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LINK BUDGET
CALCULATIONS
Otto KoudelkaInstitute of Communication Networks and
Satellite Communications
TU Graz
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