Microwave Link Theory

ERA/LN-97:1957 1997-10-10 Rev PA1

ITU RecommendationsITU Recommendations

ITU Recommendation on the Intranet:

http://krus.lme.ericsson.se/itu/itupage.htm

ERA/LN-97:1957 1997-10-10 Rev PA1

General ConfigurationGeneral Configuration

Wave guideloss

Branchingloss

Antennagain

Outputpower

Free space loss+ Additional losses

ERA/LN-97:1957 1997-10-10 Rev PA1

Link BudgetLink Budget

Feederloss

Antennagain

Free space loss +Additional losses

Branchingloss

Outputpower

Antennagain

Branchingloss

Feederloss

Receivedpower

Receiverthreshold

Fadingmargin

Additional losses:- Gas absorption- Obstacle loss

ERA/LN-97:1957 1997-10-10 Rev PA1

Fading MarginFading Margin

Receivedpower

Receiverthreshold

Fadingmargin

Fading margin:“Safety” margin. Should belarge enough to guaranteethat quality and availabilityobjectives are met duringfading conditions.Typical value ~ 40 dB

ERA/LN-97:1957 1997-10-10 Rev PA1

FadingFading

Fading

Flatfading

Frequencyselective fading

Multipath fading Rain fading

ERA/LN-97:1957 1997-10-10 Rev PA1

Free space lossGas absorption

Hop CalculationsHop CalculationsPredictable Statistically Predictable

Obstacle loss

Always presentand predictable

Predictableif present

Not always presentbut statisticallypredictable

Rain fadingMultipath fading

Link Budget Fading Prediction

Q&A Objectives

ERA/LN-97:1957 1997-10-10 Rev PA1

Free Space LossFree Space Loss

Afs = 92.4 + 20 log d + 20 log f

d: distance [km]f: frequency [GHz]

ERA/LN-97:1957 1997-10-10 Rev PA1

Link Budget, ExerciseLink Budget, Exercise

1) Calculate the fading margin for a 7 km MINI-LINK 15-E hop with 4x2 Mbit/s capacity, standard output power and 0.6 m antenna.

2) Calculate the fading margin for a 7 km MINI-LINK 15-E hop with 4x2 Mbit/s capacity, high output power and 1.2 m antenna.

3) Calculate the fading margin for a 5 km MINI-LINK 23-E hop with 2x8 Mbit/s capacity and 0.3 m antenna.

Assume a feeder loss of 0.5 dB and no branching loss.

ERA/LN-97:1957 1997-10-10 Rev PA1

threshrx

fsfeederanttxrx

ERA/LN-97:1957 1997-10-10 Rev PA1

1) Standard output power = Ltx = 18 dBm Rec. threshold 10-3 = Lthresh = -87 dBm Rec. threshold 10-6 = Lthresh = -83 dBm Antenna gain = Gant = 36 dBi

8.43)7log2015log204.92(

5.0236218

2.43)87(8.43310 threshrx LLM dB

2.39)83(8.43610 threshrx LLM dB

ERA/LN-97:1957 1997-10-10 Rev PA1

2) High output power = Ltx = 25 dBm Rec. threshold 10-3 = Lthresh = -87 dBm Rec. threshold 10-6 = Lthresh = -83 dBm Antenna gain = Gant = 42 dBi

2.62)87(8.24310 M

2.58)83(8.24610 M

ERA/LN-97:1957 1997-10-10 Rev PA1

1) Standard output power = Ltx = 20 dBm Rec. threshold 10-3 = Lthresh = -83 dBm Rec. threshold 10-6 = Lthresh = -79 dBm Antenna gain = Gant = 35 dBi

4.38)83(6.44310 M

4.34)79(6.44610 M

ERA/LN-97:1957 1997-10-10 Rev PA1

Gas AbsorptionGas Absorption

Gas Absorption

Oxygen Water vapour

Should be considered for f > 10 GHz.

: Specific attenuation for dry air [dB/km]

: Specific attenuation for water vapour [dB/km]

dgasgasA

wairgas

ERA/LN-97:1957 1997-10-10 Rev PA1

Gas Absorption, contd.Gas Absorption, contd.

0 5 10 15 20 25 30 35 40 45 50

Frequency, GHz

Oxygen Water Vapour Total

T = 15° C, Water vapour density = 20 g/m3

ERA/LN-97:1957 1997-10-10 Rev PA1

Refractive IndexRefractive Index

n n1 1 2 2 sin sin

ERA/LN-97:1957 1997-10-10 Rev PA1

RefractivityRefractivity

Refractivity: N n ( )1 106

Empirical formula:

77 64810

T: Temperature [Kelvin]p: Total air pressure in [hPa]e: Water vapour pressure [hPa]

ERA/LN-97:1957 1997-10-10 Rev PA1

Refractivity GradientRefractivity Gradient

Since p, e and T are functions ofheight N is also a function of height.

