12.3 Amateur Satellites, Doppler Shift, and Earth-Moon-Earth (EME)

12.3 Amateur Satellites, Doppler Shift, and Earth-Moon-Earth (EME)

VHF, UHF, and microwave signals can pass through the ionosphere for space communications; penetration depends on frequency and ionospheric conditions. AMSAT organisations and other amateur groups design and support satellites, while the IARU Satellite Frequency Coordination Panel coordinates amateur satellite frequencies internationally. Amateur satellites have carried the OSCAR designation (Orbiting Satellite Carrying Amateur Radio) since OSCAR 1 in 1961. Radio amateurs also use the Moon as a passive reflector for Earth-Moon-Earth (EME) communication.

Operating in the space communications realm requires mastering orbital mechanics, transponder architectures, dynamic Doppler shifts, Faraday polarization rotation, and the link budgets needed to overcome astronomical path losses.

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Amateur Radio Satellite Orbits and Keplerian Tracking

Amateur spacecraft operate across three primary orbital profiles, each presenting distinct operational trade-offs:

1. Low Earth Orbit (LEO):
   • Altitude: $400\text{ to }1500\text{ km}$ above Earth's surface.
   • Orbital Velocity: Approximately $7.5\text{ km/s}$ ($27,000\text{ km/h}$).
   • Orbital Period: $90\text{ to }115\text{ minutes}$ per orbit.
   • Pass Characteristics: Useful passes commonly last $10\text{ to }15\text{ minutes}$ between Acquisition of Signal (AOS) and Loss of Signal (LOS). For altitudes of $400\text{ to }1500\text{ km}$, the satellite's geometric footprint radius is about $2200\text{ to }4000\text{ km}$; a minimum usable elevation reduces this coverage.
   • Examples: The International Space Station (ISS, about $400\text{ km}$ altitude), SO-50, AO-91, and AO-7. AO-7 launched in 1974, fell silent after battery failure in 1981, and resumed solar-powered operation in 2002.
2. Geostationary Orbit (GEO):
   • Altitude: Exactly $35,786\text{ km}$ above the equator.
   • Orbital Velocity: $3.07\text{ km/s}$, matching the Earth's sidereal rotation period ($23\text{h }56\text{m }04\text{s}$).
   • Characteristics: The satellite appears stationary in the sky. It provides continuous, 24/7 coverage over roughly $42\%$ of the Earth's surface with zero Doppler shift and fixed dish antennas.
   • Example: QO-100 (Qatar-OSCAR 100 / Es'hail-2), launched in 2018, carries an amateur linear transponder with an uplink at $2.4\text{ GHz}$ and a downlink at $10.49\text{ GHz}$. While its footprint encompasses Europe, Africa, the Middle East, India, and parts of Brazil, it sits below the horizon for mainland Australia.
3. Highly Elliptical Orbit (HEO):
   • Geometry: A large difference between perigee and apogee produces a strongly elongated orbit. A Molniya orbit is a particular HEO with a roughly $12\text{ hour}$ period and $63.4^\circ$ inclination, chosen to limit rotation of the line of apsides.
   • Characteristics: By Kepler's second law, the satellite moves slowly near apogee, giving hours of visibility over the favoured hemisphere. Amateur HEOs need not use Molniya geometry: AO-10 had about $4000\text{ km}$ perigee, $35,440\text{ km}$ apogee and $26.5^\circ$ inclination. AO-40 was another historical amateur HEO.

Keplerian Elements (Two-Line Element Sets - TLE)

To predict precisely when a LEO satellite will rise above the local horizon and where to aim directional antennas, tracking software processes Keplerian elements. These are distributed by space agencies in standard Two-Line Element (TLE) sets:

                      Illustrative TLE Format (not tracking data)

  OSCAR 7 (AO-7)
  1 07530U 74089B   26282.45182935 -.00000012  00000-0  10000-3 0  9998
  2 07530 101.9834 234.1205 0012140 321.4589  38.5412 12.53612845341255

The fundamental classical parameters defined within a TLE are:

• Epoch: The UTC reference time to which the element set applies, expressed as a year and fractional day of year.
• Inclination ($i$): The angle between the orbital plane and Earth's equatorial plane ($101.98^\circ$ in the sample). Values above $90^\circ$ indicate retrograde motion; polar orbits have inclination near $90^\circ$.
• Right Ascension of the Ascending Node ($\Omega$ / RAAN): The celestial longitude at which the satellite crosses the equator from south to north.
• Eccentricity ($e$): The shape of the ellipse ($0.0012140$, where $0$ is a circle and values approaching $1$ become elongated).
• Argument of Perigee ($\omega$): The angular distance along the orbit from the ascending node to the point of closest approach ($321.46^\circ$).
• Mean Motion ($n$): The number of revolutions the satellite completes around Earth per solar day ($12.536\text{ revs/day}$). From this, the semi-major axis and orbital altitude are calculated.
• Mean Anomaly ($M$): An angle that increases uniformly in the ideal Keplerian orbit, from $0^\circ$ at perigee to $360^\circ$ after one revolution ($38.54^\circ$ at the sample epoch). The actual position angle is the true anomaly.

