Satellite Communication (EC-603 (C)) - Unit 3 Short Notes

UNIT 3: Satellite Communication

I. Orbital Mechanics and Kepler's Laws

A. Kepler's Three Laws of Planetary Motion

1. First Law (Law of Ellipses):

   All satellites orbit in elliptical paths with the Earth at one focus. For circular orbits, eccentricity $$\displaystyle e = 0 $$.

2. Second Law (Law of Equal Areas):

   A line joining a satellite and Earth sweeps out equal areas in equal intervals of time.

   → Satellite moves faster at perigee (closest point) and slower at apogee (farthest point).

3. Third Law (Harmonic Law):

   The square of the orbital period ($T$) is proportional to the cube of the semi-major axis ($a$):

$$T^2 = \frac{4\pi^2}{\mu} a^3$$

where $$\displaystyle \mu = GM $$ (Earth's gravitational constant, $$\displaystyle \approx 3.986 \times 10^{14} \, \text{m}^3/\text{s}^2 $$).

\boxed{T^2 \propto a^3}

B. Orbital Parameters

• Semi-major axis ($a$): Average of perigee and apogee distances from Earth's center.

• Eccentricity ($e$): Measure of orbit's shape ($0$ = circle, $$\displaystyle 0 < e < 1 $$ = ellipse).

• Perigee distance ($$\displaystyle r_p $$): Closest point: $$\displaystyle r_p = a(1 - e) $$.

• Apogee distance ($$\displaystyle r_a $$): Farthest point: $$\displaystyle r_a = a(1 + e) $$.

• Example Calculation:

  Given $$\displaystyle r_a = 36,000 $$ km, $$\displaystyle r_p = 500 $$ km, Earth radius $$\displaystyle R_e = 6,371 $$ km.

$$a = \frac{r_a + r_p}{2} = \frac{36,000 + 500}{2} = 18,250 \, \text{km}$$

$$e = \frac{r_a - r_p}{r_a + r_p} = \frac{36,000 - 500}{36,000 + 500} \approx 0.972$$

C. Application to Satellite Orbits

• Circular vs. Elliptical:

  Circular ($$\displaystyle e=0 $$) → constant speed, altitude; Elliptical ($$\displaystyle e>0 $$) → speed varies (Kepler's second law).

• Velocity Variation:

  At perigee: $$\displaystyle v_p = \sqrt{\mu \left( \frac{2}{r_p} - \frac{1}{a} \right)} $$ (maximum).

  At apogee: $$\displaystyle v_a = \sqrt{\mu \left( \frac{2}{r_a} - \frac{1}{a} \right)} $$ (minimum).

[!TIP]

For GEO, $a \approx 42,164$ km (from $$\displaystyle T = 24 $$ hours). Altitude $$\displaystyle h = a - R_e \approx 35,786 $$ km.

II. Orbit Types and Their Applications

A. Geostationary Orbit (GEO)

• Definition: Circular, equatorial orbit with:

  • Altitude $h \approx 35,786$ km.

  • Period $$\displaystyle T = 23 $$ h $56$ min $4$ s (sidereal day).

  • Zero eccentricity and inclination.

• Key Properties: Satellite appears stationary relative to Earth; fixed position in sky.

• Advantages:

  • Continuous coverage of ~1/3 Earth.

  • Fixed ground antennas (no tracking needed).

• Visibility Limits:

  Determined by Earth's geometry and minimum elevation angle ($$\displaystyle \theta_{\text{min}} $$) at ground station.

  Maximum Earth central angle: $$\displaystyle \psi_{\text{max}} = \arccos\left( \frac{R_e}{R_e + h} \cos \theta_{\text{min}} \right) - \theta_{\text{min}} $$.

  For $$\displaystyle \theta_{\text{min}} = 5^\circ $$, $$\displaystyle \psi_{\text{max}} \approx 81^\circ $$ → ~81° from subsatellite point.