For normal atmosphere:

N units

ERA/LN-97:1957 1997-10-10 Rev PA1

Ray bendingRay bending

The radio beam is bent in the atmosphere,normally slightly downwards.

The k factor is a function of the refrectivitygradient.

For design purposes, the bending effect iscompensated by introducing a correction factor k.

ERA/LN-97:1957 1997-10-10 Rev PA1

Ray Bending, contd.Ray Bending, contd.

k=-2/34/312/3

ERA/LN-97:1957 1997-10-10 Rev PA1

The k-factorThe k-factor

For normal atmosphere:

dh 40 k

ERA/LN-97:1957 1997-10-10 Rev PA1

The k-factor, contd.The k-factor, contd.

True ray beamOptical line-of-sight

True earth

ERA/LN-97:1957 1997-10-10 Rev PA1

The k-factor, contd.The k-factor, contd.

Effective ray beam

Optical line-of-sight

Effective earth

ERA/LN-97:1957 1997-10-10 Rev PA1

Earth BulgeEarth Bulge

21 h [m]d [km]

ERA/LN-97:1957 1997-10-10 Rev PA1

The Fresnel ZoneThe Fresnel Zone

The radiated power is distributed in azone surrounding the direct line-of-sight.

ERA/LN-97:1957 1997-10-10 Rev PA1

The Fresnel Zone, contd.The Fresnel Zone, contd.

d d d3 4 2 /

17 3 1 2.

d [km], rf [m], f [GHz]

ERA/LN-97:1957 1997-10-10 Rev PA1

Design objective:Full clearance of the Fresnel zone.

The Fresnel Zone, contd.The Fresnel Zone, contd.

ERA/LN-97:1957 1997-10-10 Rev PA1

The Fresnel Zone, ExerciseThe Fresnel Zone, Exercise

f = 15 GHzk = 4/3d = 20 km

1) Calculate the Fresnel zone radius at mid path.

2) Calculate the earth bulge at mid path.

f = 15 GHzk = 4/3d = 10 km

ERA/LN-97:1957 1997-10-10 Rev PA1

The Fresnel Zone, ExerciseThe Fresnel Zone, Exercise

20 km:r m

17 310 10

15 2010.

10 10 3

12 74 46

10 km: r m

17 35 5

15 107.

12 74 415

ERA/LN-97:1957 1997-10-10 Rev PA1

Calculation of Antenna HeightsCalculation of Antenna Heights

obsthrd

(74.12

hGA, hGB Height above ground for antenna [m]hA, hB Height above sea level [m]hobst Height above sea level for highest

obstacle [m]d Distance A to B [m]d1 Distance A to obstacle [km]k Effective earth radius factor

ERA/LN-97:1957 1997-10-10 Rev PA1

Calculation of Antenna Heights. contd.Calculation of Antenna Heights. contd.

r Required clearence above obstacle [m]where:

r Radius of the Fresnel zoner Required clearence above obstace [%]

ERA/LN-97:1957 1997-10-10 Rev PA1

Obstacle LossObstacle Loss

Obstacle loss

Knife edgeobstacle loss

Smooth sphericalearth obstacle loss

ERA/LN-97:1957 1997-10-10 Rev PA1

Knife Edge ObstaclesKnife Edge Obstacles

ERA/LN-97:1957 1997-10-10 Rev PA1

Smooth Spherical Earth ObstaclesSmooth Spherical Earth Obstacles

ERA/LN-97:1957 1997-10-10 Rev PA1

Knife Edge LossKnife Edge Loss

From curve or approximate formula:

)212log(204.6 2

ERA/LN-97:1957 1997-10-10 Rev PA1

Knife Edge Loss, contd.Knife Edge Loss, contd.

0 0 6 12 20 dB

Typical losses:

ERA/LN-97:1957 1997-10-10 Rev PA1

Smooth Spherical Earth LossSmooth Spherical Earth Loss

dA dBdr hB

AA hRkd 3102

R: True radius of the earth (=6370 km)

If k = 4/3 AA hd 1.4

ERA/LN-97:1957 1997-10-10 Rev PA1

Smooth Spherical Earth Loss, contd.Smooth Spherical Earth Loss, contd.

3/23112.020

f [MHz]

ERA/LN-97:1957 1997-10-10 Rev PA1

Smooth Spherical Earth Loss, contd.Smooth Spherical Earth Loss, contd.

Typical losses:

ERA/LN-97:1957 1997-10-10 Rev PA1

Rain AttenuationRain Attenuation

Two types of attenuating mechanisms:absorption and scattering caused by the rain drops.

Falling raindrop

Not round dueto air resistance

Horizontally polarized waves are attenuatedmore than vertically polarized waves.

