Satellite Communications: link budget

Satellite Communications: Link Bugdet

Francisco J. Escribano

October 23, 2014

Francisco J. Escribano Satellite Communications: Link Bugdet October 23, 2014 1 / 56

Table of contents

1 Motivation

2 Received Power

3 Attenuation

4 NoiseAntennaReceiver

5 Carrier-to-Noise Power Ratio

6 Intermodulation

7 Interferences

8 ConclusionsUplinkDownlink

9 References


Motivation

Motivation


Motivation

Satellite link

Objective of the satellite link: Deliver services with the best quality and reliability, under strict cost

constraints.

Design target: Accurately analyze the main factors involved, such as system character-

istics and propagation model.

Figure 1: System model.


Motivation

Important side factors

Side factors to be taken into account:

Satellite size and weight.

Functions developed.

Assigned frequencies.

Terrestrial Stations dimensions.

Medium access techniques.

Main references: [1], [2], [3], [4], [5], [6], [7], [8].


Received Power

Received Power


Received Power

Power radiated by an antenna

Radiated power intensity.

Power radiated by the antenna per solid angle.

Total radiated power is PT .

In general, U (θ, φ) = dP(θ,φ)dΩ W·sr−1.

If the power is radiated isotropically, U (θ, φ) = PT

4π W·sr−1.

Figure 2: Directional antenna radiation pattern.


Received Power

Antenna gain

The gain is defined as the ratio of the actual radiated intensity to theintensity of the isotropic equivalent.

Gain as a function of the direction, G (θ, φ) = U(θ,φ)PT /4π

Maximal gain, GMAX = UMAX

PT /4π .

Gain of an antena: G(dBi) = 10 log10 (GMAX).

dBi means we are taking as comparison the istropic case.

Figure 3: Directional antenna radiation pattern.


Received Power

Radiation pattern

The power captured by an antenna depends on its radiation pattern.

3dB beam width, for a parabolic reflector, θ3dB ≈ 70 · λD

o (degrees).

λ is the wavelength, D the diameter of the paraboloid.

Figure 4: Beam width.

Figure 5: Gain versus angle.


Received Power

Power density

Equivalent Isotropic Radiated Power (EIRP). EIRP (θ, φ) = PT · G (θ, φ).

Power irradiated per unit area (power density flux).

Figure 6: Isotropic antenna.

Φ = PT

4πd2 .

Figure 7: Directional antenna.

Φ (θ, φ) = PT

4πd2 · G (θ, φ).

d is the distance to the antenna.

Φ (θ, φ) = EIRP(θ,φ)4πd2 .


Received Power

Received power

Aperture area ARe = πR2 = π D2

4 .

Effective area AReff = η · ARe.

η: efficiency (ratio of the effec-tively captured power to total incidentpower).

Figure 8: Paraboloid withdiameter D.

PR = Φ · AReff . GR = 4πλ2 · AReff = η ·

(

π Dλ

)2.

Received power:

PR = EIRP4πd2 · AReff = EIRP

4πd2GRλ2

4π = EIRP·GR

( 4πdλ )

2 .


Attenuation

Attenuation


Attenuation

Free space losses

Medium: homogeneous, istropic and no obstacles.

lfs =(

4πdλ

)2, d distance from the emitter.

Lfs(dB) = 92.44 + 20 log f + 20 log d , f in GHz, d in Km.

Figure 9: Free space losses at different frequencies.

These are the minimum possiblelosses in a link.

For a geostationary sat (d ≈35786 Km over the Equator),they are around 200 dB.


Attenuation

Pointing losses

Near the maximal radiation direction, for a deviation of θ ≤ θ3dB, theantenna gain can be approximated as:

G(dB) ≈ GMAX − 12 ·(

θθ3dB

)2

.

LptTx ≈ 12 ·(

θeTxθ3dBTx

)2LptRx ≈ 12 ·

(

θeRxθ3dBRx

)2

Figure 10: Pointing mismatch.

When considering the satellite antenna coverage, it is necessary toadjust −3 dB at the coverage edge.


