1. CT-474: Satellite Communications
Yash Vasavada
Autumn 2016
DA-IICT
Lecture 7
Satellite Link Design
24th August 2016

2. Review and Preview
Review of the prior lecture: relationships between some key design parameters:
Channel capacity, Shannon information rate and trade between bandwidth and power
Preview of this lecture:
An example design of satellite link

3. Spectral Efficiencies and Required Es/No for Different Modulation and Coding Schemes

4. An Example Link Calculation

5. A Model of Downlink From SAT to the Ground Station
𝑃 𝑇𝑋
𝐺 𝑇𝑋
𝑃 𝐸𝐼𝑅𝑃 𝐿
𝐺 𝑅𝑋
𝑇 𝑎 𝑁𝐹
𝑇 𝑒 𝑇
𝐺 𝑅𝑋 /𝑇

6. EIRP, Antenna Gain 𝐺, and Path Loss 𝐿
Equivalent Isotropically Radiated Power or EIRP is given as EIRP = 𝑃 𝑇𝑋 × 𝐺 𝑇𝑋
Gain of the antenna 𝐺 is a function of the area (effective aperture) of the antenna and the transmission frequency
Free-space Path Loss is given as
Therefore, the ratio 𝐺/𝐿 is given as
𝜂: antenna efficiency, typically in the range of 0.5 to 0.7
𝐷 𝐴𝑛𝑡 : antenna diameter in meters
𝑓: carrier frequency in Hertz
𝑐: speed of light in vacuum, m / s
𝑑: path distance in meters

7. Path Length 𝑑
SAT
Three angles and three lengths define the geometry of SATGS link
Angles:
Elevation of the SAT: 𝛽
Latitude of the GS from the SAT relative to EC: 𝛼
Latitude of the GS from the EC relative to the SAT: 𝜃
Distances:
SAT to GS distance: 𝑑
Earth Radius: 𝑅 𝑒
SAT height (altitude) above the Earth Surface: 𝐻
SAT orbit radius: 𝑅= 𝑅 𝑒 +𝐻
Tangent at the location of ground station 𝛼
SAT to User Distance, 𝑑
Orbit Height 𝛽
Orbit Radius
Earth Radius 𝑅 𝑒 𝜃
Earth Center

8. Path Length 𝑑 Use Law of Cosines to determine the path length 𝑑
Therefore, 𝑑 𝛽 = 𝑅 𝑒 sin 𝛽 ± 𝑅 𝑒 2 sin 2 𝛽 − 𝑅 𝑒 2 + 𝑅 2
Use Law of Sines to determine the angles
sin 𝛼 = 𝑅 𝑒 × sin 𝜋 2 +𝛽 𝑅  𝛼= sin −1 𝑅 𝑒 × sin 𝜋 2 +𝛽 𝑅
sin 𝜃 =𝑑× sin 𝜋 2 +𝛽 𝑅  𝛼= sin −1 𝑑× sin 𝜋 2 +𝛽 𝑅

9. Transmit Antenna Gain Calculation
Color legend: green refers to input, red refers to output, yellow is a constant

10. Path Loss Calculation

11. Evaluation of SNR
We have seen that the SNR = 𝑃 𝑆 𝑃 𝑁 = 𝐶 𝑁 is a critical parameter that determines the BER and the achievable data rate
We have also seen earlier that 𝑃 𝑁 = 𝑁 0 𝐵
Here 𝑁 0 is the power spectral density
When the source of the noise is thermal
agitations of the electrons in the transceiver circuitry, the noise power spectral density 𝑁 0 is given
as 𝑘×𝑇
Here, 𝑘 is Boltzmann’s Constant with a value of × 10-23 m2 kg s-2 K-1
𝑇 is the system noise temperature in deg K
Power Spectral Density 𝑁 0
Filter Bandwidth B
Ideal (Brickwall) Filter with Bandwidth 𝐵

12. Noise Figure
Signal with Power 𝑃 𝑆 𝐺
Noise with Power 𝑃 𝑁
A device 𝐷 with a gain of 𝐺
Consider an additive noise model, where the noise is added to the
signal before the sum is fed to a device 𝐷 (e.g., an amplifier) with a gain of 𝐺
If the device 𝐷 is ideal, it won’t introduce any additional noise: SNR at input = 𝑃 𝑆 𝑃 𝑁 equals SNR at the output of the device which is 𝐺× 𝑃 𝑆 𝐺× 𝑃 𝑁 = 𝑃 𝑆 𝑃 𝑁
Actual devices add some extra noise with power 𝑃 𝑁,𝐷 such that the SNR at the output is 𝐺× 𝑃 𝑆 𝑃 𝑁,𝐷 +𝐺× 𝑃 𝑁
Ratio of the Input SNR to the Output SNR is called the Noise Factor 𝐹: 𝑃 𝑁,𝐷 +𝐺× 𝑃 𝑁 𝐺× 𝑃 𝑁
This ratio depends on three terms: device noise power 𝑃 𝑁,𝐷 , device gain 𝐺 and input noise power 𝑃 𝑁 .
For a given device, the first two terms are fixed. Input noise power 𝑃 𝑁 is fixed, by convention, to 𝑘 𝑇 0 𝐵, where 𝑇 0 =273 degK (which is the typical room temperature of 𝑜 𝑐)
Noise Figure NF = 10× log 10 𝐹 dB

13. Effective Noise Temperature
Effective noise temperature of the device is called 𝑇 𝑒 = 𝑃 𝑁,𝐷 𝑘𝐺𝐵
It can be shown that 𝑇 𝑒 = 𝑇 0 𝐹−1
Total noise temperature at the output of the device is called the system noise temperature
𝑇 𝑆𝑌𝑆 = 𝑇 𝑖𝑛 + 𝑇 𝑒
where 𝑇 𝑖𝑛 is the noise temperature at the device input. This can be different from 𝑇 0 = 273 𝑜 𝐾
If there are two devices 𝐷 1 and 𝐷 2 in cascade with noise factors of 𝐹 1 and 𝐹 2 , effective noise temperatures of 𝑇 𝑒1 and 𝑇 𝑒2 and gains of 𝐺 1 and 𝐺 2 , the cascaded system’s overall noise factor and overall effective temperature are given as follows:
𝐹= 𝐹 1 + 𝐹 2 −1 𝐺 1 , and
𝑇 𝑒 = 𝑇 𝑒1 + 𝑇 𝑒2 𝐺 1

14. Receiver Antenna Gain and Figure of Merit Calculation Worksheet

15. Link Equation (linear scale)
Definition of 𝐶 𝑁 0
Received power 𝑃 𝑅𝑋 = 𝐺 𝑅𝑋 ×𝑅𝐼𝑃
Received noise power N 0 =𝑘𝑇
𝑅𝐼𝑃= 𝑃 𝐸𝐼𝑅𝑃 𝐿
𝑃 𝐸𝐼𝑅𝑃 = 𝑃 𝑇𝑋 × 𝐺 𝑇𝑋 ; 𝑇= 𝑇 𝑎 + 𝑇 𝑒
𝑇 𝑒 = 𝑇 0 (𝐹−1)

16. Link Equation (decibel scale)
Link equation in dB scale: multiplications and divisions turn into additions and subtractions
All the values are in dB, including Receiver Figure of Merit ( 𝐺 𝑅𝑋 /𝑇) which is a ratio that is evaluated in linear scale (using Noise Figure, 𝑇 𝑒 and 𝑇 𝑎 ) and converted in dB

17. An Example Link Calculation (Continued)