of the 3 parameters, Pr6 , M s and M c, the figures for the 4 grid points surrounding the hop’s midpoint are used in order to calculate the corresponding figures for the midpoint applying bilinear calculation - see formula [174] on page 58. The midpoint’s rainfall intensity, J 0,01, is then calculated with the help of the midpoint figures for Pr6 , M s and M c:



[72] J 0.01

1.033 ⋅ 10 4 ⋅ A  = − B + B 2 M s + M c 

−

1.936 ⋅ 10 −4 C ( M s



A

+ M c )   

[73] A = Pr 6 1 − e −0.0117 ⋅ M s Pr 6

3

The corresponding data files, ESARAINPR6.txt, ESARAIN_Mc.txt a nd ESARAIN_Ms.txt c an be downloaded from ITU-R’s website. Alternatively, tables - P-Pr6.xls, P-MC.xls and P-MS.xls showing the corresponding parameters versus longitude and latitude can be downloaded from K&K Engineering’s website (see page 2).

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ECHNICAL PAPER KKE 5201/5 [74] B

Rev. N-A5

= 1.11 + 1.3736 ⋅10 − 3 ⋅

2005-03-06

M s + M c A

⋅ C

 0.01    A 

C = ln 

[75]

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

4.5.4

Effective path length [76]

[77]

d o

d eff

=

d

1 + d d o

= 35 ⋅ e −0.015⋅ J 0.01

geodetic path length in km effective path length in km

d... d eff ...

Note: For J 0.01 > 100 mm/h, use J 0.01 = 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 margin, M F , is estimated to be:

[78]

p Ri

= 1011.628 (− 0.546 +

p Ri... M F ...

0.29812 + 0.172 ⋅ lg [0.12 ⋅ A R 0.01 M F ]

)  A R0.01  

M F

≥ 0.154023

fading probability in % of time for a radio hop due to rain fading margin in dB

Equation [78] converges quickly to % as the factor decreases and approaches 0.154. For values <0.154024, a figure of 0.155 is used for A R0.01 /M F in the above equation, giving a p Ri of 8⋅10-7%.

4.5.6

Prediction procedure for path going via a passive repeater

Plane reflector type The rain fading probability is calculated applying the same calculation method as described in sections 4.5.1-4.5.5, but using

[79] in formula [76]

d = d leg1 + d leg 2



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Antenna back-to-back type

∗

If both legs utilise the same polarisation, the calculations is as described for the plane reflector type

∗

If both legs operate at different polarisations, proceed as follows: − apply the formulae in sections 4.5.1-4.5.5 plus formula [79] for verti olarisation and obtain p R-V calp

− −

perform the same for horizontalp olarisation and obtain p R-H obtain the final rain fading probability, p R: [80] p Ri

=

p R −V ⋅ d leg −V + p R − H ⋅ d leg − H d

4.5.7

Worst-month concept and average annual probability

4.5.7.1

Average annual probability:

[81] p Ri... P Rai...

P Rai

= 0.01 ⋅ p Ri

fading probability according to formula [78] average annual probability, during which the rain attenuation exceeds the

available fading margin. When the fading margin, M F , in formula [78] refers to the BERSES threshold level of the receiver, the above formula [81] changes to

[82] p Rai-SES ...

P Rai − SES

= 0.01 ⋅ p Rai − SES ⋅ UP

100

fading probability in % according to formula [78], with fading margin, M F , referred to the BERSES threshold level of the receiver

P Rai-SES ... UP...

4.5.7.2

resulting average annual probability rate, during which the rain attenuation exceeds the available fading margin portion in percentage of the average annual probability rate, which lasts longer than 10 consecutive seconds and, thus, has to be treated as unavailability Worst month probability

[83]

P Rwmi

= 0.01 ⋅ (3.33 ⋅ p Ri )0.87

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ECHNICAL PAPER KKE 5201/5 P Rwmi...

Rev. N-A5

2005-03-06

average worst month probability, during which the rain attenuation exceeds

the available fading margin Consequently, that part, UP, of the average annual p robability rate, which lasts shorter than 10 consecutive seconds, has also to be converted to an average worst monthp robability rate, applying formula [83]:

[84] P Rwmi-UP...

P Rwmi −UP

100 = 0.01 ⋅   3.33 ⋅ p Rai − SES ⋅ − UP  100  

0.87

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

rain attenuation exceeds the available fading margin to the BERSES threshold level of the receiver p Rai-SES and 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] I fi I fi... f...

∆ f... *

d ... M F ...

