Lecture No. 11

Satellite Communications

Atmospheric Loss - Part I

•  •  •  • 

Uses of ITU-R reports

Weather effects

Atmospheric absorption

Fog and cloud attenuation

Weather satellite image, NASA!

Lect 11

© 2012 Raymond P. Jefferis III

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Uses of relevant ITU Reports •  Rain attenuation in dB (ITU-R P.618-8) •  Attenuation by atmospheric gases (ITU-R P.676-6 Annex 2) •  Rain attenuation model (ITU-R P.838-3) •  Rain height model (ITU-R P.839-3) •  Clouds attenuation in dB (ITU-R P. 840-3) Note: ITU reports are constantly updated. Those working in this field should subscribe to these at: http://www.itu.int/publ/R-REC-OL/en Lect 11


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Weather Effects •  Attenuation –  by atmospheric gases –  by rain –  by snow and ice

•  Depolarization –  by rain –  by ice particles –  by multipath propagation Lect 11


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Attenuation - Atmospheric Gases •  Ref: ITU-R P. 676-6 (2005) •  Ref: ITU-R P. 676-7 (2007)

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Region of Validity •  Frequency: to 1000 GHz •  Elevation angles: 0 to 90 degrees

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Model Inputs •  •  •  •  •  • 

Frequency, f [GHz] Dry air pressure, p [hPa] Water vapor partial pressure. e [hPa] Water vapor density, ρ [g/m3] Air temperature, T [K] ITU Reference Standard Atmosphere (ITU-R P.835-4)

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Atmospheric Absorption •  Atmospheric absorption of radio waves is frequency dependent, as shown in the following two slides. •  Atmospheric absorption of radio waves has several components –  Absorption by water vapor –  Absorption by oxygen and other gases (dry air) Lect 11


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Specific Attenuation (Blue) Water vapor (Red) Dry air (Black) Total Note: units [dB/km ]

ITU-R P.676-6!

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Specific Attenuation (C & Ku Bands) Specific Attenuation: Units [dB/km] vs Frequency: Units [GHz] Red: Dry Air Blu: Water vapor Blk: Total

ITU-R P.676-6!

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Assumptions for Attenuation Model Assumptions: –  The radio wave propagation is on a slant path –  Elevation angle to the satellite is: 5° < θ < 90° –  Ground station elevation is: < 10 km –  Frequency is: 1 < f < 350 GHz

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Approximate Gaseous Attenuation •  The exact calculations of Slide 8 are complex, and can be found in: ITU-R P.676-6 (indicated in the slide) •  An approximate calculation, is in Annex 2 of the same document. The calculation steps follow.

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Attenuation Approximation: Step 1a •  For the following variables: f: frequency [GHz] p: pressure [hPa] T: air temperature [degC] ρ: water vapor density [g/m3]

•  Compute the pressure and temperature normalizations rp and rt given by the formulas to follow. Lect 11


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Computation of rp and rt p rp = Pressure normalization 1013 288 rt = Temperature normalization (273 + T )

These values will be used in the calculations to follow

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Attenuation Approximation (dry air): Step 1b For dry air at frequencies below 54 GHz, compute the following specific attenuation [dB/km] for oxygen: ξ1 = rp0.0717 rt−1.8132 exp[0.0156(1 − rp ) − 1.6515(1 − rt )] ξ2 = rp0.5146 rt−4.6368 exp[−0.1921(1 − rp ) − 5.7416(1 − rt )] ξ3 = rp0.3414 rt−6.5851 exp[0.2130(1 − rp ) − 8.5854(1 − rt )] ⎡ ⎤ 2 2 7.2rt2.8 o.62ξ3 −3 γo = ⎢ 2 + f r × 10 ⎥ p 1.16 ξ1 2 1.6 f + 0.34r r ( 54 − f ) + 0.83ξ2 ⎥⎦ ⎢⎣ p t Lect 11


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Attenuation Approximation (water vapor): Step 2a For water vapor at frequencies: 1 to 350GHz, where fi = 1780: η1 = 0.955rp rt0.68 + 0.006 ρ η2 = 0.735rp rt0.5 + 0.0353rt 4 ρ ⎛ f − fi ⎞ g( f , f1 ) = 1 + ⎜ ⎝ f + fi ⎟⎠

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then, Lect 11


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Attenuation Approximation (water vapor): Step 2b ⎧ 3.98η1 exp[2.23(1 − rt )] 11.96η1 exp[0.7(1 − rt )] γw = ⎨ g( f , 22) + 2 2 2 2 ( f − 22.235) + 9.42 η ( f − 183.31) + 11.14 η 1 1 ⎩ 0.081η1 exp[6.44(1 − rt )] 3.66η1 exp[1.6(1 − rt )] + + ( f − 321.226)2 + 6.29η12 ( f − 325.153)2 + 9.22η12 25.37η1 exp[1.09(1 − rt )] 17.4η1 exp[1.46(1 − rt )] + + 2 ( f − 380) ( f − 448)2 844.6η1 exp[0.17(1 − rt )] 290η1 exp[0.41(1 − rt )] + g( f , 557) + g( f , 752) 2 2 ( f − 557) ( f − 752) ⎫ 2 2.5 8.3328 × 10 4 η2 exp[0.99(1 − rt )] −4 + g( f ,1780) f r ρ × 10 ⎬ t ( f − 1780)2 ⎭