B. Sun-Synchronous Orbit (SSO)

• Definition: Precessing orbit maintaining constant local solar time over any given point.

• Design Parameters:

  • Altitude: Typically 600–800 km (LEO) or 700–1,000 km.

  • Inclination: High ($$\displaystyle i \approx 98^\circ $$ for LEO).

  • Nodal precession rate $$\displaystyle \dot{\Omega} \approx 0.9856^\circ/\text{day} $$ (360°/365.25 days).

• Importance: Earth observation satellites (e.g., weather, imaging) get consistent lighting conditions.

• Local Mean Solar Time (LMST):

  Solar time corrected for longitude and equation of time. SSO ensures same LMST for repeat passes.

C. Elliptical Orbits (e.g., Molniya)

• Characteristics: High eccentricity ($e \approx 0.7$), long dwell time at apogee.

• Use Cases: High-latitude coverage (e.g., Russia, Canada) where GEO is low on horizon.

D. Inclined Orbits

• Definition: Orbit plane inclined relative to equatorial plane ($$\displaystyle i \neq 0^\circ $$).

• Causes: Perturbations (e.g., J2 effect) or deliberate design.

• Applications: Specific regional coverage, scientific missions.

III. Orbit Perturbations and Station Keeping

A. Perturbation Sources

1. Earth's oblateness (J2 effect): Causes RAAN drift and argument of perigee rotation.

2. Gravitational pull from Moon and Sun: Long-term inclination changes.

3. Solar radiation pressure: Affects eccentricity, especially for large, lightweight satellites.

4. Atmospheric drag (LEO): Reduces altitude, increases decay.

B. Effects on Orbital Elements

• Inclination drift: Due to lunar/solar gravity.

• Eccentricity changes: Solar radiation pressure, thrust errors.

• RAAN drift: Primarily J2 effect: $$\displaystyle \dot{\Omega} \approx -\frac{3}{2} J_2 \left( \frac{R_e}{a} \right)^2 n \cos i $$.

C. Station Keeping Maneuvers

1. North-South (N-S): Controls inclination (counteracts lunar/solar perturbations). Fuel-intensive.

2. East-West (E-W): Controls eccentricity and longitude (counteracts J2, solar pressure).

3. Fuel consumption: Major factor in satellite lifetime. Typical GEO satellite carries fuel for 10–15 years of station keeping.

4. Inclined Orbit Operation:

   Allow natural perturbations to reduce fuel use → extended life but coverage varies diurnally.

[!TIP]

GEO satellites require frequent N-S station keeping (~weekly) due to lunar/solar gravity.

IV. Frequency Allocation and Spectrum Usage

A. Frequency Allocation Concept

• International regulation: ITU (International Telecommunication Union) coordinates global spectrum use.

• Coordination: Avoids interference between satellite systems and terrestrial services.

B. Satellite Frequency Bands

C. Bandwidth and Capacity Considerations

• Higher bands (Ka) offer more bandwidth but suffer greater rain attenuation.

• Frequency reuse via spot beams and polarization increases capacity.

V. Satellite Subsystems

A. Telemetry, Tracking, and Command (TT&C) Subsystem

• Telemetry: Downlink of satellite health data (temperature, voltage, pressure).

• Tracking: Determines satellite position/velocity (via Doppler, ranging).

• Command: Uplink instructions for orbit/attitude control, payload management.

B. Attitude and Orbit Control Subsystem (AOCS)

• Attitude Control: Maintains orientation (e.g., three-axis stabilization, spin stabilization).

• Orbit Control: Station keeping, orbit adjustments using thrusters.

C. Power Subsystem

• Solar arrays: Primary power source (photovoltaic cells).

• Batteries: Supply power during eclipse (e.g., Ni-H₂, Li-ion).

D. Thermal Control Subsystem

• Passive: Coatings, radiators, insulation.