Attenuation

Atmospheric propagation impairments

Propagation impairment Physical cause Prime importanceAttenation and sky noise in-crease

Atmospheric gases, clouds, rain Fequencies above around 10GHz

Signal depolarization Rain, ice crystals Dual-polarization systems at Cand Ku bands (depends on sys-tem configuration)

Refraction, atmospheric multi-path

Atmospheric gasses Communication and tracking atlow elevation angles

Signal scintillations Tropospheric and ionospheric re-fractivity fluctuations

Tropospheric at frequenciesabove 10 GHz and low ele-vation angles; ionospheric atfrequencies below 10 GHz

Reflection multipath, blockage Earth’s surface, objetcts on sur-face

Mobile satellite services

Propagation delays, variations Troposphere, ionosphere Precise timing and location sys-tems; time division multiple ac-cess (TDMA) systems

Intersystem interference Ducting, scatter, diffraction Mainly C band; rain scatter maybe significant at higher frequen-cies

Table 1: Propagation concerns for Satellite Communication Systems.


Attenuation

Attenuation due to rain

The attenuation due to rain is calculated according to ITU-R.PN618as

ARAIN(dB) = γR · LE .

γR(dB/Km) is the specific attenuation due to rain.

LE (Km) is the effective link length accross the rain.

The specific attenuation depends onthe quantity of precipitations and onthe frequency.

These data are based on statisticalestimations recorded throughout thedifferent geographical regions.

Figure 11: Rainy day in Switzerland.


Attenuation

γR , LE calculations I

Rain height (Km) as a function of latitude:

hR =

4 , 0 < lat < 36o

4 − 0.075 · (lat − 36o) , lat > 36o .

Trajectory accross the rain (Km) asa function of the elevation:

LS = hR −hS

sin(El) when El > 5o.

Rain inhomogeneity factor:

r0.01 = 9090+4LS cos(El) .

The effective length (Km) results:

LE = LS · r0.01. Figure 12: Rainy atmosphere model.


Attenuation

γR , LE calculations II

Determine R0.01(mm/h), precipitations exceded 0.01% of the time dur-ing an average year.

This is done with the help of recorded precipitation maps.

Figure 13: Rain profile inAmerica.

Figure 14: Rain profile inAfroeurope. Figure 15: Rain profile in Asia.


Attenuation

γR , LE calculations III

Once R0.01 is calculated, onepossibility is to calculate γR

with the help of a so-callednomogram.

Figure 16: Nomogram.


Attenuation

γR , LE calculations IV

Other possibility to calculate γR as reported in ITU-R.P838:

γR = k · (R0.01)αk =

4.21 · 10−5 · f 2.42 , 2.9 < f (GHz) < 54

4.09 · 10−2 · f 0.699 , 54 < f (GHz) < 180.

α =

1.41 · f −0.0779 , 8.5 < f (GHz) < 25

2.63 · f −0.272 , 25 < f (GHz) < 164.

The attenuation exceeded 0.01% of the time during an average yearwould be:

A0.01(dB) = γR · LE .

For percentages p other than 0.01%, the attenuation would be calcu-lated as:

Ap = A0.01 · 0.12 · p−(0.546+0.043 log10(p))

Please note how all these calculations rely partly on theoretical results,partly on experimental data and partly on heuristics.


Attenuation

Attenuation by atmospheric gases

We follow recommendation ITU-R.P676.

The expressions listed below are simplifications.

These losses are mainly related to oxigen and water vapor.

Their effects are less important than those of the rain, except for specificfrequencies.

γo (dB/Km) =(

7.1f 2+0.36

+ 4.5(f −57)2+0.98

)

· f 2 · 10−3 .

γw (dB/Km) =(

0.067 + 3(f −22.3)2+7.3

)

· ρw · f 2 · 10−4 .

ρw = 10 gr/m3 .

ho (Km) = 6.

hw (Km) = 2.2 + 3

(f −22.3)2+3.

AG (dB) =γo ·ho ·e

−

hSho +γw ·hw

sin(El).

hS in Km, f in GHz.


Attenuation

Attenuation due to clouds and fog

We follow recommendation ITU-R.PN840.

The procedure is similar to the one proposed for rain attenuation.

ACLOUD(dB) = L·Kl

sin(El)

Figure 17: Specific attenuation by waterdroplets, Kl .

Figure 18: Normalized total columnar content of cloud liquidwater, L.