Ground tracking software (e.g., Gpredict, SatPC32) utilizes the SGP4 (Simplified General Perturbations) mathematical model to propagate these elements forward in time. The software outputs real-time Azimuth ($0^\circ\text{ to }360^\circ$) and Elevation ($0^\circ\text{ to }90^\circ$) angles, controlling computer-automated antenna rotators.

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Doppler Shift in Space Communications

Because a LEO satellite travels at an orbital velocity of roughly $v_{\text{orb}} \approx 7.5\text{ km/s}$ relative to a ground observer, electromagnetic waves experience a substantial Doppler frequency shift.

$$\Delta f = f_0 \frac{v_{\text{rel}}}{c}$$

where:

• $f_0$ is the nominal transmitted frequency,
• $v_{\text{rel}}$ is the relative radial velocity between the satellite and ground station along the line of sight (defined as positive when the spacecraft is approaching and negative when receding),
• $c \approx 3.00 \times 10^8\text{ m/s}$ is the speed of light.

         Received downlink frequency during an overhead LEO pass

 f0 + Δf   o  AOS: approaching
           |\
           |  \
           |    \
 f0        +------o  TCA: radial velocity zero
           |        \
           |          \
 f0 - Δf   |            o  LOS: receding
           +------------+------------> Time
           AOS   TCA    LOS

          Schematic: frequency decreases through nominal f0.

Magnitude of Doppler Shift Across Bands

At low elevation angles near AOS or LOS, the line-of-sight radial velocity approaches the spacecraft's orbital velocity ($v_{\text{rel}} \approx 7.0\text{ to }7.5\text{ km/s}$):

• 2-Meter Band ($145\text{ MHz}$): $$\Delta f_{\text{max}} \approx 145 \times 10^6 \times \frac{\pm 7.2 \times 10^3}{3.00 \times 10^8} \approx \pm 3.48\text{ kHz}$$ The total frequency excursion from AOS to LOS is approximately $7\text{ kHz}$.
• 70-Centimeter Band ($435\text{ MHz}$): $$\Delta f_{\text{max}} \approx 435 \times 10^6 \times \frac{\pm 7.2 \times 10^3}{3.00 \times 10^8} \approx \pm 10.44\text{ kHz}$$ The total frequency excursion from AOS to LOS is approximately $21\text{ kHz}$.
• 23-Centimeter Band ($1.296\text{ GHz}$): $$\Delta f_{\text{max}} \approx \pm 31.1\text{ kHz} \quad (\text{Total excursion } \approx 62\text{ kHz})$$

Operational Doppler Tuning Rules

1. Acquisition of Signal (AOS): The satellite is rapidly approaching the ground station ($v_{\text{rel}} > 0$). The received downlink signal is shifted higher than nominal ($f_{\text{nominal}} + \Delta f$). The receiver must be tuned high.
2. Time of Closest Approach (TCA): As the satellite reaches its maximum elevation angle, the radial velocity passes through zero ($v_{\text{rel}} = 0$). The received frequency equals the exact nominal frequency ($f_{\text{nominal}}$). The rate of change of frequency ($df/dt$) is at its maximum slope.
3. Loss of Signal (LOS): The satellite is rapidly receding ($v_{\text{rel}} < 0$). The received downlink signal is shifted lower than nominal ($f_{\text{nominal}} - \Delta f$). The receiver must be tuned low.

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Satellite Transponder Architectures

Amateur satellites carry two distinct types of communication transponders: channelized FM repeaters and linear transponders.

1. Channelized FM Voice Repeaters

FM satellites operate as orbiting cross-band repeaters (e.g., VHF uplink and UHF downlink, termed Mode V/u). They are popular because they can be operated using inexpensive handheld dual-band transceivers and portable handheld Yagi antennas (such as an Arrow or Elk antenna).

• The FM Capture Effect Bottleneck: Frequency Modulation exhibits the capture effect: an FM discriminator demodulates only the single strongest received carrier, suppressing weaker signals. If multiple stations transmit simultaneously, the signals collide, creating a loud heterodyne squeal and mutually destructive blocking. Only one QSO can occur at any instant across the satellite's entire continental footprint.
• CTCSS Tones: Accessing an FM satellite transponder almost always requires transmitting a continuous sub-audible CTCSS tone (e.g., $67.0\text{ Hz}$) to un-mute the uplink receiver.

2. Linear Inverting Transponders

A linear transponder does not demodulate incoming signals. Instead, it acts as a wideband RF translator, receiving a whole slice of spectrum (typically $30\text{ to }100\text{ kHz}$ wide), translating it to a different frequency band, amplifying it linearly, and retransmitting it. Linear transponders permit dozens of stations to conduct simultaneous independent contacts using Single Sideband (SSB) and Morse code (CW).

