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

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

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

An Example Link Calculation

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

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, 299792458 m / s 𝑑: path distance in meters

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

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

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

Path Loss Calculation

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 1.38064852 × 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

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 16.8 𝑜 𝑐) Noise Figure NF = 10× log 10 𝐹 dB

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

Receiver Antenna Gain and Figure of Merit Calculation Worksheet

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)

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

An Example Link Calculation (Continued)