• Active: Heaters, coolers for extreme temperatures.

E. Structure and Propulsion

• Structure: Supports components, withstands launch loads.

• Propulsion: Thrusters (e.g., bipropellant, monopropellant) for orbit/attitude control.

VI. Transponders and Antenna Systems

A. Transponder Functionality

1. Frequency translation: Up-converts uplink, down-converts downlink (typically 500 MHz bandwidth).

2. Amplification: Using TWTA (Traveling Wave Tube Amplifier) or SSPA (Solid-State Power Amplifier).

3. Types:

   • Bent-pipe (transparent): Simple frequency shift and amplify (most common).

   • Regenerative: Demodulates, processes, remodulates (improves C/N, used in digital systems).

B. Satellite Antenna Subsystems

1. Types:

   • Parabolic reflectors: Focused beams (e.g., horn feed).

   • Phased arrays: Electronically steered beams (advanced missions).

2. Beam Patterns:

   • Global beam: Covers entire visible Earth.

   • Spot beam: Focused on small area (higher gain).

   • Shaped beam: Custom coverage (e.g., country-shaped).

3. Polarization:

   • Linear: Horizontal (H) or Vertical (V).

   • Circular: Right-Hand (RHCP) or Left-Hand (LHCP) → reduces polarization mismatch due to rotation.

4. Cross-Polarization Discrimination (XPD):

   Isolation between orthogonal polarizations (e.g., H vs V).

   \boxed{\text{XPD (dB)} = 10 \log_{10} \left( \frac{P_{\text{co-pol}}}{P_{\text{cross-pol}}} \right)}

   Importance: Enables frequency reuse (same band, opposite polarizations) → doubles capacity.

C. Antenna Gain and Coverage

• Gain $$\displaystyle G = \eta \left( \frac{\pi D}{\lambda} \right)^2 $$ (for parabolic, $\eta$ = efficiency, $D$ = diameter).

• Coverage area determined by beamwidth: $\theta \approx 70 \lambda / D$ (degrees).

VII. Link Budget Analysis and Signal Propagation

A. Key Link Parameters

1. Effective Isotropic Radiated Power (EIRP):

   \boxed{\text{EIRP (dBW)} = P_t + G_t - L_t}

   where $$\displaystyle P_t $$ = transmitter power (dBW), $$\displaystyle G_t $$ = transmit antenna gain (dBi), $$\displaystyle L_t $$ = losses (dB).

   Significance: Measures signal strength at receiver input.

2. System Noise Temperature ($$\displaystyle T_s $$):

   $$\displaystyle T_s = T_{\text{antenna}} + T_{\text{receiver}} + T_{\text{atmospheric}} $$.

   Noise figure $$\displaystyle NF = 10 \log_{10}(T_s / T_0) $$, $$\displaystyle T_0 = 290 $$ K.

3. Carrier-to-Noise Ratio (C/N):

   • Uplink: $$\displaystyle (C/N)_u = \text{EIRP}_u - L_u + G_r - kT_e $$ (in dB: subtract $$\displaystyle 10\log_{10}(kT_s) $$).

   • Downlink: $$\displaystyle (C/N)_d = \text{EIRP}_d - L_d + G_r - kT_e $$.

   • Overall (including intermodulation):

     \boxed{\frac{1}{C/N_{\text{total}}} = \frac{1}{C/N_u} + \frac{1}{C/N_d} + \frac{1}{C/N_{IM}}}

B. Transmission Losses

1. Free-space path loss:

$$L_{fs} = \left( \frac{4\pi d}{\lambda} \right)^2$$

In dB: $$\displaystyle L_{fs} (\text{dB}) = 92.4 + 20\log_{10}(d) + 20\log_{10}(f) $$, $d$ in km, $f$ in GHz.

2. Atmospheric attenuation:

   • Rain attenuation: $$\displaystyle \gamma_R = k R^\alpha $$ (dB/km), where $R$ = rain rate (mm/hr).

