1. Satellite Communications
Firoz Ahmed Siddiqui

2. Satellite link design
The cost to build and launch a GEO satellite is about $25,000 per kg.
Weight is the most critical factor in the design of any satellite, since the heavier the satellite the higher the cost.
The overall dimensions of the satellite are critical because the spacecraft must fit within the confines of the launch vehicle.
Typically the diameter of the spacecraft must be less than 3.5m.

3. Satellite link design
The weight of the satellite depends on two factors: the number and output power of the transponders and the weight of station-keeping fuel.

4. Satellite link design
Satellite link design is nothing but estimation of power that is to be transmitted from an earth station towards the satellite or from a satellite towards the earth station so that at both ends the received power is reasonable.

5. Satellite link design
This link design calculation takes into account several factors such as absorption of signal by the space through which it propagates, various noise sources present in the satellite system, gain of transmitting and receiving antennas, and also the uplink and downlink frequencies because the absorption of signal by the atmosphere varies with frequencies.

6. Satellite link design
The design of uplink is simpler than the design of downlink, because any amount of required power can be generated in an earth station by using large number of vacuum devices.
However this is not possible inside a satellite due to its limited size.

7. Satellite link design
Figure – Flux density produced by an isotropic source.

8. Satellite link design
Consider a transmitting source, in free space, radiating a total power 𝑃 𝑡 watts uniformly in all directions as shown in figure.
At a distance R meters from the isotropic source transmitting RF power 𝑃 𝑡 watts, the flux density crossing the surface of a sphere with radius R is given by

9. Satellite link design
𝐹= 𝑟𝑎𝑑𝑖𝑎𝑡𝑒𝑑 𝑝𝑜𝑤𝑒𝑟 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎 𝑜𝑓 𝑠𝑝ℎ𝑒𝑟𝑒 𝐹= 𝑃 𝑡 4𝜋 𝑅 2 𝑊/ 𝑚 2
For a transmitter with output 𝑃 𝑡 watts driving a lossless antenna with gain 𝐺 𝑡 , the flux density in the direction of the antenna at distance R meters is given by
(1)

10. Satellite link design
𝐹= 𝑃 𝑡 𝐺 𝑡 4𝜋 𝑅 2 𝑊/ 𝑚 2 The product 𝑃 𝑡 𝐺 𝑡 is called the Effective Isotropically Radiated Power (EIRP)
(2)

11. Satellite link design
Figure – Power received by an ideal antenna

12. Satellite link design
If we had an receiving antenna with an aperture area of 𝐴 𝑒 𝑚 2 , the received power 𝑃 𝑟 is given by
𝑃 𝑟 =𝐹× 𝐴 𝑒
Thus the power received by a real antenna with an effective aperture area 𝐴 𝑒 𝑚 2 is given by
𝑃 𝑟 = 𝑃 𝑡 𝐺 𝑡 𝐴 𝑒 4𝜋 𝑅 2 𝑤𝑎𝑡𝑡𝑠
(3)
(4)

13. Satellite link design
From antenna theory, the gain of an antenna is related to its effective aperture by 𝐺= 4𝜋 𝐴 𝑒 𝜆 2 Where 𝜆 is the wavelength Substituting the value of 𝐴 𝑒 from equation (5) to equation (4) we get 𝑃 𝑟 = 𝑃 𝑡 𝐺 𝑡 𝐺 𝑟 4𝜋𝑅/𝜆 2 𝑤𝑎𝑡𝑡𝑠
(5)
(6)

14. Satellite link design
This expression is known as the link equation, and it is essential in the calculation of power received in any radio link.
The term 4𝜋𝑅/𝜆 2 is known as path loss, and it is represented by 𝐿 𝑝 .
It is not a loss in the sense of power being absorbed, it accounts for the way energy spreads out as an electromagnetic wave travels away from a transmitting source in three-dimensional space.