Attenuation

Attenuation due to cross-polarization / angle of arrival

The rain also induces losses as it affects signal polarization.

Recommendation ITU-R.PN618 handles this issue. Depends on frequency, elevation angle, polarization angle, exceeded value for a given probability.

Refraction in the atmosphere (ITU-R.P834) allows calculation of the apparentelevation angle to account for losses due to mismatched angle of arrival:

Figure 19: Signal angular deviation.


Noise

Noise


Noise

Noise in Communications Systems

How to characterise noise in communications?

How could we cope with it?

Figure 20: Cases of signal to noise balance. Figure 21: Signal vs noise.


Noise

Gaussian Noise

Different sources of noise add contributions to the overall system noise.

There are other sources to take into account wrt conventional systems.

Figure 22: Galactic noise. Figure 23: Solar noise. Figure 24: Storm noise.

Additive white Gaussian noise is a convenient and realistic model.


Noise

Noise modelling: pdf

Gaussian noise and its probability density function (pdf).

Zero mean and power σ2.

Figure 25: Noise pdf. Figure 26: Noise.


Noise

Noise modelling: spectrum

White Gaussian noise model: constant power density spectrum (pds).

It has infinite power: Rn (0) = ∞.

Makes sense within a limited band.

Figure 27: Noise autocorrelation.Figure 28: Noise pds.


Noise

Thermal noise

It is one of the main sources of noise.

Associated to the random movements of electrons.

It is mainly flat when f < 1013Hz.

Figure 29: Thermal noise psd.

Figure 30: Noise equivalent circuit.

E[

ν2n

]

=< ν2n >= Rn (0) = 4kTBRideal

N = <ν2n>/4

Rideal= kTB


Noise

Transmitter & receiver

TX: signal is far larger than noise → limited problem.

RX: signal and noise have similar values → the problems are locatedhere.

Figure 31: Transmitter and receiver typical models.


Noise

Noise factor/figure

It is a way to measure the noise added by a device.

F = (S/N)|in(S/N)|out

= Sin/Nin

G ·Sin/G ·(Nin+Na) = 1 + Na

Nin

Na: noise added by the device.

G : device gain.

F : is the so-called noise factor.

NF (dB) = 10 · log10 (F ) is the noise figure.

This quantity is relative to the input noise level.

The standard reference is kT0, with T0 = 290oK.

kT0 = −204dBW/Hz


Noise

Noise temperature

The device can be modelled as an additional noise source.

Na = (F − 1) · Nin

kTdB = (F − 1)kT0B

Td = (F − 1)T0

Figure 32: Noise temperature setup.

Nout = G · (Nin + Na) = G · k · (Ts + Td) · B


Noise

Noise factor for an attenuator

Noise at the output is equal to the noise at the input.

Signal is attenuated!

If all the components have the same temperature:

Figure 33: Attenuator model.

kTgB = GKTSB + GNLi

NLi = 1−GG

kTSB = kTLB

TL = 1−GG

TS

TL = (L − 1)TS → F = L


Noise

Noise in cascaded systems

Equivalent noise factor at the input for N cascaded systems.

Leftmost system, 1; rightmost system N .

Feq = F1 + F2−1G1

+ F3−1G1G2

+ · · · + FN−1G1G2G3···GN−1

Equivalent noise temperature at the input.

Teq = T1 + T2G1

+ T3G1G2

+ · · · + TN

G1G2G3···GN−1

The two first elements in the cascaded system are the main contributorsto the resultant noise!!!


Noise

System noise temperature

We consider the typical first stages of a receiver in Satellite Communi-cations.

We have the antenna, the attenuation determined by the transmission line linking the antenna to the receiver,together with all the connectors involved.

Figure 34: RX model.

Tsys = Tant + Teq = Tant + TL + LTR

Tsys = Tant + (L − 1)T0 + L(F − 1)T0

Tsys = Tant + (LF − 1)T0


Noise Antenna

Antenna temperature

The antenna acts as a lens whose contribution depends on its direction.

Figure 35: Earth station.

Tant = Tsky + TEarth + TRAIN

Figure 36: Satellite.

Tant = TEarth ≈ 290oK


Noise Antenna

Contributions to antenna temperature

Figure 37: Clear sky temperature.

