LINK BUDGET

CALCULATIONS

Otto KoudelkaInstitute of Communication Networks and

Satellite Communications

TU Graz

koudelka@tugraz.at

PERFORMANCE

• characteristics of

– TX station

– RX station

• propagation

• noise, interference

• characteristics of satellite

NOISE

• noise voltage

• independent of frequency, “white” noise

kTBRun 42

k = 1.38 10-23 J/K, Boltzmann constant

B... noise bandwidth

R...resistance

T...absolute temperature

NOISE

f

S(f)

NOISE

• at very high frequencies thermal noise

vanishes, only quantum noise remains

• Noise power

kTBBNN 0

UPLINK

EARTH - SPACE

R

Earth

Ground Station

Satellite

CARRIER POWER• Inverse square law

• C…Carrier power (S…signal)

• PT…transmit power

• Aeff... effective antenna aperture

• R...distance

• GT...transmit antenna gain

AGR

PC effT

T

24

ANTENNA FORMULA

• effective aperture

AG

Aeff

4

2

2

222

2 4

4 DDG

44

2

2

G

R

GPC RTT

CARRIER POWER

GPEIRP TT

RLs

42

free-space loss

CARRIER/NOISE RATIO

BTkN

CN

N

CC s

kBT

G

R

GP

N

C

s

RTT 1

/42

kT

G

R

GP

N

C

s

RTT

o

1

/42

Signal/noise

ratio

Signal/noise

density

FIGURE OF MERIT

• G/T [dB/K]

• important characteristic for

– satellite

– ground station

LINK BUDGET

CALCULATION

• figures may vary widely

– EIRP high

– free-space loss very high

– receive carrier power very low

• logarithmic representation

advantageous

LOGARITHMIC

REPRESENTATION

• Signal-to-noise ratio [dB]

)log(10)log(10)log(10

)log(10/4log20)log(10)log(10

BkT

GRGPN

C

s

RTT

BkTGLEIRP dBHzKdBJKdBdBdBWN

C][]/[]/[][][ /

C/No

• carrier power / noise density

• Normaliset to 1 Hz noise bandwidth

kTGLEIRP KdBJKdBdBsdBWoN

C]/[]/[][][ /

C/T• sometimes used in link budgets

• in [dBW/K]

• leaves out k = -228.6 dB(J/K)

• at the end of calculation B, k considered

TGLEIRP KdBdBsdBWT

C/

]/[][][

Eb/No

• energy contrast ratio

• energy per bit / noise density

• r...rate of information rate (not

necessarily channel rate)

r

B

N

C

N

E

o

b

EXAMPLE (1)

• P = 10 W

• G = 18 dB

dBmdBWEIRP 582818)10log(10

Corresponds to 631 W!

EXAMPLE (2)

• free-space loss

• Distance: 1000 km

• f = 438 MHz, = 0.68 m

68.0

614log20

4log20log10

42

ERRLs

= 145.3 dB

EXAMPLE (3)

• free-space loss, distance = 1000 km

• f = 2.4 GHz, l = 0.125 m

125.0

614log20

4log20log10

42

ERRLs

= 160 dB

EXAMPLE (4)

• free-space loss, distance = 1000 km

• f = 8 GHz, l = 0.0375 m

0375.0

614log20

4log20log10

42

ERRLs

= 170.5 dB

EXAMPLE (5)

• free-space loss, distance = 1000 km

• f = 8 GHz, l = 0.0375 m

0375.0

624log20

4log20log10

42

ERRLs

= 176.5 dB

RECEIVER G/T

• amplifier and antenna

TantNo,ant= kTant

No,v1= Gk(Tant+ T1)

No,v1,in= k(Tant+ T1)

RECEIVER G/T• cascaded amplifiers and antenna

Tant

No,v1,in

No,ant= kTant

No,v1= G1k(Tant+ T1)

No,v2,in= G1k(Tant+ T1)+k T2

SYSTEM NOISE

TEMPERATURE

• referred to input of first stage

No,v1,in= k(Tant+ T1 + T2/G1)

Tsys= Tant+ T1 + T2/ G1

T = (F - 1)To

Friis formula

LOSSY SYSTEMS

• lossy lines (e.g. coaxial cables,

waveguides)

• L = input power / output power = 1/G

• Te = Tsource (L - 1)