15. Satellite link design Collecting the various factors, we can write
𝑃𝑜𝑤𝑒𝑟 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑= 𝐸𝐼𝑅𝑃×𝑅𝑒𝑐𝑒𝑖𝑣𝑖𝑛𝑔 𝑎𝑛𝑡𝑒𝑛𝑛𝑎 𝑔𝑎𝑖𝑛 𝑃𝑎𝑡ℎ 𝑙𝑜𝑠𝑠 𝑤𝑎𝑡𝑡𝑠
The link equation is usually evaluated in decibels, therefore writing equation (7) in decibels
𝑃 𝑟 =𝐸𝐼𝑅𝑃+ 𝐺 𝑟 − 𝐿 𝑝 𝑑𝐵𝑊
(7)
(8)

16. Satellite link design
Where 𝐸𝐼𝑅𝑃=10 𝑙𝑜𝑔 10 𝑃 𝑡 𝐺 𝑡 𝑑𝐵𝑊 𝐺 𝑟 =10 𝑙𝑜𝑔 10 4𝜋 𝐴 𝑒 / 𝜆 2 𝑑𝐵 𝐿 𝑝 =10 𝑙𝑜𝑔 10 4𝜋𝑅/𝜆 2 𝑑𝐵 𝐿 𝑝 =20 𝑙𝑜𝑔 10 4𝜋𝑅/𝜆 𝑑𝐵 Equation (8) represents an ideal case, in which there are no additional losses in the link. But in practical we have to include the losses in the atmosphere due to attenuation, losses in the antenna at transmitting and receiving end.

17. Satellite link design Therefore the equation (8) can be written as
𝑃 𝑟 =𝐸𝐼𝑅𝑃+ 𝐺 𝑟 − 𝐿 𝑝 − 𝐿 𝑎 − 𝐿 𝑡𝑎 − 𝐿 𝑟𝑎 𝑑𝐵𝑊
Where
𝐿 𝑎 = attenuation in atmosphere
𝐿 𝑡𝑎 = losses associated with transmitting antenna
𝐿 𝑟𝑎 = losses associated with receiving antenna

19. Example - 1
A satellite at a distance of 40,000 km from a point on the earth’s surface radiates a power of 10 W from an antenna with a gain 17 dB in the direction of the observer. Find the flux density at the receiving point, and the power received by an antenna at this point with an effective area of 10 𝑚 2 .

20. Example Contd.
Given- R = 40,000 km 𝑃 𝑡 = 10 W 𝐺 𝑡 = 17 dB 𝐴 𝑒 = 10 𝑚 2 F = ? 𝑃 𝑟 = ?

21. Example Contd.
𝐹= 𝑃 𝑡 𝐺 𝑡 4𝜋 𝑅 2 𝐹= 10×50 4𝜋 4× 𝑭=𝟐.𝟒𝟗× 𝟏𝟎 −𝟏𝟒 𝑾/ 𝒎 𝟐 The power received with an effective collecting area is 𝑃 𝑟 =𝐹× 𝐴 𝑒 𝑃 𝑟 =2.49× 10 −14 ×10 𝑷 𝒓 =𝟐.𝟒𝟗× 𝟏𝟎 −𝟏𝟑 𝑾

22. Example Contd. In decibels the flux density is given by
𝐹 =10 𝑙𝑜𝑔 10 𝑃 𝑡 𝐺 𝑡 −10 𝑙𝑜𝑔 10 𝑅 2 −10 𝑙𝑜𝑔 10 4𝜋 𝐹=10 𝑙𝑜𝑔 ×50 −20 𝑙𝑜𝑔 ×10 7 −10 𝑙𝑜𝑔 10 4𝜋 𝐹=27−152−11 𝑭=−𝟏𝟑𝟔 𝒅𝑩 𝑾/ 𝒎 𝟐
And
𝑃 𝑟 =− 𝑙𝑜𝑔 10 𝐴 𝑒 𝑃 𝑟 =− 𝑷 𝒓 =−𝟏𝟐𝟔 𝒅𝑩𝑾

23. Example - 2
A satellite at a distance of 40,000 km from a point on the earth’s surface radiates a power of 10 W from an antenna with a gain of 17 dB in the direction of observer, operates at a frequency of 11 GHz. The receiving antenna has a gain of 52.3 dB. Find the received power.

24. Solution –
R = 40,000 km
𝑃 𝑡 = 10 W
𝐺 𝑡 = 17 dB
f = 11 GHz
𝐺 𝑟 = 52.3 dB
𝑃 𝑟 =?

25. Example Cond.
𝑃 𝑟 =𝐸𝐼𝑅𝑃+ 𝐺 𝑟 − 𝐿 𝑝 𝑃 𝑟 =10 𝑙𝑜𝑔 10 𝑃 𝑡 −20 𝑙𝑜𝑔 10 4𝜋𝑅/𝜆 𝑃 𝑟 =10 𝑙𝑜𝑔 −20 𝑙𝑜𝑔 10 4𝜋× 4× × 10 −2 𝑃 𝑟 = − 𝑷 𝒓 =−𝟏𝟐𝟔 𝒅𝑩𝑾