     Total rain loss $$\displaystyle A_R = \gamma_R \cdot L_{\text{path}} $$ (effective path length).

     Frequency dependence: Increases with frequency (severe at Ka-band).

   • Gaseous absorption: Oxygen (60 GHz), water vapor (22 GHz).

3. Other losses:

   • Polarization mismatch loss (if XPD poor).

   • Pointing error loss (antenna misalignment).

C. Link Margin

• Definition: Excess $C/N$ over required threshold ($$\displaystyle (C/N)_{\text{req}} $$).

  \boxed{\text{Link Margin (dB)} = (C/N){\text{actual}} - (C/N){\text{req}}}

• VSAT star network example: Calculate for each VSAT-to-hub link, considering smallest EIRP (VSAT uplink) and largest path loss (edge VSAT).

D. Intermodulation Noise

• Cause: Nonlinearities in TWTAs with multiple carriers → third-order intermodulation products.

• Reduction:

  • Input backoff (IBO): Reduce uplink power to operate TWTA in linear region.

  • Output backoff (OBO): Corresponding output reduction.

  • Linearization techniques: Predistortion, feedforward.

VIII. Earth Stations

A. Earth Station Types

1. Full-Function Transmit-Receive Earth Station:

   • Large antenna (10–30 m), high-power amplifiers (kWP).

   • Used for gateway, control stations.

2. Receive-Only Earth Station (ROES):

   • Components: Antenna, LNB (Low-Noise Block downconverter), receiver.

   • Application: Home TV reception (DBS-TV).

3. VSAT (Very Small Aperture Terminal):

   • Small antenna (0.6–2.4 m), low-power uplink (BUC: Block Upconverter).

   • Indoor unit (modem, interface equipment).

   • Network topologies:

     • Star: All VSATs communicate via hub (most common).

     • Mesh: VSAT-to-VSAT direct (requires larger antennas).

   • Transmission techniques: TDMA, FDMA, CDMA.

B. Earth Station Design and Installation

1. Network Planning:

   • Coverage analysis (satellite footprint).

   • Frequency planning (avoid interference, polarization reuse).

   • Link budget for each link (uplink/downlink).

2. Equipment Selection:

   • Antenna size/gain (based on link margin).

   • HPA/BUC power (to meet EIRP).

   • LNB noise temperature (lower $$\displaystyle T_e $$ better).

   • Modem capabilities (modulation, FEC).

3. Installation Considerations:

   • Site survey: Obstacles (buildings, trees), interference sources (radars, other satellites).

   • Antenna pointing: Azimuth/elevation accuracy (±0.5° typical).

   • Cable routing, grounding, weatherproofing.

C. DBS-TV Antenna Installation

1. Steps:

   • Site selection (clear view south for GEO in Northern Hemisphere).

   • Mounting (pole/wall, secure).

   • Alignment (using signal meter, set azimuth/elevation).

   • Weatherproofing (seal connectors, radome).

2. Obstacle avoidance: Must have line-of-sight to satellite; use tools (e.g., dishpointer.com) to check.

3. Signal strength testing: Ensure margin > 10 dB for fade margin.

IX. Satellite Applications and Systems

A. Direct Broadcast Satellite (DBS) Television

1. System architecture:

   Headend → Uplink → Satellite (transponders) → Downlink → ROES/Set-top box.

2. Digital DBS-TV: Standards (DVB-S, DVB-S2).

3. Error Control Methods:

   • Forward Error Correction (FEC):

     • Convolutional codes (rate 1/2, 2/3, etc.) + Viterbi decoding.

     • Reed-Solomon (RS) codes (e.g., RS(204,188)) for burst error correction.

   • Interleaving: Scrambles bits to disperse burst errors (from fading, interference).

   • Importance: Maintains broadcast quality (minimizes pixelation, audio dropouts).