=

80 ⋅ ∆ f f ⋅ d ∗ 2

⋅10 M F 10

improvement factor due to frequency diversity for the individual hop band centre frequency in GHz frequency separation between the two diversity paths, r.f.1 – r.f.2, in GHz beam path length in km flat fading margin according to section 4.3.2. In case the main and the diver-

sity path have different fading margins (due to different Tx output levels, etc.), the lower of the two fading margins has to be used. The above formula is verified by measurements for the following data ranges: 2 < f < 13 GHz 30 < d * < 75 km

∆ f / f < 0.05 If ∆ f > 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]

PdfFi

=

PFi I fi

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PdfFi...

probability for the worst month for exceeding the planning criterion due to

PF ...

fading for a 1+1 frequency-diversity configuration for the individual hop probability in 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

4.6.1.2

For distortions

[87]

PdfSi

=

2 PSi

2 ) η (1 − k fSi

PdfSi...


PSi...

distortions for a 1+1 frequency-diversity configuration for the individual hop probability for the worst month for exceeding the planning criterion due to distortions fading for an unprotected configuration according to equation [63] for the individual hop

η...

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

[88]

2 k fSi

= 0.8238

[89]

2 k fSi

= 1 − 0.195 (1 − r wi )0.109 − 0.13 lg (1− r wi ) for 0.5 <

r wi < 0.9628

[90]

2 k fSi

= 1 − 0.3957(1 − r wi )0.5136

for

r wi > 0.9628

[91]

r wi

2 ) = 1 − 0.9746 (1 − k fFi

for

k fFi < 0.26

[92]

r wi

2 ) = 1 − 0.6921(1 − k fFi

for

k fFi > 0.26

[93]

2 k fFi

for

2.17

1.034

= 1−

r wi < 0.5

2

2

I fi ⋅ PFi

η

4.6.2

Improvement by space diversity

4.6.2.1

For flat fading:

With f and d* having their previous significance, the equation for the space-diversity im provement factor can be written as follows:

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ECHNICAL PAPER KKE 5201/5 [94] I si

Rev. N-A5

2005-03-06

−4 −0.12 ∗0.48 −1.04 0.87 =  1 − e − 3.34⋅10 ⋅ ∆h ⋅ f ⋅ d ⋅ Po  ⋅ 10 M F 10





I si...

improvement factor due to space diversity for the individual hop

∆h... M F ...

vertical spacing of receiving antennas, centre-to-centre, in m flat fading margin in dB according to section 4.3.2. In case the main and the diversity path have different fading margins (due to different antenna sizes, waveguide length, etc.), the fading margin has to be corrected accordingly:

[95] M F [96]

= M F − m − ∆G

∆G = Gm − Gd − AW − m + AW − d

If M F-m...

∆G < 0 → ∆G = 0

Po... Gm...

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

Gd ... AW-m...

gain in dB for the diversity antenna

AW-d ...

waveguide attenuation dB for the diversity-antenna path

flat fading margin in dB for the main-antenna path gain in dB for the main antenna waveguide attenuation dB for the main-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]

PdsFi

=

PFi I si

PdsFi...

probability rate for the worst month for exceeding the planning criterion due

PFi...

to fading for a space-diversity configuration for the individual hop 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]

PdsSi

=

2

PSi

2 η (1 − k sSi )

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PdsSi...


PSi...

distortions for a frequency-diversity configuration for the individual hop probability for the worst month for exceeding the planning criterion due to distortions for an unprotected configuration according to equation [63] for the individual hop

η... [99]

multipath activity factor, see equation [65] for the individual hop 2 k sSi

= 0.8238

2 [100] k sSi 2 [101] k sSi

for

= 1 − 0.195 (1 − r wi )0.109 − 0.13 lg (1− r wi ) for 0.5 <

r wi < 0.9628

= 1 − 0.3957 (1 − r wi )0.5136

for

r wi > 0.9628

for

k sFi < 0.26

for

k sFi > 0.26

[102] r wi

2 ) = 1 − 0.9746(1 − k sFi

[103] r wi

2 ) = 1 − 0.6921(1 − k sFi

2 [104] k sFi

r wi < 0.5

2.17

1.034

= 1−

2

2

I si ⋅ PFi

η

4.6.3

Improvement by combined frequency and space diversity - 2 Rx

4.6.3.1

For flat fading:

The flat fading improvement, I s,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] k f , sFi

= k fFi ⋅ k sFi

with k sFi according to formula [104], and k fFi according to formula [93].

