Appunti 2 - Space Missions and Systems

T24delays

Without relativistic effects we can compute in the same proper time scale. A signal is generated by the clock A at coord time and after some instrument delay is emitted at coord time from the antenna. The signal arrived at the receiving antenna at time t2 and after some delay t∆R arrives at the comparator at time t5. Meanwhile, a replica of the signal has been generated with some delay B since time t2.

The observable quantity provided by the system is ∆τ45. The delay ∆τ is the time difference needed to align the local replica and the incoming signal. In the 1-way case, the observable was ∆τ45, obtained by the clock comparator.

For de-synchronisation:

A - B = ∆τ (t5) - ∆τ (t1) = ∆τ (t2) - ∆τ (t1) + ∆τ (t5) - ∆τ (t2) + ∆τ (t1) - ∆τ (t5) = 5 - 5 + 5 - 1 + 1 - 5 + 1 - 5 + 15

To obtain the above equation for the uplink channel:

A - B = -∆τ (t5) + ∆τ (t1) = 0.1 - 5 + A - tB + tT = [∆T] + T + [∆R] + [∆τ]

The last term is...

observed/measured quantity.

In general byt each clock starts generating the signal at its own proper time, for nearby clocks̸t = t1 5

Clock errors are contained in the observable quantity .B A Bτ (t ) = τ (t ). ∆τ5 1 45

The terms introduces transformations between coordinate and proper times, which depend upon theT15gravitational potential and velocities of the clocks (require relativity). In general, the relationship between2isproper time and coordinate time expanding and retaining only terms of order dτ 1 v2 −τ t, 1/c = 1 + (U )2dt c 2where U is the potential. The terms coming from clock B (∆R ) go through a double time scaleBB , ∆τ 452transformation. We can demonstrate that writing the de-synchronisation at coordinate time allows skippingt4the double time scale transformation. 113

Observables quantities for space navigation ground systems

Main satellites categories are: communication, Earth observation, meteo, space research, planetary exploration,surveillance,

navigation system is responsible for guiding and controlling the mission goals. It involves the use of radio or laser tracking from a ground station. The Ground segment includes all the satellite and terrestrial facilities for monitoring and controlling the mission, such as telemetry, tracking, and command stations (TTC). The telecommand, telemetry, and tracking functions are essential for space navigation. The telecommand is the type of commands sent from the ground station to the satellite, while telemetry is the type of data received from the satellite to the ground station. Tracking involves measuring the range, range rate, and angular observables of the satellite. Tracking configurations can be classified based on the source of the reference signal and the number of intervening stations. There are three types: - One-way tracking: In this configuration, only the downlink signal is used, and the carrier signal is generated onboard the satellite using a suitable oscillator. - Two-way tracking: In this configuration, the carrier signal is generated by the ground station using the station master frequency standard (clock). The uplink signal is received by an onboard transponder, which coherently retransmits it back to the ground station. - Three-way tracking: This configuration is similar to two-way tracking, but the downlink signal is established via a different, receiving-only antenna. These tracking configurations are crucial for ensuring accurate navigation and control of the satellite during the mission.

1. Opacity of the atmosphere as a function of frequency shows the Earth atmosphere and EM spectrum exploitable regions of the electromagnetic EM spectrum. Higher frequencies are desirable to increase data rate, but counterbalanced by high opacity. The opacity in the microwave region is largely affected by the presence of liquid water and water vapour.
2. 3.0.1 Telecommand
   Sends commands to the satellite, housekeeping and instruments commands (maneuvers, battery controls, instrument turn-on/off, change of operational modes)
   Frequency bands used: 2025-2120 MHz (S-band, less used), 7145-7235 MHz (x-band, standard), 34.2-34.7 GHz (Ka-band, future for deep space missions)
3. 3.0.2 Telemetry
   Satellite parameters, payload data, scientific data.
   Frequency bands used: 220-2300 MHz (S-band, emergency use), 8025-8400 MHz (x-band, Earth exploration sats), 8400-8500 MHz (x-band, today standard), 25.5-27.0 GHz (K/Ka-band, future high data rate Earth sats), 31.8-32.3 GHz (Ka-band, deep space missions).
4. Satellite

communication systems- antennas- amplifiers- transmitters- receivers- channel model

The last three are the All elements are present both onboard the s/c and on ground.transponders.

4.1 Antenna

Device used to transmit and receive EM waves. It can be seen as a bidirectional transducer that transforms electric signals into EM waves and vice versa. The received electric signal is proportional to the EM field impinging on the antenna and the transmitted EM field is proportional to the magnitude of the input signal.

Parabolic reflectors concentrate all power in a single point, the "prime focus" F of the paraboloid. The phase between all incoming rays is preserved, since all the rays reach F at the same phase (WA+AF=WO+OF).

Figure 6: Uplink, the signal is transmitted to s/c

In general, all s/c signals reaching an antenna, coming from large distances, can be approximated as plane waves over the spatial scale of the receiving antenna.