• if network (resistor) at To : L = F,

T=(F-1).290 = (L-1).290

RECEIVER WITH LOSSY

LINES

Tant

T1 T2

G1 G2

L

G

TLTLTTT Lantsys

1

21

EXAMPLE A

• Tant = 150 K

• T1 = 200 K

• G1 = 25 dB

• F2 = 8 dB

• G2 = 40 dB

• L = 1 dB

RESULT A

G

TLTLTTT Lantsys

1

21

KLFT L 75290)1(290)1(290)1( 1010

1

KFT 8.1539290)1(290)1( 1010

8

22

10

1539.8.1.25810.20075150

10

2510

1

T sys

KT sys 483

EXAMPLE B

Tant

T1 T2

G1 G2

L

G

TL

G

TTTT

L

antsys

1

2

1

1

RESULT B

10

1539.8.1.258

10

75200150

10

25

10

25T sys

KT sys 356

EXAMPLE C

Tant

T1T2

G1G2

L

G

TL

G

TTTT

L

antsys

2

1

2

2

RESULT C

10

200.1.258

10

758.1539150

10

40

10

40T sys

KT sys 1670

RESULT C

10

200.1.258

10

758.1539150

10

40

10

40T sys

KT sys 1670

CONCLUSION

• Avoid losses in front of LNA

• Use LNA with lowest possible NF

• Use LNA with highest possible gain

SATELLITE ANTENNA

NOISE TEMP.

• Noise from earth

• Noise captured from outer space

• Oceans radiate more noise than land

masses

• Conservative figure: 290 K

G/T (spacecraft)

• Satellite antenna gain: 0 dB

• Tsys = 483 K (from example A)

• G/T = 0 – 10log(483) = - 26.8 dB/K

C/N• f = 438 MHz

• GT= 18 dB

• P = 10 W = 10 dBW

• R = 1000 km

• G/T = -26.8 dB/K

• B = 200 kHz = 10log(200000) = 53 dBHz

BkTGLEIRP dBHzKdBJKdBdBsdBWN

C][]/[]/[][][ /

dBN

C5.3153)6.228(8.263.14528

C/No

• normalized to 1 Hz noise bandwidth

dBHzN

C5.84)6.228(8.263.14528

0

ADDITIONAL LOSSES

POLARIZATION LOSS

• If polarization plane of TX antenna and RX

antenna are misaligned

• Lpol

• If TX and RX are circular: no loss

POINTING LOSS• antennas not totally aligned

• movement of satellite

• pointing loss,

• Around 0.5…1 dB

• Lpu

ATMOSPHERIC

ATTENUATION

• gaseous absorption in atmosphere

• attenuation by hydrometeors

• depending on rain rate, drop size,

frequency

• Latu

PROPAGATION EFFECTS

• Influence by troposphere

– region up to 15 km

– absorption

– depolarization

• Influence by ionosphere

– much less significant

PRECIPITATION

• rain drop size important

• hail produces very significant

attenuation

• wet snow

• dry snow less critical

PRECIPITATION

• Occurrence of precipitation defined by

percentage of time during which a given

intensity is exceeded

• Rain rate in mm/h

• Different climatic zones

• Measurements necessary for each zone

EUROPE

AFRICA

K

Q

AMERICAS

K

N

P

A

BC

CUMULATIVE STATISTICS

0.001 0.01 0.1 1.0

f >

Lat

% of time

CLEAR SKY ATTENUATION

• Depends on

– frequency

– elevation angle

– atmosphere

• pressure

• temperature

• water vapour content

IONOSPHERIC LOSSES

• Interaction between charged particles

and electromagnetic wave

• Absorption, Faraday rotation,

szintillation

• At microwave frequencies negligible

• Small effect at VHF/UHF

C/N at SATELLITE

BkTGLLLLLEIRPN

Catupolipusu /

EXAMPLE• f = 438 MHz

• GT= 18 dB

• P = 10W = 10 dBW

• R = 1,000,000 m

• G/T = -26.8 dB/K

• Lpol = 1.5 dB

• Li = 0.7 dB

• Lpu = 0.5 dB

• Latu = 2 dB

• B = 200 kHz

RESULT

BkTGLLLLLEIRPN

Catuipolpusu /

dBN

C5.26536.2288.2627.05.15.03.14528

P = 1 W

dBN

C5.16536.2288.2627.05.15.03.14518

P = 10 W

DOWNLINK

SPACE - EARTH

R

Earth

Ground Station

Satellite

SATELLITE EIRP

• Maximum EIRP satellite: specified EIRPsat

• EIRP due to drive level:

EIRP = EIRPsat – Bout Bout…back-off

• Example:

• EIRPsat = -3 dBW (0.5 W into 0 dBi antenna)