26. System Noise Temperature & G/T Ratio
Noise temperature is a useful concept in communications receivers.
It provides a way of determining how much thermal noise is generated by active and passive devices in the receiving system.
At microwave frequencies, a black body with physical temperature Tp degrees kelvin, generates electrical noise over a wide bandwidth. The noise power is given by

27. 𝑃 𝑛 =𝑘 𝑇 𝑝 𝐵 𝑛 Where k = Boltzmann’s constant (1
𝑃 𝑛 =𝑘 𝑇 𝑝 𝐵 𝑛 Where k = Boltzmann’s constant (1.39× 10 −23 𝐽/𝐾) 𝑇 𝑝 = physical temperature of source in kelvin degrees 𝐵 𝑛 =noise bandwidth in which the noise power is measured, in hertz

28. Calculation of System Noise Temperature

29. Calculation of System Noise Temperature
Figure shows a simplified communications receiver with an RF amplifier and single frequency conversion.
This is the form used for all radio receivers. It is known as the superhet (superheterodyne).
The superhet receiver has three main sybsystems: a front end (RF amplifier, mixer and local oscillator), an IF amplifier (IF amplifiers and filters), and a demodulator and baseband section.

30. Calculation of System Noise Temperature
The RF amplifier in a satellite communications receiver must generate as little noise as possible, so it is called a low noise amplifier of LNA.
The mixer and local oscillator form a frequency conversion stage that down converts the RF signal to a fixed intermediate frequency (IF), where the signal can be amplified and filtered accurately.

31. Calculation of System Noise Temperature

32. Calculation of System Noise Temperature
Many earth station receivers use the double superhet configuration shown in fig, which has two stages of frequency conversion.
The front end of receiver converts the incoming RF signals to a first IF in the range 900 to 1400 MHz. This allows the receiver to accept all the signals transmitted from a satellite in a 500 MHz bandwidth.
The next section of the receiver is called low noise block converter (LNB).

33. Calculation of System Noise Temperature
The MHz signal is sent over a coaxial cable to a set-top receiver that contains another down-converter and a tunable local oscillator.
The local oscillator is tuned to convert the incoming signal from a selected transponder to a second IF frequency.
The second IF amplifier has a bandwidth equal to the spectrum of the transponder signal.

34. Calculation of System Noise Temperature

35. Calculation of System Noise Temperature
The equivalent circuits in figure (a) can be used to represent a receiver for the purpose of noise analysis.
The noisy devices in the receiver are replaced by equivalent noise less blocks with the same gain.
The entire receiver is then reduced to a single equivalent noiseless block with the same end-to-end gain as the actual receiver and a single noise source at its input with temperature 𝑇 𝑠 .

36. Calculation of System Noise Temperature
The total noise power at the output of the IF amplifier of the receiver in fig. (a) is given by
𝑃 𝑛 = 𝐺 𝐼𝐹 𝑘 𝑇 𝐼𝐹 𝐵 𝑛 + 𝐺 𝐼𝐹 𝐺 𝑚 𝑘 𝑇 𝑚 𝐵 𝑛 + 𝐺 𝐼𝐹 𝐺 𝑚 𝐺 𝑅𝐹 𝑘 𝐵 𝑛 ( 𝑇 𝑅𝐹 + 𝑇 𝑖𝑛 )
Where 𝐺 𝑅𝐹 , 𝐺 𝑚 and 𝐺 𝐼𝐹 are the gains of the RF amplifier, mixer and IF amplifier and 𝑇 𝑅𝐹 , 𝑇 𝑚 and 𝑇 𝐼𝐹 are their equivalent noise temperatures. 𝑇 𝑖𝑛 is the noise temperature of the antenna, measured at its output port.
(1)

37. Calculation of System Noise Temperature
Equation (1) can be rewritten as
𝑃 𝑛 = 𝐺 𝐼𝐹 𝐺 𝑚 𝐺 𝑅𝐹 𝑘 𝐵 𝑛 𝑇 𝑅𝐹 + 𝑇 𝑖𝑛 + 𝑇 𝑚 / 𝐺 𝑅𝐹 + 𝑇 𝐼𝐹 / 𝐺 𝑅𝐹 𝐺 𝑚
The single source of noise shown in fig. (b) with noise temperature 𝑇 𝑠 generates the noise power 𝑃 𝑛 at its output
𝑃 𝑛 = 𝐺 𝐼𝐹 𝐺 𝑚 𝐺 𝑅𝐹 𝑘 𝑇 𝑠 𝐵 𝑛
The noise power at the output of the noise model in fig. (b) will be the same as the noise power at the output of the noise model in fig. (a) if
(2)
(3)