The sensing element of the antenna is called feed, or horn.

The electric field of the wave is transformed at the feed into the electric signal that is then manipulated to obtain the telemetry stream and the radio-metric observables. In space applications, the feed is never placed in the primary focus. Instead, the Cassegrain scheme is adopted, with the feed placed on the secondary focus (SF). In order to preserve the phase coherence at SF, the surface S must be hyperboloid. These antennas reduce the noise pickup from the ground. Antenna parameters: - Gain - Radiation pattern - Angular beamwidth - Polarisation - EIRP 13 - Power flux density - G/T 4.1.1 Gain The gain is the ratio of radiated power in a given direction to the power radiated per unit solid angle by an isotropic, lossless antenna fed with the same power. It measures the directivity of the antenna. Alternatively, it can be defined as the power produced by the antenna's beam axis to the power produced by a hypothetical lossless isotropic antenna. For an isotropic antenna, we mean an antenna whose gain is independent of direction, flux.density is the same over the sphere. Diffraction angles depend on the ratio of the wavelength of the radiation and the physical size of the body, has order: 24D4πλ (21) → ≈ =Gθ = λ 2D λ2π( )D where is radiofrequency wavelength (c/f ) and D is the diameter of the antenna. λ The precise value of the gain for reflector antenna (disc) requires the computation of the effective aperture, since at boresight (max gain direction). For reflector antennas: A = Aeff eff,max2 2D D (22) A = π A = ηA A = ηπeff,max eff,max4 4 with aperture efficiency (circa 0.6). η For max gain: 4π πD (23) 2G = π A = η( )max eff,max2λ λ The radiation pattern indicates the variation of the gain with direction. For circular aperture antenna, the pattern has rotational symmetry and can be represented in a plane of co-polar coordinated or Cartesian coordinates. , it's the full angular between two directions where the gain is

3dB below θ Half power beamwidth: 3dB maximum. λ (24)θ = 70 (degrees)3dB D θ3dB (25)–f or small of f axis angles 0 < θ < 2θ (26)2–> | –G(θ)| = G 12( )dBi max dBi θ 3dB (27)where G(θ)| = 10log (G(θ))dBi 10Maximum gain can be expressed as a function of the half-power beamwidth and independently from frequency: ( πD 2G = η( ) 70π ηmax (28)2λ –> –>G = η( ) G = 14.9( )max max 2λ θ θ)θ = 70( 3dB3dB 3dBD 144.1.2 EIRPThe equivalent isotropically radiated power is the apparent power transmitted towards the receiver, productof the power supplied to the antenna and the antenna gain in the receiver’s direction relative to an isotropicantenna. (29)EIRP = G P [W ]T Twhere is the gain of transmitted antenna in the direction of receiver and is the power supplied toG PT Tantenna.4.2 Link budgetIs a series of mathematical computations

Designed to model the performance of a communication link. In a two-way sat link, there are two link budget calculations: the uplink (from ground to sat) and the downlink (from sat to ground). Link budgets are used to check that the communications link meets the designer's criteria for reliability and performance.

Ingredients:

• Power flux emitted from the transmit antenna
• Attenuation of the atmosphere, scintillation from ionosphere
• Power received by receiving antenna
• Thermal noise
• Carrier power over noise power P/N, P/Nc or C
• Energy per bit over noise power E/Nb or
• Equations for uplink, downlink, thermal and atmospheric losses

4.2.1 Link budget equation

The received signal power at ref. point is:

1 P = EIRP * TX * (30) = A = (G * AP) = (eff,max * TX * eff,RX * RX) / (4 * pi * R^2 * L * atm)

A = G * eff,RX * RX / (4 * pi * lambda)

2 => P = P * G * (GRX * TX * TX) / (4 * pi * R * L * atm)

Where other losses may need to be added, such as polarization loss and...

poiting loss.4.2.2 Noise model

The nominal channel for most space missions is Additive White Gaussian Noise (AWGN), which source may be characterised by an equivalent noise temperature.

For example, considering the measurement of a voltage across an unpolarised resistor: the resistor motion of the electrons creates random potential differences, which depend on the temperature, the spectrum voltage is white at all freq below If the voltage is bandpass-filtered, the noise power in the bandwidth is :kT /h. TZ Z1 11 (33)2 2< V >= V dt = S (f )df = kT BNR T R0 B

For each white noise source in the link it’s possible to define a temperature T that allows to define the generated Noise Power Spectral Density : −204kT 10log (kT ) = dB Hz.10 0 W

In satellite communication generally we define two temperatures, antenna noise temperature (T ) and antsystem noise temperature (T ).sys 15- is the temperature of a resistor that would produce the same noise power per unit bandwidth as

That's the amount of noise present in the antenna output (and receiver output). Typical noise sources include galactic noise (approximately