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Dry Air Attenuation Results •  press = 1013 [hPa] •  temp = 15.0 [C] •  Water vapor density = 7.5 [g/m3]

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Dry Air Attenuation Calculation(1)

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Water Vapor Attenuation Results •  press = 1013 [hPa] •  temp = 15.0 [C] •  Water vapor density = 7.5 [g/m3]

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Water Vapor Attenuation Calculation(1)

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Equivalent Heights Definition

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Equivalent Heights •  •  •  • 

These are scaled heights Based on an exponential atmosphere profile Heights vary with latitude, season, etc. Accuracy: ~10% for dry air, ~5% for water vapor

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Equiv. Height for Oxygen 6.1 0.3 ho = 1 + t + t + t where, h ≤ 0.7r when f 〈70GHz ( ) 1 2 3 o p −1.1 1 + 0.17rp 2 ⎡ ⎤ ⎛ ⎞ 4.64 f − 59.7 ⎥ t1 = exp ⎢ − ⎜ ⎟ −2.3 1 + 0.066rp ⎢ ⎝ 2.87 + 12.4 exp[−7.9rp ] ⎠ ⎥ ⎣ ⎦

t2 =

0.14 exp[2.12rp ]

( f − 118.75 )2 + 0.031exp[2.2rp ]

0.0114 −0.0247 + 0.0001 f + 1.61i10 −6 f 2 t3 = f −2.6 1 + 0.14rp 1 − 0.0169 f + 4.1i10 −5 f 2 + 3.2i10 −7 f 3

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Equiv. Height for Water Vapor ⎧ ⎫ 1.39σ w + ⎪1 + ⎪ 2 ( f − 22.235) + 2.56 σ w ⎪ ⎪ ⎪ ⎪ 3.37σ w hw = 1.66 ⎨ + ⎬ 2 ( f − 183.31) + 4.69σ w ⎪ ⎪ ⎪ ⎪ 1.58σ w ⎪ ⎪ 2 ( f − 325.1) + 2.89σ w ⎭ ⎩

where,

1.013 σw = 1 + exp[−8.6(rp − 0.57)] Lect 11


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Equivalent Heights (simplified) •  For oxygen [1 < f < 56.7 GHz] ho = 5.386 − 3.332734 *10 −2 f + 1.87185 *10 −3 f 2 − 3.52087 *10 −5 f 3 +

83.26 [km] 2 ( f − 60) + 1.2

•  For water vapor [f < 350 GHz] ⎡ 1.61 3.33 1.90 ⎤ hw = 1.65 ⎢1 + + + ⎥ [km] 2 2 2 ( f − 22.23) + 2.91 ( f − 183.3) + 4.58 ( f − 325.1) + 3.24 ⎣ ⎦

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Zenith Attenuation At elevation θ = 90°, the attenuation is:

Az = γ o ho + γ w hw where γo , ho , γw , and hw are as calculated previously

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Total Path Attenuation •  Atmospheric link (constant altitude) [dB] A = γ ad •  where, γ = γ + γ [dB/km] a

air

water

•  Satellite link (slant path through atmosphere) h0γ 0 + hwγ w Agas = [dB] sin (θ ) where, θ is the elevation angle and the h values are equivalent heights for the corresponding vapor components. Lect 11


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Specific Attenuation (Blue) Water vapor (Red) Dry air (Black) Total Note: units [dB/km ]

ITU-R P.676-6!

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ITU-R P.840-3 •  Describes a model for the attenuation of radio waves due to fog and clouds •  This model includes cloud attenuation •  The model calculates specific attenuations of radio waves [(dB/km)/(g/m3)]

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Cloud Attenuation •  Clouds are suspended water droplets •  Droplet diameters are typically < 100 µ •  Cloud attenuation is significant when radio waves have frequencies above 20 GHz •  It increases with frequency •  Increases with decreasing elevation angle •  Ice particles in clouds cause depolarization but not significant radio wave attenuation Lect 11


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Cloud Attenuation Model ITU-R P.840-3 •  Calculates attenuation on slant earth-satellite path due to clouds and fog •  Validity: f < 1200 GHz Droplet size < 0.01 cm

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Specific Attenuation •  The following variables are defined: γc: specific attenuation [dB/km] in cloud Kl: attenuation coefficient [(dB/km)/(g/m3) M: liquid water density in cloud/fog [g/m3]

•  The specific attenuation is,

γ c = K l M [dB/km] Lect 11


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Specific Attenuation Constant •  Calculation of Kl Kl =

0.819 f ε ′′(1 + η 2 )

Where ε” and η are dielectric properties of water as given below

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Calculation of η •  η is given by, 2+ε' η= ε"

ε’ and ε” are calculated below.