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4.6.4

Improvement by combined frequency and space diversity - 4Rx

4.6.4.1

For flat fading:

[106] Pdf , sF − 4i

[107] m D

=

4 PFi

m D

2 2 )(1 − k sFi ) = η3 ⋅ (1 − k fFi

Pdf,sFi...


PFi...

to fading for a combined frequency/space-diversity configuration with 4 Rx probability rate for the worst month for exceeding the planning criterion due

k sFi...

to fading for an unprotected configuration according to equations [55] or [56] multipath activity factor acc. to equation [65] flat fading correlation coefficient for space diversity configuration according

k fFi...

to formula [104] flat fading correlation coefficient for frequency diversity configuration ac-

η...

cording to formula [93] 4.6.4.2

For distortions:

4

[108] P df , sS − 4i

=

PSi

2 )] 2 [η(1 − k sSi

Pdf,sS-4i...


PSi...

to distortions for a combined frequency/space-diversity configuration with 4 Rx probability rate for the worst month for exceeding the planning criterion due

k sS ...

to distortions for an unprotected configuration according to equation [63] 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 Path type

BERSES and block sizes...

Bit rate

BER SES

Blocks/s

Bits/block

(Note ii)

(Note ii)

(Note ii)

n

N B

(Mbit/s)

...for various PDH systems Note i

2

4x10

-4

2x2

2x10

E1 2xE1

2 000

1 120

-4

2 000

2 000

8

1.1x10 -4

2 000

4 224

8x2

8.8x10 -5

4 000

5 170

34

6.5x10 -5

8 000

6 120

E2 8xE1 E3

...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-2

6

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

2.3x10-5

8 000

19 940

-4

192 000

801

STM-1

i

155

2.33x10

No figures are stated so far for PDH systems. P.530 advises to select the BERSES closest to the SDH transmission rate. This applies for 2 and 34 Mbit/ss ystems. For the other PDH capacities, the author proposes the above figures.

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ECHNICAL PAPER KKE 5201/5 ii

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Rev. N-A5

2005-03-06

The BER SES 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. 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 be 192 000 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, unprotected hop is:

[109] P Mi − SES = PFi − SES + PSi − SES

P Mi-SES ...

probability rate for the worst month for exceeding BERSES on an unpro-

PFi-SES ...

tected hop due to multipath propagation probability rate for the worst month for exceeding BERSES on an unprotected hop due to multipath fading; calculated acc. to formulae [55] or [58], applying the relevant fading margin to BERSES

BERSES ...

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

PSi-SES ...

exceeds 30% (Table 1) probability rate for the worst month for exceeding BERSES on an unprotected hop due to distortions; calculated acc. to formula [63], applying the relevant signature data for BERSES

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] P Mi − SES = PdFi − SES 0.75

P Mi-SES ... PdFi-SES ...

+ PsSi − SES 0.75 ) 4 3

probability rate for the worst month for exceeding BER SES on a diversity protected hop due to multipath propagation probability rate for the worst month for exceeding BER SES on a diversity protected hop due to multipath fading; calculated acc. to formulae [55] or [58], applying the relevant fading margin to BERSES

BERSES ...

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

PSi-SES ...

exceeds 30% (Table 1) probability rate for the worst month for exceeding BER SES on a diversity protected hop due to distortions; calculated acc. to formula [63], applying the relevant signature data for BERSES

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i...

ordinal No for the individual hop

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 for P Mi-SES has, thus, to be reduced to:

[111] P Mi − SES '

= P Mi − SES ⋅ 100 − UM 100

P Mi-SES-1’... resulting probability rate for the worst month for exceeding BERSES on a hop due to multipath propagation

P Mi-SES ... UM...

probability rate for the worst month for exceeding BER SES on a hop due to multipath propagation as per formulae [109] or [110] part in percentage of the probability rate, which has to be treated as unavailability

Unavailability part

[112] P Mi − u

[113]

= P Mi − SES ⋅ UM ⋅ 10 − ∆G 10 100

∆G = 10.5 − 5.6 ⋅ lg 1.1 ± cos2ξ 0.7 )− 2.7 ⋅ lgd ∗ + 1.7 ⋅ lg(1 + ε ) For ∆G> 10,8:

P Mi-u...

use 10,8

average annual unavailability rate on a hop due to multipath propagation

P Mi-SES and UM as above

ξ... ε...

latitude in degrees + 1 decimal + for ξ≤45ο − for ξ >45 o N or S of the Equator hop length in km path inclination in mrad (formula [49])

4.7.1.4

Resulting block-based severely errored seconds ratio (SESR)

±... * d ...

