satellite communications: link budget
DESCRIPTION
Simple slides intended for an undergraduate course on Satellite Communications.TRANSCRIPT
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
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Motivation
Motivation
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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.
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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].
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Received Power
Received Power
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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.
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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.
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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.
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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 .
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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 .
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Attenuation
Attenuation
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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Noise
Noise
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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.
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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.
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Noise
Noise modelling: pdf
Gaussian noise and its probability density function (pdf).
Zero mean and power σ2.
Figure 25: Noise pdf. Figure 26: Noise.
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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.
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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
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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.
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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
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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
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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
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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!!!
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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
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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
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Noise Antenna
Contributions to antenna temperature
Figure 37: Clear sky temperature.
Tsky + TEarth
Rain temperature:
TRAIN = Tab
(
1 − 1ARAIN
)
where Tab ≈ 275oK
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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.
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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.
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Carrier-to-Noise Power Ratio
Carrier-to-Noise Power Ratio
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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).
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Carrier-to-Noise Power Ratio
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.
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Carrier-to-Noise Power Ratio
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.
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Intermodulation
Intermodulation
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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.
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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.
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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
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Interferences
Interferences
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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
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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.
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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.
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Conclusions
Conclusions
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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.
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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.
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References
References
Francisco J. Escribano Satellite Communications: Link Bugdet October 23, 2014 55 / 56
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:
http://www.itu.int/rec/R-REC-P.840/en
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
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