EIRP = = -3 – 1 = -4 dBW

EARTH STATION ANTENNA

• noise from sky

• noise from earth

• above 2 GHz: dominant contribution

from non-ionized region of atmosphere

• depends on elevation angle

ANTENNA NOISE

T

f

oxygen

water

vapour

SKY NOISE TEMPERATURE

T

elevation angle

4 GHz

AVAILABILITY

• Percentage of time in which defined

QoS is met

• e.g. bit error rate of 10-6 for 99.9 %

• Outage: percentage of time in which

attenuation is too high to meet QoS

• e.g. 0.1 % = 8.76 hours /year

• 0.01 % = 53 minutes /year

AVAILABILITY

• directly related to precipitation time

statistics

CLEAR SKY ATTENUATION

OXYGEN

WATER

VAPOUR

ABSORPTIONL

f

at zenith

PROPAGATION

MEASUEREMENTS

• Beacon receivers

• Radiometers

• Radar

• Rain gauge

INCREASE IN NOISE

TEMPERATURE

• Atmosphere: “lossy line”

• Tm … medium temperature, 280 K

• to be added to overall noise

temperature

TL

T m

at

at )1

1(

ATMOSPHERIC

ATTENUATION

• specific attenuation a in [dB/km]

• l… path length in

• Rp…rain rate

Ra b

pa

lLat a

OVERALL NOISE

TEMPERATURE

• Precipitation:

LTTL

TT atdLNBm

atd

antsys .)1

1(

EXAMPLE

• Latd = 2 dB = 10 0.2 = 1.58

• Tatm = (1 - 1/1.58) 280 = 102.8 K

VARIATIONS

• can reach up to 1 dB/s at Ka-band

• slower at Ku-band

• any fade countermeasure technique

must be able to cope with fluctuations

OTHER EFFECTS

DEPOLARIZATION

x

y

rain

droplet

SCATTERING

• on rain cell

• no interference

in clear sky

SCATTERING

• in precipitation

condition:

• attenuation

• scattering

• interference

SCINTILLATIONS

• Variation of refraction index of

atmosphere (troposphere and

atmosphere)

• Refraction index of troposphere

– decreases with altitude

– independent of frequency

FARADAY ROTATION

• Ionosphere introduces a rotation of

linearly polarized wave

– inversely proportional to frequency

– function of electronic content

• varies with time

• planes rotate in same direction for up -

and downlink

• no compensation by rotating feed!

IONOSPHERIC EFFECTS

• can be neglected for normal satcom

systems

• if exact propagation delay matters

(GPS) ionospheric model and effects

must be taken into account

C/N for DOWNLINK

BkTGLLLLLEIRPN

Ciatd

epdsdpolsat

d

/

)log(10)/( TGTG sysRe

EXAMPLE

• EIRP = -4 dBW

• Polarisation loss: 1.5 dB

• Pointing loss: 0.5 dB

• Ionospheric losses: 0.7 dB

• LNB noise temperature: 120 K

• Input loss: 1 dB

• Atmospheric attenuation: 2 dB

G/T Earth Station• calculate system noise temperature

TLTT LNALRX

KT sys 4.510226*)58.1(280)10

11(50

2.0

KdBTG e /07.9)4.510log(1018/

KT RX 226120*258.175

dB

E

E

DG 28.30

92

83

25.0log10log10

2

22

2

22

Gain of Parabolic Dish

C/N DOWNLINK

BkTGLLLLLEIRPN

Ciatd

epdsdpolsat

d

/´

dBN

C

d

53.12536.22807.97,025.03.1455.14

dBER

Ls3.145

68.0

614log20

4log20

OVERALL C/No

• Composed of uplink and downlink

N

C

N

C

N

C

du

111

N

C

N

CN

C

du

11

1

EXAMPLE

• Overall C/N

)1010

1log(10

)10/53.12()10/5.26(

T

C

dBN

C34.12

INTERFERENCE

• Co-channel interference

• Adjacent channel interference

I

C

N

C

N

C

N

C

du

1

111

Eb/No

• Bandwidth = 200 kHz,

• Uncoded, user data rate= 200 kbit/s

• Eb/No = C/N*B/r

• Eb/No = 12.34 dB

• Coded, code rate = ½

• B/r = 200.000/100.000 = 2 = 3 dB

• Eb/No = 15.34 dB

BER

SYSTEM MARGIN

• Min Eb/No= 7 dB (BER = 10-6, 1 dB

implementation loss)

• Margin = Eb/No -Eb/Nomin

• Margin = 15.34 – 7 = 8.34 dB