Tsky + TEarth

Rain temperature:

TRAIN = Tab

(

1 − 1ARAIN

)

where Tab ≈ 275oK


Noise Receiver

Linear components, bandlimited

To characterise the noise at the receiver, we need to evaluate how linearsystems respond to additive white Gaussian noise.

Figure 38: Linear Time-invariant System.

Input/output: Gaussian noise

GY (f ) = GX (f ) · |H(f )|2

Figure 39: Bandpass filtering.

Bandpass filtering reduces noise: one

of the first stages at RX.


Noise Receiver

Narrowband noise at the mixer

Figure 40: Mixer & noise.

Figure 41: Equivalent baseband noise.

The mixer is a nonlinear device.

All this gives reason of the effectsof linear/nonlinear systems on inputnoise.

Total noise at the input is given by the system tem-perature (cascaded systems: filters and mixers havecorresponding noise factors).

Then the noise power is calculated taking into accountthe band limitations.


Carrier-to-Noise Power Ratio




Evaluation of the link quality

The quality of a satellite link is measured as a function of its carrierpower to the noise power, depending on the type of system.

For digital systems:

CN0

(Hz) = PR

k·Tsys= EIRP·GR/Ltot

k·Tsys= EIRP·GR

k·Ltot ·Tsys

CN0

(dBHz) = EIRP (dBW) − Ltot (dB) + GR

Tsys(dB/K) + 228.6

For analog systems:

CN

(dB) = CN0

(dBHz) − 10 · log10 (BN (Hz))

Ltot comprises all the losses and attenuation effects (these, in fact, actas margins for a given disponibility).

BN is the noise bandwidth (in most of the cases, we will take it asequal to the signal bandwidth).



Uplink & Downlink

Figure 42: Uplink setup.

CN0

∣

∣

∣

U= EIRP|TS − L|U + GR

Tsys

∣

∣

∣

sat+ 228.6

CN0

∣

∣

∣

D= EIRP|sat − L|D + GR

Tsys

∣

∣

∣

TS+ 228.6

Figure 43: Downlink setup.

EIRP is a characteristic of the TX. G/T is a figure of merit of the RX.



Total CN0

Figure 44: Complete link balance.

Signal and noise:

C |T =PT |TS · GT |TS · GR |sat ·Gsat · GT |sat GR |TS

L|U · L|D,

N0|T =N0|U · GT |sat ·Gsat · GR |TS

L|D+ N0|D .

Rearranging:

(

CN0

∣

∣

∣

T

)−1=

(

CN0

∣

∣

∣

U

)−1+

(

CN0

∣

∣

∣

D

)−1

(C/N0)|T given above is calculated in natural units (Hz).

Note that the lowest term dominates the final carrier-to-noise ratio.


Intermodulation

Intermodulation


Intermodulation

Sources of nonlinear effecs

Intermodulation is mainly due to the presence of nonlinear distortionin the devices. Principles in [9].

The main source of nonlinearity is the power amplifier (PA) in the satellite: high power travelling-wave tube(TWT) PAs.

PAs are more efficient near the saturation region → need for a trade-off.

One solution is to drive the PA below the saturation region: input/output backoff

Effect of input backoff:

CN0

∣

∣

∣

U= C

N0

∣

∣

∣

Usatur.

− BOi

Effect of output backoff:

CN0

∣

∣

∣

D= C

N0

∣

∣

∣

Dsatur.

− BOo

Figure 45: Amplifier I/O curve.


Intermodulation

Multicarrier case

Figure 46: Multicarrier setup.

Model for n equal carriers.

CN

∣

∣

IM≈ 10.532 − 0.09 · n + 1.7−4 · n2 + 0.82 · BOi dB Figure 47: Typical IM curves.


Intermodulation

Total CN0

Figure 48: CN0

curves.

The final carrier-to-noise ratio wouldbe:

(

CN0

∣

∣

T

)

−1=

(

CN0

∣

∣

U

)

−1+(

CN0

∣

∣

D

)

−1+(

CN0

∣

∣

IM

)

−1


Interferences

Interferences


Interferences

Global effect of interferences

Figure 49: Interferences between two systems.

The interferences are mainlycaused by the secondary lobes inthe radiation pattern of the an-tennas.