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Preliminary Calculations •  Dielectric constants and temperature scaling ε 0 = 77.6 + 103.3(θ − 1) ε1 = 5.48 ε 2 = 3.51 θ = 300 / T

•  Principal and secondary relaxation frequencies: f p = 20.09 − 142(θ − 1) + 294(θ − 1)2 [GHz] fs = 590 − 1500(θ − 1) [GHz]

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Dielectric Permittivity Calculations •  The complex permittivity constants for water are: f (ε 0 − ε1 ) f (ε1 − ε 2 ) ε ′′( f ) = + 2 f p [1 + ( f / f p ) ] fs [1 + ( f / fs )2 ]

ε 0 − ε1 ε1 − ε 2 ε ′( f ) = + + ε2 2 2 [1 + ( f / f p ) ] [1 + ( f / fs ) ]

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Cloud Attenuation

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Cloud Attenuation •  To calculate the attenuation through clouds, using the previous formulas and columnar water content, L [kg/m2]: LK l A= [dB for 5° ≤ θ ≤ 90°] Sin[θ ]

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ITU-R P.618-8 Other effects •  Rain attenuation •  Ionospheric scintillation •  Site diversity •  Depolarization

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Rain •  Is an important cause of attenuation in Ku and Ka bands. •  Wave intensity decays exponentially with propagation length through rain •  Raindrops are assumed spherical for analysis •  Raindrop effects are independent and additive Lect 11


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Rain Attenuation - Overview

Reference unknown!

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Rain Attenuation AdB = 4.343ρQt L

•  ρ = drop density [drop/m3] •  Qt = attenuation cross-section [dB m2/drop] •  k = ρQt is an empirical constant related to the rain rate and drop size distribution •  L = rain thickness [m]

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Rain Model - ITU-R P.838-3 γ R = kRα [dB/km] •  The rain rate is, R [mm/h] •  The constants k and a are determined by the formulas to follow.

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Rain Model - ITU-R P.838-3 ⎡ ⎛ log f − b ⎞ 2 ⎤ 10 j ⎥ + mk log10 f + ck log10 k = ∑ a j exp ⎢ − ⎜ ⎟ cj ⎢ ⎝ ⎠ ⎥⎦ j =1 ⎣ 4

⎡ ⎛ log f − b ⎞ 2 ⎤ 10 j ⎥ + mk log10 f + cα α = ∑ a j exp ⎢ − ⎜ ⎟ cj ⎢ ⎝ ⎠ ⎥⎦ j =1 ⎣ 5

•  Coefficients are tabulated in ITU-R P.838-3 •  f is in GHz

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Simplified Rain Model - ITU-R P.838-3 k = [kH + kV + (kH − kV ) cos 2 θ cos 2 τ ] / 2

α = [kH α H + kV α V + (kH α H – kV α V )cos 2 θ cos 2 τ ] / 2k

All coefficients tabulated in ITU-R P.838-3

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Depolarization •  Changes in polarization are due to: –  Rain –  Ice particles –  Multipath propagation

•  It rotates polarization angle •  Is prominent in, and above, the Ku band •  Affects both linear and circular polarizations Ref: ITU-R P.618-8!

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ITU-R P.618-8 Depolarization Model ITU-R P.618-8 •  Contains a calculation model for calculating cross-polarization from rain attenuation statistics for the slant path •  Valid for 8 ≤ f ≤ 35 GHz and θ ≤ 60°. •  Can be scaled down to 4 GHz

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Factors •  •  •  •  • 

Frequency: f Rain attenuation: Ap Polarization tilt angle: τ Elevation angle: θ Canting angle: σ

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Step 1 – Frequency Dependent Term

C f = 30Log[ f ] [dB]

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Step 2 – Rain Attenuation Term C A = V ( f )Log[Ap ] [dB] where, V(f) = 12.8f0.19 8 ≤ f ≤ 20 GHz V(f) = 22.6 20 ≤ f ≤ 35 GHz

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Step 3– Polarization Improvement Factor Cτ = −10Log[1 − 0.484(1 + Cos[4τ ])] [dB]

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Step 4 – Elevation Angle Term Cθ = −40Log[Cos(θ )] [dB]

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Step 5 – Canting Angle Factor Cσ = 0.0052σ 2 [dB] where, σ takes the value 0°, 5°, 10° and 15° for 1%, 0.1%, 0.01% and 0.001% of the time, respectively.

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Step 6 - Calculating XPD XPD rain = Cf – C A + Cτ + Cθ + C σ

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Sky Noise Temperature Ts = Tm (1 − 10 − A /10 )

where, Ts = sky noise temperature [K] A = path attenuation [dB] Tm = effective temperature of the medium [K] 280 K for clouds 260 K for rain Ref: ITU-R P.372!

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Diversity Reception •  •  •  • 

Uses multiple receivers Has a ground link to common point voter The voter selects the best signal The effect of fade in the path is reduced

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Diversity Reception Model

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Workshop 11 •  Please duplicate the graph given on page 307 in the text by implementing the calculations of ITUR P.676-6 /Annex 2. Write this up as a graded assignment, with mathematical calculations and appropriate ITU-R report reference.

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End

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