[114] P Mi − SES "

=P Mi − SES ' + P Rwmi −UP

P Mi-SES ”... final probability rate for the worst month for exceeding BERSES on a hop due to multipath propagation

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2005-03-06

P Mi-SES ’..

resulting probability rate for the worst month for exceeding BERSES on a

P Rwmi-UP...

hop due to multipath propagation acc to formula [111] above probability rate for the worst month for exceeding BERSES on a hop due rain fading acc to formula [84]

4.7.2

Fading exceeding theb ackground 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] P Mi − BBE = P Mi − SES ⋅

[116] m1

=

α1 2.8 ⋅ α 2 ⋅ (m1 − 1)

lg RBER − lg BERSES lg P Mi − RBER

− lg P Mi − SES

P Mi-BBE ...

BBER probability rate for the worst month due to multipath propagation

P Mi-SES ...

probability rate for the worst month for exceeding BERSES due to multipath

RBER... BERSES ...

propagation acc. to formula [109], [110] or [111] residual bit-error ratio the bit-error ratio for which the number of errored blocks within one second exceeds 30% (Table 1)

P Mi-RBER... from the next formula: [117] P Mi − RBER

= PFi − RBER + PSi − RBER

PFi-RBER...

probability rate for the worst month for exceeding RBER on a hop due to

PSi-RBER...

fading; calculated acc. to formulae [55] or [58], applying the relevant fading margin to RBER probability rate for the worst month for exceeding RBER on a hop due to

α1...

distortions; calculated acc. to formula [63], applying the relevant signature data for RBER number of error/burst for the BER in the range between BER = 10-3 and

α2... i...

BERSES ; normally between 10 and 30 number of error/burst for the BER in the range between BERSES ; and RBER; normally between 1 and 10 ordinal No for the individual hop

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Prediction of BBER due to rain fading

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

[118] P Rwmi − BBE = P Rwmi − SES ⋅

α1 2.8 ⋅ α 2 ⋅ (m2 − 1)

P Rwmi-BBE ...BBER probability rate for the worst month due to rain P Rwmi-SES ... probability rate for the worst month for exceeding BERSES due to rain, calculated acc. to formula [78], applying the relevant fading margin to BERSES , and transferred to the worst-month value by formula [83] RBER... BERSES ...

residual bit-error ratio the bit-error ratio for which the number of errored blocks within one second exceeds 30% (Table 1)

α1...

number of error/burst for the BER in the range between BER = 10-3 and

α2...

BERSES ; normally between 10and 30 number of error/burst for the BER in the range between BERSES ; and RBER; normally between 1and 20

whereby:

[119]

α1 ≤2 α2

and:

[120] m2

=

lg RBER − lg BERSES lg P Rwmi − RBER

− lg P Rwmi − SES

P Rwmi-RBER...probability rate for the worst month for exceeding RBER due to rain, calculated acc. to formula [78], applying the relevant fading margin to BER RBER, i...

and transferred to the worst-month value by formula [83] ordinal No for the individual hop

4.7.2.3

Prediction of BBER due to equipment contribution

[121] P Ei − BBE = N B ⋅ RBER

P Ei-BBE ...

BBER probability rate due to equipment contribution

RBER... N B...

residual bit-error ratio number of bits/block - see Table 1

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4.7.3

Rev. N-A5

2005-03-06

Fading exceeding the errored second ratio (ESR)o bjective

This fading event is caused both by multipath propagation and rain. 4.7.3.1

Prediction of ESR due to multipath propagation

[122] P Mi − ES = P Mi − SES ⋅

m1

n

P Mi-ES ...

ESR probability rate for the worst month due to multipath fading

n... m1...

number of block/s - see Table 1 according to formula [116]

The other parameters have their previous significance 4.7.3.2

Prediction of ESR due to rain fading

[123] P Rwmi − ES = P Rwmi − SES ⋅

m2

n

P Rwmi-ES ... ESR probability for the worst month due to rain according to formula [120] m2... The other parameters have their previous significance 4.7.3.3

Prediction of ESR due to equipment contribution

[124] P Ei − ES = n ⋅ N B ⋅ RBER

P Mi-ES ...

ESR probability rate due to equipment contribution

N B... n...

number of bits/block - see Table 1

4.7.4

Total performance for the circuit

number of block/s - see Table 1

The total rate of time, Pc, during which the planning objectives are not met for the circuit is the sum of the cumulated rates, i.e.: i ≤10

[125] Pc x −

Pc-x...

= ∑ (P Mi − x + P Rwmi − x + P Ei − x ) i =1

fading probability rate for exceeding SESR, ESR or BBER respectively for the radio circuit

P Mi-x...

fading probability rates for exceeding SESR, ESR or BBER respectively for the individual hop due to multipath propagation

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2005-03-06 P Rwmi-x...