The effect is modeled as an ad-ditional carrier-to-noise contribu-tion.

(

CI

∣

∣

T

)

−1=

(

CI

∣

∣

U

)

−1+

(

CI

∣

∣

D

)

−1

(

CN

∣

∣

T

)

−1=

(

CN

∣

∣

U

)

−1+

(

CN

∣

∣

D

)

−1+

(

CN

∣

∣

IM

)

−1+

(

CI

∣

∣

T

)

−1


Interferences

Limiting interferences

In order to limit the amount of interference, the following diagrampattern has been proposed.

Frequency range, from 2 to 30GHz.

Antennas with D < 100 · λ G (θ) =

29 − 25 · log (θ) , 1o < θ < 48o

−10, 48o ≤ θ < 180o

Antennas with D > 100 · λ G (θ) =

52 − 10 · log(

Dλ

)

− 25 · log (θ) , 100·λD

< θ < 48o

−10 − 10 · log(

Dλ

)

, 48o ≤ θ < 180o

Figure 50: Beam width.

Figure 51: Gain versus angle.


Interferences

Estimating interferences

Under the hypothesis of equal frequencies, equal polarization and linksymmetry, the interference of B on A, in the uplink, is:

EIRPI = EIRPmax − GTI,max+ GTI

(θB→A)

The corresponding carrier-to-interference ratio would thus be:CI

∣

∣

U= EIRPU −

(

EIRPI − GRU+ GRI

(θA→B ))

Similar expression holdsfor the downlink, consider-ing the corresponding TXand RX involved.

Figure 52: Interferences setup.


Conclusions

Conclusions


Conclusions Uplink

Uplink

The satellite antenna beamwidth provided to cover a specific servicearea determines the gain of the receiver antenna.

To avoid large gain variations due to pointing mismatches, antennaswith large D require tracking.

Rain attenuates the received power, but it does not contribute sig-nificantly to the noise temperature (relatively high, around 290oK); acountermeasure could be increasing the transmitted power.

The input power density reaching the satellite should be controlled toavoid intermodulation due to PA saturation.

The orbital separation between geostationary satellites that operate inneighbour bands is low (a few degrees): it is important to have TSnarrow beamwidth antennas with low secondary lobes.


Conclusions Downlink

Downlink

The transmitted power is strictly limited.

The antenna gain needs to be adjusted to the coverage area to avoidinterferences and issues with band licensing, nationally owned rightsand so forth.

Rain attenuates the received power and, besides, may increase signifi-cantly the noise temperature of the TS.

The ouput power density of the satellite should be controlled as wellto avoid intermodulation due to PA saturation.

Another important reason to limit the ouput power of the satellitedownlink is the need to limit interferences.


References

References


References

Bibliography I

G. Maral, Satellite Communications Systems: Systems, Techniques and Technology. Chichester: John Wiley & Sons,

Inc., 1998.

T. Pratt, Satellite Communications. New York: John Wiley & Sons, Inc., 2003.

G. E. Corazza, Digital Satellite Communications. New York: Springer, 2007.

ITU-R.PN618, “Propagation data and prediction methods required for the design of Earth-space telecommunication

systems,” International Telecommunication Union. [Online]. Available: https://www.itu.int/rec/R-REC-P.618/en

ITU-R.P838, “Specific attenuation model for rain for use in prediction methods,” International Telecommunication Union.

[Online]. Available: http://www.itu.int/rec/R-REC-P.838/en

ITU-R.P676, “Attenuation by atmospheric gases,” International Telecommunication Union. [Online]. Available:

http://www.itu.int/rec/R-REC-P.676/en

ITU-R.PN840, “Attenuation due to clouds and fog,” International Telecommunication Union. [Online]. Available:


ITU-R.P834, “Effects of tropospheric refraction on radiowave propagation,” International Telecommunication Union.

[Online]. Available: http://www.itu.int/rec/R-REC-P.834/en

ITU-R.SM.2021, “Production and mitigation of intermodulation products in the transmitter,” International

Telecommunication Union. [Online]. Available: http://www.itu.int/pub/R-REP-SM.2021


https://www.itu.int/rec/R-REC-P.618/en





http://www.itu.int/pub/R-REP-SM.2021

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