B. Satellite Radio Broadcasting

• Principle: Digital audio broadcast via satellite (e.g., SiriusXM).

• Advantages: Wide coverage, mobile reception (cars), diverse channels, no terrestrial interference.

• Technical aspects:

  • Frequency bands: S-band (2.3 GHz) for mobile, Ku/Ka for fixed.

  • Error correction: Concatenated codes (convolutional + RS).

  • Conditional access: Encryption for subscription services.

C. VSAT Networks

1. Design and Implementation Steps:

   • Requirements analysis (number of sites, traffic volume, latency).

   • Topology selection (star vs. mesh).

   • Hub earth station design (antenna size, power).

   • VSAT terminal specification (antenna, BUC, LNB, modem).

   • Network management system (NMS) for control.

2. Star Network Operation:

   • Central hub controls all communications; VSATs only talk to hub.

   • Link margin calculation: For each VSAT, compute $$\displaystyle (C/N)_d $$ (downlink from satellite) and $$\displaystyle (C/N)_u $$ (uplink to hub). The bottleneck is usually VSAT uplink (low power, small antenna).

3. Applications: Enterprise networks (retail, banking), maritime, rural connectivity.

X. Case Studies: Notable Satellites

A. Morelos Satellites (Mexico)

• Overview: Series of Mexican communications satellites (Morelos 1, 2, 3).

• Technical specifications:

  • Frequency bands: C-band (12 transponders), Ku-band (18 transponders).

  • Coverage: Mexico, Central America, parts of USA.

• Role: Provided telecommunications, TV broadcasting, telephony to remote areas.

B. Satmex 5 (Mexico)

• Overview: High-power satellite (launched 1998), built by Hughes.

• Capabilities:

  • 24 Ku-band transponders, 2 Ka-band.

  • Coverage: Americas (from Canada to Argentina).

  • High EIRP → small ground antennas (0.8 m for DBS-TV).

• Significance: Advanced capacity for Latin America, supported broadband, TV, data.

XI. Advanced and Contextual Topics

A. Space Segment's Role in Global Communications

1. Enabling worldwide coverage: Especially remote/underserved regions (oceans, deserts, mountains).

2. Revolution:

   • Instant communication across continents.

   • Broadcasting (TV, radio) to millions simultaneously.

   • Support for navigation (GPS), weather forecasting, disaster response.

3. Evolution: Analog → digital → high-throughput satellites (HTS) with spot beams and frequency reuse (Ka-band).

B. Launching Orbits for Geostationary Satellites

1. Geostationary Transfer Orbit (GTO):

   • Elliptical orbit: perigee ~200–300 km, apogee at GEO altitude (35,786 km).

   • Advantage: Launch vehicle requires less energy (Δv).

   • Disadvantage: Satellite must use own propulsion for circularization at apogee → consumes fuel.

2. Direct Insertion:

   • Launch directly to GEO (rare, requires powerful launcher).

   • Advantage: Saves satellite fuel (longer life).

   • Disadvantage: Higher launch energy/cost.

3. Trade-off: GTO common for cost savings; direct insertion for premium satellites.

C. Local Mean Solar Time (LMST)

1. Definition: Solar time corrected for longitude and equation of time (difference between apparent solar time and mean solar time due to Earth's elliptical orbit and axial tilt).

2. Importance for SSO: Earth observation satellites require consistent LMST for each pass → uniform illumination/shadows in images.

3. Relationship with orbit design: SSO's nodal crossing time is set to achieve desired LMST; precession rate ensures this time remains constant over the year.

[!TIP]

For SSO, nodal precession $\dot{\Omega}$ must equal Earth's orbital rate around Sun ($$\displaystyle \approx 0.9856^\circ/\text{day} $$). Use formula: $$\displaystyle \dot{\Omega} = -\frac{3}{2} J_2 \left( \frac{R_e}{a} \right)^2 n \cos i $$ to solve for $i$ given $a$.