38. Calculation of System Noise Temperature
𝑇 𝑠 = 𝑇 𝑅𝐹 + 𝑇 𝑖𝑛 + 𝑇 𝑚 / 𝐺 𝑅𝐹 + 𝑇 𝐼𝐹 / 𝐺 𝑅𝐹 𝐺 𝑚 Succeeding stages of the receiver contributes less and less noise to the total system noise temperature. When the RF amplifier in the receiver has a high gain, the noise contributed by the IF amplifier and later stages can be ignored and the system noise temperature is simply the sum of the antenna noise temperature and the LNA noise temperature, so
(4)

39. Calculation of System Noise Temperature
𝑇 𝑠 = 𝑇 𝑎𝑛𝑡𝑒𝑛𝑛𝑎 + 𝑇 𝐿𝑁𝐴 The noise model shown in fig. (b) assumes that all the noise comes in from the receiver or is internally generated in the receiver. In some cases, we need to use a different model to deal with noise that reaches the receiver after passing through a lossy medium. The noise model for an equivalent output noise source is shown in fig. (c) and produces a noise temperature 𝑇 𝑛𝑜 given by

40. Calculation of System Noise Temperature
𝑇 𝑛𝑜 = 𝑇 𝑝 1− 𝐺 𝑙 Where 𝐺 𝑙 is the linear gain(less than unity, not in decibels) of the attenuating device or medium, and 𝑇 𝑝 is the physical temperature in degrees kelvin of the device or medium. For an attenuation of A dB, the value of 𝐺 𝑙 is given by 𝐺 𝑙 = 10 𝐴/10
(5)
(6)

41. Numerical on System Noise Temperature
A 4-GHz receiver has the following gains and noise temperature
𝑇 𝑖𝑛 =25𝐾 𝐺 𝑅𝐹 =23 𝑑𝐵 𝑇 𝑅𝐹 =50𝐾 𝐺 𝐼𝐹 =30 𝑑𝐵 𝑇 𝐼𝐹 =1000𝐾 𝑇 𝑚 =500 𝐾
Calculate the system noise temperature assuming that the mixer has a gain 𝐺 𝑚 =0 𝑑𝐵. Recalculate the system noise temperature when the mixer has 10 dB loss. How can the noise temperature of the receiver be minimized when the mixer has a loss of 10 dB.

42. The system noise temperature is given by 𝑇 𝑠 = 𝑇 𝑅𝐹 + 𝑇 𝑖𝑛 + 𝑇 𝑚 / 𝐺 𝑅𝐹 + 𝑇 𝐼𝐹 / 𝐺 𝑅𝐹 𝐺 𝑚 𝑇 𝑠 = / /200 𝑻 𝒔 =𝟖𝟐.𝟓 𝑲 For 𝐺 𝑚 =−10 𝑑𝐵 𝑇 𝑠 = / /200×0.1 𝑻 𝒔 =𝟏𝟐𝟕.𝟓 𝑲

43. The lowest system noise temperatures are obtained by using a high gain LNA, suppose 𝐺 𝑅𝐹 =50 𝑑𝐵, for this value the system noise temperature is given by 𝑇 𝑠 = / / 10 4 𝑻 𝒔 =𝟕𝟓.𝟎𝟏 𝑲 The high gain of the RF LNA amplifier has made the system noise temperature almost as low as possible ( 𝑇 𝑠 = 𝑇 𝑖𝑛 + 𝑇 𝑅𝐹 =75 K)

44. Noise Figure and Noise Temperature
Noise figure is frequently used to specify the noise generated within a device. The operational noise figure (NF) is defined by
𝑁𝐹= 𝑆/𝑁 𝑖𝑛 𝑆/𝑁 𝑜𝑢𝑡
Because noise temperature is more useful in satellite communication systems, it is best to convert noise figure to noise temperature 𝑇 𝑑
𝑇 𝑑 = 𝑇 0 𝑁𝐹−1

45. Where 𝑇 0 is the reference temperature used to calculate the standard noise figure (usually 290 K). NF is frequently given in decibels and must be converted to a ratio before being used.