Rev. N-A5


fading probability rates for exceeding ESR or BBER respectively for the individual hop due to rain fading

P Ei-x...

fading probability rates for exceeding ESR or BBER respectively for the individual hop due equipment contribution Remember: Concerning the SESR, it should be observed, that:

P Rwmi-SES = P Ei-SES = 0 x...

either SESR, ESR or BBER

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

[126] Pc − x

Pc-x...

≤ P pl − x

predicted total probability rate during which the planning objective is not met for a radio-relay circuit

P p-xl...

allowed probability rate for exceeding the planning objective for a radio-

x...

relay circuit, i.e. the planning objective either SESR, ESR or BBER

Formula [125] can be expressed in time:

[127] s x s x...

=   2.628 ⋅ 10 6 − hUN ⋅ 

 ⋅ Pc − x

12 

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

hUN ...

3600 

from formula [138]

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5

Unavailability calculations for radio-relay systems

5.1

Unavailability and reliability of hardware

5.1.1

Single (unprotected) structures

[128] PuS =

M rS ⋅ λ S

1 + M rS ⋅ λ S

PuS ...

unavailability rate for the single structure

λS ...

failure rate (failures per time unit) - the sum of the failure rates for the individual units, λi, connected in tandem: n

[129]

λ S = ∑ λ i i =1

M rS ...

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

The mean-time-to-repair figures do no include any waiting time for spare parts. It is thus assumed that there is always access to spare parts when a fault occurs. The failure rate, λ, can also be expressed in terms of mean-time-between-failure (MTBF) :

[130] MTBF = MTBF...

1

λ

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

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5.1.2

Duplicated (protected) structures

5.1.2.1

The duplicated structures are of the same type

The unavailability of a this type of duplicated structure, including the protection switching facilities, is calculated according to the following formula:

[131] P uD

    M rND ⋅ λ ND   = M rS ⋅ λ S  M rS ⋅ λ S + M rS  1+   M rND  

PuD...

unavailability rate for the duplicated structure as per above figure

λS ...

failure rate (failures per time unit) for one of the duplicated equipment (=

λ ND...

single structure as per above figure failure rate (failures per time unit) for the (non-duplicated) splitting and

M rS ...

switching device proper - see also below mean-time-to-repair for one of the duplicated equipment, in same time unit

M rND...

as the failure rate mean-time-to-repair for the (non-duplicated) splitting and switching device proper, 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, λ ND, includes only the values for the splitting and switching elements themselves, together with those for the switch’s 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, λS , 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 = M rS . For the complete path, including the non-protected interface units (I), equation [132] is extended to:

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ECHNICAL PAPER KKE 5201/5 [132] PuP

Rev. N-A5

2005-03-06

= PuD + PuI 1 + PuI 2

where PuI(1,2) are calculated according to equation [128], using the same value for M rS as in formula [131], and the failure rate, λ I(1,2), instead of λS . 5.1.2.2

The duplicated structures are different equipment types

For this type of configuration, the following formula can apply for the calculation of the unavailability, PuD

= P ND + P

[133] PuD

According to the figure below, these parameters have the following significance: P …

unavailability rate for the two single structures in parallel according to formula:

[134] P

= PuS 1 ⋅ PuS 2

unavailability rate for single structure No 1 or 2 resp. acc. to formulas [128] and [129].

PuS1,2…

If one of the single structures itself consists of an 1+1-protected structure, its unavailability

Structural type: single

non-dupl.

two parallel single T

non-duplicated

R L

I1

R

T

PND

single

P 

PuD PuP

I2

D

PND

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rate (PuS1 or PuS2 in formula [134]) has to be obtained from formula [131] or [132] resp. P ND is calculated applying formula [128], with the failures rates for the (non-protected) switching and splitting elements proper, and the corresponding mean-time-to-repair. (Concerning the distribution of the different hardware parts of the switching and splitting device to the non-duplicated and duplicated structures, reference should be made to the previous section 5.1.2.1.)

For the complete hardware structure, including the non-protected interface units (I), equation [133] is extended to:

[135] PuP

= PuD + PuI 1 + PuI 2

where PuI 1,2 is calculated according to equation [128], using the same value for M rS as in formula [133], and the failure rate, λ I 1,2, instead of λ S .

5.2

Unavailability due to propagation disturbances

The unavailability due t o propagation disturbances, P Ra, consists of contributions from rain and from multipath fading:

[136] P Rai P Rai... P Ri-SES ...