ERA/LN-97:1957 1997-10-10 Rev PA1

Rain Attenuation, contd.Rain Attenuation, contd.

Rain intensity [mm/h].

For the calculations the cumulative distributionof rain intensity, i.e. the percentage of timeduring which a given rain intensity is exceeded,is interesting.

The reference level is the rain intensity that isexceeded 0.01% of all time (R0.01).

ITU-R presents the cumulative distribution ofrain intensity for 15 different rain zones on earth.

ERA/LN-97:1957 1997-10-10 Rev PA1

effdRRA

:R Specific rain attenuation [dB/km]

:effd Effective path length, km

ERA/LN-97:1957 1997-10-10 Rev PA1

:, ffk Coefficients reflecting assumptionsconcerning the distribution of raindropsize, form, temperature and polarization.

ERA/LN-97:1957 1997-10-10 Rev PA1

fkVVkHHkVVkHHk

VKHkVkHkfk

2cos2cos)(

:,,, VVkHHk Frequency dependent coeff.,from table

The path elevation angle

The polarization tilt anglerelative to the horizontal plane

ERA/LN-97:1957 1997-10-10 Rev PA1

01.0015.00

d: Actual path lengthr: Reduction factor

The reduction factor transforms actual path lengthto equivalent path length along which the rain canbe regarded as having a uniform distribution.

ERA/LN-97:1957 1997-10-10 Rev PA1

0 20 40 60 80 100

Rain intensity (R0.01), mm/h

23 GHz, H

23 GHz, V

15 GHz, H

15 GHz, V

7 GHz, H

7 GHz, V

H/V: Horizontal/Vertical polarisation

ERA/LN-97:1957 1997-10-10 Rev PA1

Rain FadingRain Fading

The probability that a given fade marginis exceeded, on an annual basis:

01.012.0log172.029812.0546.0628.11

AR The rain attenuation exceeded 0.01 %of the time

Fade margin

ERA/LN-97:1957 1997-10-10 Rev PA1

Rain Fading, contd.Rain Fading, contd.

monthyear

yearmonth

Conversion between yearly values andworst month values:

Formulas based on climatic constants.

ERA/LN-97:1957 1997-10-10 Rev PA1

Multipath FadingMultipath Fading

Flatfading

Frequencyselective fading

Multipath fading

ERA/LN-97:1957 1997-10-10 Rev PA1

Multipath Fading, contd.Multipath Fading, contd.

Atmospheric layer

ERA/LN-97:1957 1997-10-10 Rev PA1

Multipath Fading, contd.Multipath Fading, contd.

Flat fading Frequencyselective fading

ERA/LN-97:1957 1997-10-10 Rev PA1

Flat FadingFlat Fading P.530

The probability that a given fade marginis exceeded, on a worst month basis:

104.189.06.3 10)1(M

flat fdKP

D: Path length [km]f: Frequency [GHz]: Path slope [mrad]M: Fade margin [dB]K: Geoclimatic factor

ERA/LN-97:1957 1997-10-10 Rev PA1

Flat Fading, contd.Flat Fading, contd.

Path slope:

hA, hB: Antenna height + ground elevation [m]

ERA/LN-97:1957 1997-10-10 Rev PA1

The geoclimatic factor K is a function of thePL factor. The PL factor is the percentage oftime that the average refractivity gradient at theearth surface is lower than -100 N-units/km.

PL factor estimates in the form of contour mapsavailable in ITU-R Rec. P.453.

ERA/LN-97:1957 1997-10-10 Rev PA1

5.1)1.7(10 LCC PK LonLat

Overland with antennasless than 700 m abovemean sea level

Overland with antennasmore than 700 m abovemean sea level

Over medium-sizedbodies of water

Over large bodiesof water

ERA/LN-97:1957 1997-10-10 Rev PA1

Frequency Selective FadingFrequency Selective Fading F.1093

The prediction of frequency selective fadingis very difficult and there exists many differentprediction models.

220103.4

ERA/LN-97:1957 1997-10-10 Rev PA1

Frequency Selective Fading, contd.Frequency Selective Fading, contd.

Probability of the occurrence of mp fading

P0 from the formula for flat fading

W Signature width [GHz]Equipment dependent

B Signature depth [dB]Equipment dependent

ERA/LN-97:1957 1997-10-10 Rev PA1

m Mean value of the echo delay

m0 is the mean relative delay for astandard path of 50 km [ns].Normally 0.7 ns.

d is the path length [km]

ERA/LN-97:1957 1997-10-10 Rev PA1

r The time delay used during measurementsof the signature curves (reference delay)[ns]. Normally 6.3 ns.

ERA/LN-97:1957 1997-10-10 Rev PA1

DiversityDiversity

Primarely used to reduce the effects ofmultipath fading.