46. G/T Ratio for Earth Stations
The link equation can be rewritten in terms of C/N at the earth station
𝐶 𝑁 = 𝑃 𝑡 𝐺 𝑡 𝐺 𝑟 𝑘 𝑇 𝑠 𝐵 𝑛 𝜆 4𝜋𝑅 𝐶 𝑁 = 𝑃 𝑡 𝐺 𝑡 𝑘 𝐵 𝑛 𝜆 4𝜋𝑅 𝐺 𝑟 𝑇 𝑠
Thus 𝐶 𝑁 𝛼 𝐺 𝑟 𝑇 𝑠 , and the terms in the square brackets are all constants for a given satellite system.

47. G/T Ratio for Earth Stations
The ration 𝐺 𝑟 𝑇 𝑠 , which is usually known as G/T in decibels, with units dB/K, can be used to specify the quality of a receiving earth station or a satellite receiving system.

48. Numerical
An earth station antenna has a diameter of 30 m, has an overall efficiency of 68%, and is used to receive a signal at 4150 MHz. At this frequency, the system noise temperature is 79 K when the antenna points at the satellite at an elevation angle of what is the earth station G/T ratio under these conditions? If heavy rain causes the sky temperature to increase so that the system noise temperature rises to 88 K, what is the new G/T value?

49. Given
D = 30 m
𝜂 𝐴 = 68%
f = 4150 MHz
𝑇 𝑠 = 79 K
G/T = ?

50. Antenna gain for a circular aperture 𝐺 𝑟 = 𝜂 𝐴 4𝜋𝐴 𝜆 2 𝐺 𝑟 = 𝜂 𝐴 𝜋𝐷/𝜆 2 At 4150 MHz, 𝜆 = m, then 𝐺 𝑟 =0.68× 𝜋×30/ 𝐺 𝑟 =1.16× 10 6 𝑜𝑟 60.6 𝑑𝐵 Converting 𝑇 𝑠 into dBK 𝑇 𝑠 =10𝑙𝑜𝑔79=19 𝑑𝐵𝐾

51. 𝐺 𝑇 =60. 6−19 𝑮 𝑻 =𝟒𝟏. 𝟔 𝒅𝑩/𝑲 If 𝑇 𝑠 = 88 K in heavy rain, 𝐺 𝑇 =60

52. Design of Downlinks
The design of any satellite communication is based on two objectives:
Meeting a minimum C/N ratio for a specified percentage of time, and carrying the maximum revenue earning traffic at minimum cost.
Any satellite link can be designed with very large antennas to achieve high C/N ratios under all conditions, but the cost will be high.

53. The art of good system design is to reach the best compromise of system parameters that meets the specification at the lowest cost.
All satellite communications links are affected by rain attenuation.
Satellite links are designed to achieve reliabilities of 99.5 to 99.99%, over one year. That means the C/N ratio in the receiver will fall below the minimum permissible value for proper operation of the link for between 0.5 and 0.01 % of the specified time. This specified time is called outage.

54. Link Budgets
C/N ratio calculation is simplified by the use of link budgets.
A link budget is a tabular method for evaluating the received power and noise power in a radio link.
Link budget use decibel units for all quantities so that signal and noise powers can be calculated by addition and subtraction.

55. Since it is impossible to design a satellite link at the first attempt, link budgets make the task much easier because, once a link budget has been established, it is easy to change any of the parameters and recalculate the result.
The link budget must be calculated for an individual transponder, and must be recalculated for each of the individual links.

56. Link budgets are usually calculated for a worst-case scenario like earth station located at the edge of the satellite coverage zone where the received signal is 3 dB lower than in the center of the zone, maximum path length from the satellite to the earth station, a low elevation angle at the earth station, maximum rain attenuation on the link.

58. Table – C-Band Downlink Budget in Rain

59. Uplink Design
The uplink design is easier than the downlink design, since it is feasible to use much higher power transmitters at earth stations than on a satellite.
Earth station transmitter power is set by the power level required at the input to the transponder.
At C band, a typical uplink earth station transmits 100 W with a 9-meter antenna, giving a flux density at the satellite of -100 W/ 𝑚 2 .

60. Analysis of uplink requires calculation of the power level at the input to the transponder so that the uplink C/N ratio can be found.
Link equation is used to calculate C/N ratio.
When a C/N ratio is specified for the transponder, the calculation of required transmit power can be easily calculated.
Let 𝐶/𝑁 𝑢𝑝 be the specified C/N ratio in the transponder, measured in a noise bandwidth 𝐵 𝑛 Hz.