= Rai − SES + P Mi − u

probability rate for a radio hop due to rain for the average annual year average annual probability rate, during which the rain attenuation exceeds

the available fading margin acc to formula [82]

P Mi-u...

average annual unavailability rate on a hop due to fading and distortions acc

i...

to formula [112] 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 be considered for both the go and the return direction of transmission, i.e. twice, while that for rain is counted only once:

[137] UR = 2 ⋅ P t u

n

+ ∑ P Rai i =1

URt ...

total unavailability rate of a radio circuit

Pu...

unavailabili ty rate of the total hardware, according to section 5.1

P Rai... n...

unavailability due to precipitations, see above number of radio hops included in the circuit

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Formula [137] expressed in time:

[138] h UN = URt ⋅ 8760 hUN ...

total unavailability in hours / average year

2005-03-06

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6

Frequency planning

6.1

The number of disturbing signals reaching a receiver  n     1 

[139] N =  ∑ x  − y N ... n... x... y...

number of disturbing signals at each receiver number of hops in the area concerned number of parallel r.f. channels on the individual hop number of parallel r.f. channels on the own hop

and the number of total interferences possible is

[140] K = N ⋅ n K ...

number of interference connections

6.2

General formula for the calculation of interfering signal levels

[141] I Ii

= LTx − ATPC − Ao − AWTx , Rx − A BTx , Rx − ATx , Rx − A A + GG

L Ii... LTx...

level of a single interfering signal in dBm

ATPC … Ao...

selected control range of the adaptive transmitter power control in dB free-space attenuation in dB between disturbing transmitter and disturbed

AWTx,Rx .. A BTx,Rx AWTx,Rx A A... GG...

operating max output level of the disturbing transmitter in dBm

receiver waveguide attenuation in dBi n the transmitting alt. receiving station branching attenuation in dBi n the transmitting alt. receiving station r.f. attenuators in dBi n the transmitting alt. receiving station additional attenuation in dB due to non-clearance of the interference path and/or other attenuations in the interference path total antenna gain in dB(i) for angles ψ 1 and ψ 2, according to the following formula [142]:

[142] GG

= GGTx + GGRx = (GTx + G Rx ) − ( AGTx + AGRx )

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 in stead:

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ECHNICAL PAPER KKE 5201/5 [143] G G

GTx... G Rx... GTx||... G Rx⊥... GTx⊥...

= 10 lg  10 

G ⊥ 10

+ 10G ⊥

Rev. N-A5

10 

 = (GTx 

2005-03-06

+ G Rx ) + 10 lg  10

[144] G ⊥

= GTx + G Rx ⊥

[145] G ⊥

= GTx ⊥ + G Rx

[146] A ⊥

= ATx + A Rx ⊥

[147] A ⊥

= ATx ⊥ + A Rx

− A ⊥

10



+ A

− A⊥

10 

antenna gain for the main direction in dB(i) of the transmitting antenna, referred to an isotropic radiator ditto for the receiving antenna antenna gain in dB(i) of the transmitting antenna for angle

ψ 2

and parallel

polarisation, referred to an isotropic radiator ditto for the receiving antenna for angle ψ 1 and cross polarisation ditto for the transmitting antenna cross polarisation,

G Rx||... ATx|| ...

ditto for the receiving antenna and parallel polarisation antenna discrimination in dB of the transmitting antenna for angle

A Rx⊥ ... ATx⊥...

ditto for the transmitting antenna cross polarisation

ψ2 and

parallel polarisation, referred to the antenna gain in the direction of transmission ditto for the receiving antenna for angle ψ 1 and cross polarisation

A Rx||...

ditto for the receiving antenna and parallel polarisation

6.3

Formulae for triangular network configuration

 

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6.3.1

Rev. N-A5


Nodal station disturbs outstation

(Tx A1 _ RxC)

[148] L Ii−C = L Rx−C − AG − A1 + ∆G + ∆ LTx

− ∆ ATPC − ∆ ATx − ∆ A BTx − ∆ A WTx

∆G = G A1 − G A2 [150] ∆ LTx = LTx − A 1 − LTx − A2 [151] ∆ ATx = ATx − A 1 − ATx − A2 [152] ∆ A BTx = A BTx − A 1 − A BTx − A2 [153] ∆ A WTx = AWTx − A 1 − AWTx − A2 [154] ∆ ATPC = ATPC A1 − ATPC A2 [149]

L Ii... i... L Rx-C ...

∆G ..