Diversity

SpaceDiversity

FrequencyDiversity

Requiresmorebandwidth

ERA/LN-97:1957 1997-10-10 Rev PA1

Space DiversitySpace Diversity

Height

Field strength

Optimum antennaseparation

ERA/LN-97:1957 1997-10-10 Rev PA1

Space Diversity ImprovementSpace Diversity Improvement

PP selflatmp

101001034.3

04.1048.012.087.04 GMP

s Vertical separation between antennas [m]f Frequency [GHz]d Path length [km]M Fade margin [dB]G The difference in antenna gain between the

two antennas [dB]

P0 from theformula forflat fading

ERA/LN-97:1957 1997-10-10 Rev PA1

Space Diversity Improvement, contd.Space Diversity Improvement, contd.

2 GHz f 11 GHz

43 km d 240 km

3 m s 23 m

In cases where any of these boundaries havebeen exceeded (within reasonable limits) theparameters may be set equal to the boundaryvalue (E.g. for 15 GHz, use f = 11 GHz).

ERA/LN-97:1957 1997-10-10 Rev PA1

Hardware UnavailabilityHardware Unavailability

MTBFMTTR

MTTRMTBFMTTR

Unavailability of one equipment module

ERA/LN-97:1957 1997-10-10 Rev PA1

Hardware Unavailability, contd.Hardware Unavailability, contd.

iis NN

Unavailability of cascaded modules

ERA/LN-97:1957 1997-10-10 Rev PA1

Unavailability of parallel modules

iis NN

ERA/LN-97:1957 1997-10-10 Rev PA1

22 RAUMMUSMUs NNNN

MINI-LINK 1+1 system:

ERA/LN-97:1957 1997-10-10 Rev PA1

Quality and Availability ObjectivesQuality and Availability Objectives

Unavailable time (UAT)A period of unavailable time begins when one or both ofthe following conditions occur for 10 consecutive seconds:1. The digital signal is interrupted,2. The bit error ratio in each second of the 10 consecutive seconds are worse than 110-3. These 10 seconds are considered to be unavailable time.

Available Time (AT)A period of available time begins with the first second ofa period of 10 consecutive seconds of which each secondhas a bit error ratio (BER) better than 110-3.

ERA/LN-97:1957 1997-10-10 Rev PA1

Q & A Objectives, contd.Q & A Objectives, contd. G.821

Errored Second (ES)Any second containing one or more errors.

Severely Errored Second (SES)An errored second with a bit error ratio (BER) worsethan 110-3.

Degraded Minutes (DM)Obtained by substracting severely errored seconds fromthe available time and collecting the remaining secondsinto groups of 60 seconds. Any group with a bit errorratio worse than 110-6 is considered a degraded minute.

ERA/LN-97:1957 1997-10-10 Rev PA1

Q & A Objectives, contd.Q & A Objectives, contd.

Time > 10 sTime< 10 s

AT UAT AT

BER 10-3

BER 10-6

ERA/LN-97:1957 1997-10-10 Rev PA1

25000 km 1250 km1250 km G. 821

SES 0.1 % +0.1 % forHRDP

DM 10 %

ES 8 %

0.015 0.015 0.04 0.015 0.015

Hypothetical Reference Connection - HRX 27500 km

1.5 1.5 4 1.5 1.5

1.2 1.2 3.2 1.2 1.2

0.05 0.052500 km0.004+0.05

2500 km0.4

2500 km0.32 INT LE

Local Medium High Medium Local

Q & A Objectives, contd.Q & A Objectives, contd. G.821

ERA/LN-97:1957 1997-10-10 Rev PA1

50 km280 km

SES 0.1 % +0.1 % for HRDPin Class 1 & 2(0.05 % per end)

DM 10 %

ES 8 %

0.006 = 0.0075 0.002 0.005

Hypothetical Reference Digital Section - HRDS 280 & 50 km

0.045 0.2 0.2 0.5

0.036 0.16 0.16 0.4

High Medium Medium Medium

Class 1 Class 2 Class 3 Class 4

0.45 % 2 % 2 % 5 % ITU-R Rec. 696

0.10.1% x % x 0.450.45 + + 0.050.05 x 280 / 2500 x 280 / 2500

Q & A Objectives, contd.Q & A Objectives, contd. F.696

0.033 0.05 0.05 0.1 UAT

ERA/LN-97:1957 1997-10-10 Rev PA1

UAT: Rain Fading +Hardware Unavailability

DM: Rain Fading + Multipath Fading

ES: Rain Fading + Multipath Fading

SES: Multipath Fading

The relationships are not described by ITU!

ERA/LN-97:1957 1997-10-10 Rev PA1

hwrain PPUAT 310

310310610610

mprainmprain PPPPDM

310 mpPSES

UATPPES mprain 610610

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