61. The bandwidth 𝐵 𝑛 Hz is the bandwidth of the band-pass filter in the IF stage of the earth station receiver.
The noise power to the transponder input is given by
𝑁 𝑥𝑝 =𝑘+ 𝑇 𝑥𝑝 + 𝐵 𝑛 𝑑𝐵𝑊
Where 𝑇 𝑥𝑝 is the system noise temperature of the transponder in dBK and 𝐵 𝑛 is in units of dBHz.

62. The power received at the input to the transponder is given by
𝑃 𝑟𝑥𝑝 = 𝑃 𝑡 + 𝐺 𝑡 + 𝐺 𝑟 − 𝐿 𝑝 − 𝐿 𝑢𝑝 𝑑𝐵𝑊
Where 𝑃 𝑡 𝐺 𝑡 is the uplink earth station EIRP in dBW, 𝐺 𝑟 is the satellite antenna gain in dB in the direction of the uplink earth station and 𝐿 𝑝 is the path loss in dB. The factor 𝐿 𝑢𝑝 dB accounts for all uplink losses other than path loss.

63. 𝐶 𝑁 =10 𝑙𝑜𝑔 10 𝑃𝑟/(𝑘 𝑇 𝑠 𝐵 𝑛 ) = 𝑃 𝑟𝑥𝑝 − 𝑁 𝑥𝑝 𝑑𝐵
The value of 𝐶/𝑁 𝑢𝑝 at the LNA input of the satellite receiver is given by
𝐶 𝑁 =10 𝑙𝑜𝑔 10 𝑃𝑟/(𝑘 𝑇 𝑠 𝐵 𝑛 ) = 𝑃 𝑟𝑥𝑝 − 𝑁 𝑥𝑝 𝑑𝐵
The received power at the transponder input is also given by
𝑃 𝑟𝑥𝑝 =𝑁+ 𝐶 𝑁 𝑑𝐵𝑊

64. Link Design Procedure
The design procedure for a one-way satellite communication link can be summarized by the following 10 steps. The return link design follows the same procedure.
Determine the frequency band in which the system must operate.
Determine the communications parameters of the satellite.
Determine the parameters of the transmitting and receiving earth stations.

65. 4. Start at the transmitting earth station
4. Start at the transmitting earth station. Establish an uplink budget and a transponder noise power budget to find 𝐶/𝑁 𝑢𝑝 in the transponder. 5. Find the output power of the transponder based on transponder gain or output backoff. 6. Establish a downlink power and noise budget for the receiving earth station. Calculate 𝐶/𝑁 𝑑𝑛 and 𝐶/𝑁 𝑜 for a station at the edge of the coverage zone (worst case).

66. 7. Calculate S/N in the baseband channel. Find the link margins. 8
7. Calculate S/N in the baseband channel. Find the link margins. 8. Evaluate the result and compare with the specification requirements. Change parameters of the system as required to obtain acceptable 𝐶/𝑁 𝑜 or S/N values. 9. Determine the propagation condition under which the link must operate. Calculate the outage time for the uplinks and downlinks.

67. 10. Redesign the system by changing some parameters if the link margins are inadequate. Check that all parameters are reasonable, and that the design can be implemented within the expected budget.

68. DESIGN FOR SPECIFIED C/N
The S/N ratio in the baseband channel of an earth station receiver is determined by the ratio of the carrier power to the noise power in the IF amplifier at the input to the demodulator.
The noise present in the IF amplifier comes from many sources.

69. The noise in the earth station IF amplifier will have contributions from the receiver itself, the receiving antenna, sky noise, the satellite transponder from which it receives the signal, and adjacent satellites and terrestrial transmitters which share the same frequency band.
When more than one C/N ratio is present in the link, we can add the individual C/N ratios reciprocally to obtain an overall C/N ratio.

70. DESIGN FOR SPECIFIED C/N
𝐶 𝑁 0 =1/ 1 𝐶/𝑁 𝐶/𝑁 𝐶/𝑁 3 +… 𝐶 𝑁 0 = 1 𝑁 1 𝐶 + 𝑁 2 𝐶 + 𝑁 3 𝐶 +… 𝐶 𝑁 0 = 𝐶 𝑁 1 + 𝑁 2 + 𝑁 3 +…

71. DESIGN FOR SPECIFIED C/N
In decibel units
𝐶 𝑁 0 =𝐶 𝑑𝑏𝑊−10 𝑙𝑜𝑔 10 𝑁 1 + 𝑁 2 + 𝑁 3 +… 𝑑𝐵