G A1... G A2...

level of a single interfering signal in dBm ordinal number of the interfering signal received level of the wanted carrier signal in dBm during fading-free time at disturbed receiver C antenna discrimination or side- and back lobe attenuation for angle !in dB, for antenna A1 in the nodal station, considering the polarisation for the disturbed and disturbing signal antenna gain in dBf or the disturbing transmitter A1 in the nodal station antenna gain in dBf or 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 A2

ATx-A1... ATx-A2...

RF attenuator in dB in the disturbing transmitter A1

A BTx-A1.. A BTx-A2..

branching attenuator in dBi n the disturbing transmitter A1

AWTx-A1 ..

waveguide attenuation in dB in the disturbing transmitter A1

AWTx-A2 ..

waveguide attenuation in dB in the transmitter A2

ATPCA1… ATPCA2…

automatic transmitter power control range for transmitter A1 automatic transmitter power control range for transmitter A2

RF attenuator in dB in the transmitter A2 branching attenuator in dB in the transmitter A2

If there is only one interference path to receiver C, equation [148] can be used to select the antenna A1 by writing:

[155] AG

= LTrI − L I + M Fi + ∆G + ∆ LTx − ∆ ATPC − ∆ ATx − A BTx − AWTx

Applying the definition of CIR, this equation can be expressed as:

k&k engineering

ECHNICAL PAPER KKE 5201/5 [156] AG

51

Rev. N-A5

2005-03-06

= CIR + M Fi + ∆G + ∆ LTx − ∆ ATPC − ∆ ATx − A BTx − AWTx

This equation shows, that the higher the CIR, and the higher the flat fading margin, M Fi, the higher the antenna discrimination necessary.

6.3.2

Outstation disturbs nodal point

(TxC _Rx A1)

[157] L Ii − A1

= L Rx − A1 − AG − A1 + ∆G + ∆ L Rx − ∆ A Rx − ∆ A BRx − ∆ A WRx [158] ∆ L Rx = L Rx − A 2 − L Rx − A1 [159] ∆ A Rx = A Rx − A 1 − A Rx − A2 [160] ∆ A BRx = A BRx − A 1 − A BRx − A2 [161] ∆ A WRx = AWRx − A 1 − AWRx − A2

L Rx-A1...

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

L Rx-A2...

disturbed receiver A1 receiver input level of the wanted signal in dBm during fading-free time at

A Rx-A1... A Rx-A2...

receiver A2 RF attenuator in dB in the disturbed receiver A1 RF attenuator in dB in the receiver A2

A BRx-A1.. A BRx-A2..

branching attenuation in dB in the disturbed receiver A1

AWRx-A1.. AWRx-A2..

waveguide attenuation in dB in the disturbed receiver A1

branching attenuation in dB in the receiver A2 waveguide attenuation in dB in the receiver A2


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Also equation [157] can be expressed with the antenna discrimination as the unknown parameter:

[162] AG

= CIR + M Fi + ∆G + ∆ L Rx − ∆ A Rx − A BRx − AWRx

6.4

Interference via passive repeater

6.4.1

Passive repeater as first-source transmitter

[163] L Ii = LTx − ATPC − Ao1 − Ao 2 − AWTx − A WRx − A A2 + GG + G S For GG, equation [142] is valid. Ao1... Ao2...

free-space attenuation in dB between PR and its associated transmitter, Tx free-space attenuation in dB for the interference path between PR and the

A A2...

disturbed receiver, Rx (eventual) additional attenuation in dB due to obstacle in the interference

GS ...

path to Rx passive repeater gain in dB for the interfering signal at angle -

for antenna back-to-back:

[164] G S = G S 1 -

+ G S 2 − AG 2

for plane reflector:

[165] G S = 22.5 + 20 ⋅ lg

Y ⋅ f b ⋅ sin Θ S

ΘS

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[166] G R.... GS1... GS2... AG2...

If : G S ≥ G R

Rev. N-A5

2005-03-06

= 20 ⋅ lg 139.5 ⋅ f 2 ⋅ Y ⋅ cos ψ  ⇒ GS = G R 

2 

gain in passive repeater, plane reflector type, in dB for the wanted signal, and angle ψ passive repeater - antenna back-to-back type - gain in dB for the parabolic antenna towards Tx (main direction) ditto for the parabolic antenna towards Rx' antenna discrimination in dB for angle

ΘS for the passive repeater antenna

f .....

towards Rx' radio frequency in GHz

Y ..... b.....

physical area of the plane reflector in m2 largest side dimension of the reflector in m

Θ Rx...

angle in degrees between the wanted and the interfering signal paths for

ΘS .... ψ .....

receiver Rx 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 [141] Formula [165] is valid for:

Θ S < 90 − ψ ,

if ΘS is outside the reflection angle

Θ S ≤ ψ ,

if ΘS is inside the reflection angle

2

2

If

Θ S ≥ 90 − ψ , and outside ψ : 2

ψ ψ.

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2 [167] G S = 21.25 + 10 ⋅ lg  Y ⋅ f ⋅ cos



6.4.2

ψ 



2 

Passive repeater as receiver of interfering signals

The level of the interfering signal, L Ii is calculated according to the same formula [163] as above, but with changed Tx-Rx co-ordination. Formulae [164] to [167] are also valid here, including the conditions for their application, as well as their limitations.

6.5

Total interference

If more than one interfering signal has to be considered at a receiver’s input, the various contributions are added together on a power law basis:

[168] L I

= 10 ⋅ lg ∑ 10 ( L Ii −∆CIRi − A j ) 10 n

i =1

L I . L Ii...

combined level in dBmo f all interfering signals

A j...

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

∆CIR…

level in dBm of an individual interfering signal see above. For co-channel interference ( ∆ f = 0): A j= 0. power density compensation in dB:

The influence of interfering signals on the wanted signal depends on the power distribution within the spectrum of t he interfering signal. When summing up the various interferer signal levels as per formula [168] we have to compensate for the different power densities by in-

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troducing the parameter ∆CIR. This parameter has to be calculated for each interfering signal; it is the difference between the highest CIR and the CIR of the individual interferer: [169]

∆CIRi = CIRref − CIRi

CIRref …

the CIR figure in dB for an interfering signal from a transmitter of the same system type as the disturbed receiver

CIRi…

the CIR figure of the individual interferer in dB

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7

Bibliography

{1}

Heinz Karl, Performance and availability as applied to digital radio-relay systems, K&K Engineering Heinz Karl, Planning and engineering of radio-relay networks, K&K Engineering

{2}

@

Heinz Karl, 2005

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Annex 1.

The co-ordin ates for the hop’s midpo int are calculated as follows:

-

for the longitude:

-

[170] xo

=

[171] y o

=

x1 + x 2

2

for the latitude:

y1 + y 2

2

xo... x1...

longitude for the midpoint in degrees 

x2... yo...

longitude for site B in degrees

y1... y2...

latitude for site A in degrees

2.

The co-or din ates for the cor ners of the 110x110 km area around a hop’s midpoi nt:

longitude for site A in degrees latitude for the midpoint in degrees

 negative figures for ⌡ W of Greenwich   negative figures for ⌡ S of the equator

latitude for site B in degrees

[172] yC = a sin (cosΘ1 ⋅ 0.0122165 ⋅ cos y1 + 0.999925 ⋅ sin y o ) [173] xC = xo

+ a cos

0.999925 − sin y o ⋅ sin yC cos y o ⋅ cos yC

xo and yo are the co-ordinates in degree of the hop’s midpoint as calculated above.

∗ ∗ ∗ ∗

NE corner: SE corner: SW corner NW corner

Θ1 = 45 o Θ1 = 135 o Θ1 = 225 o Θ1 = 315 o

cos cos cos cos

Θ1= 0.707107 Θ1= - 0.707107 Θ1= - 0.707107 Θ1= 0.707107

acos = + acos = + acos = acos = -

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Bili near interpol ation

The co-ordinates of a hop’s midpoint, xo and yo, have been calculated according to section 1 above. 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 1.5 o - see the below figure.

GP II xa yb z12 1.5

GP III xb yb z22

o

xo yo zo 1.5

o

GP I xa ya z11

GP IV xb yb z21

x and y are the longitudes and latitudes in degree, z11-22 are the co-ordinated third parameters, eg the refractivity gradient, dN 1- section 4.2.3 - or the rainfall intensity, J 0.01 - section

4.5.1. The unknown parameter, zo, is obtained by the following calculation:

z o

= z11 +

[174]

+

( x o − x a )( z 21 − z11 ) ( y o − y a )( z12 − z11 )

− x a xb − x a xo

+ y b − y a − x a y o − y a ( z 22 − z12 − z 21 + z11 ) y b − y a xb

+

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Appendix I Water vapour density - a World atlas The 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 be used the following way:

∗

for the small time-percentage calculation , use the higher of the two values for the location 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 clockminute 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 chapter 4.5.3. For the charts of other regions of the World, reference should be made to bibliography {1} or to ITU-R Rec.P.837-3.

Formel KKE5201 5 Rev N A5 d

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