                     Linear Inverting Transponder Architecture

       Uplink Passband (145.900 - 145.950 MHz)             Downlink Passband (435.200 - 435.250 MHz)
       Low Freq                  High Freq                 Low Freq                   High Freq
       [---------------------------------]                 [----------------------------------]
            Station A        Station B                          Station B         Station A
            (145.910)        (145.940)                          (435.210)         (435.240)
             (LSB)            (LSB)                               (USB)             (USB)

           =======================================================================
                                 Transponder Mixing: f_down = f_LO - f_up
                                  Frequency & Sideband Inversion!

Almost all modern amateur linear transponders are inverting transponders:

• Mathematical Inversion: The internal mixer subtracts the incoming uplink frequency from a fixed local oscillator ($f_{\text{down}} = f_{\text{LO}} - f_{\text{up}}$). Consequently, an uplink signal transmitted at the lower end of the uplink passband appears at the higher end of the downlink passband.
• Sideband Inversion: Frequency inversion reverses the sidebands: a USB uplink becomes LSB on the downlink, and an LSB uplink becomes USB. The usual amateur operating convention for an inverting transponder is LSB uplink and USB downlink.
• Doppler Self-Correction Advantage: Inverting transponders provide an invaluable physical benefit: as Doppler shift drives the uplink frequency upward, the inverted downlink is transmitted at a lower frequency. For an operator listening to their own downlink signal, the uplink Doppler shift and downlink Doppler shift oppose each other, substantially reducing the net frequency drift heard on their own voice.

Power-Sharing and Transponder Discipline

A linear transponder has a strictly limited total RF output power (typically $1\text{ to }5\text{ Watts}$) shared among all active stations in the passband. The satellite utilizes an Automatic Gain Control (AGC) loop referenced to total composite received power.

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Wave Polarization and Faraday Rotation

When a linearly polarized electromagnetic wave (horizontal or vertical) propagates through the ionosphere, it interacts with free electrons in the presence of the Earth's geomagnetic field. This interaction causes the wave's plane of polarization to continuously rotate as it travels—a phenomenon known as Faraday rotation.

The total angle of polarization rotation ($\Omega_{\text{rot}}$) is:

$$\Omega_{\text{rot}} \propto \frac{B \cdot \text{TEC}}{f^2}$$

where $B$ is the geomagnetic field component along the path, $\text{TEC}$ is the Total Electron Content of the ionosphere, and $f$ is frequency.

Because the ionosphere's electron density varies continuously, the polarization of a wave reaching the ground station will rotate dynamically. If the receiving station uses a fixed linearly polarized antenna, the incoming wave will periodically arrive cross-polarized ($90^\circ$ out of alignment) with the antenna, causing polarization fading nulls exceeding $20\text{ to }30\text{ dB}$.

The Circular Polarization Solution

To eliminate Faraday fading nulls, space communications systems employ Circular Polarization:

• Right-Hand Circular Polarization (RHCP) or Left-Hand Circular Polarization (LHCP), where the electric field vector rotates continuously in a helical spiral as the wave travels.
• A circularly polarized antenna responds equally to any linear polarization angle (with a fixed, constant $3\text{ dB}$ penalty compared to perfectly matched linear polarization), completely eliminating the deep $20 - 30\text{ dB}$ nulls caused by Faraday rotation.
• Antenna Implementation: Ground stations use crossed-Yagi antennas consisting of two orthogonal sets of dipole elements mounted on the same boom. The two driven elements are fed in quadrature—differing in phase by exactly $90^\circ$—achieved using a quarter-wavelength ($\lambda/4$) coaxial phasing harness or an RF hybrid coupler.

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Earth-Moon-Earth (EME / Moonbounce)

Earth-Moon-Earth (EME) communication represents one of the most extreme technical challenges in radio engineering: using the Moon as a passive bistatic radar reflector to establish intercontinental VHF, UHF, and microwave links.

                       Earth-Moon-Earth (EME) Link Geometry

                    Total distance: 2d ≈ 768,800 km
                    Propagation delay: τ ≈ 2.56 seconds
       Ground transmitter --------------------------> Moon
       Ground receiver    <-------------------------- radar echo

       Nominal lunar radar cross-section: σ ≈ 0.07 × πR_Moon²
       Basic path loss at 144 MHz: approximately 252 dB
       Antenna gains and equipment losses complete the link budget.

Lunar Geometry, Albedo, and Path Delay

• Distance and Path Delay: The mean distance to the Moon is $d \approx 384,400\text{ km}$, giving a total round-trip travel distance of $2d \approx 768,800\text{ km}$. The round-trip propagation latency ($\tau$) is: $$\tau = \frac{2d}{c} = \frac{768,800\text{ km}}{300,000\text{ km/s}} \approx 2.56\text{ seconds}$$ An operator transmitting a CW call hears their own echo return through their headphones roughly $2.5\text{ seconds}$ after releasing the key.
• Angular Diameter: Viewed from Earth, the Moon subtends an angular diameter of only $0.5^\circ$.
• Lunar Radar Albedo: A nominal value is $\rho \approx 0.065\text{ to }0.07$. This is the Moon's backscatter radar cross-section divided by its projected disc area: $\sigma = \rho\pi R_{\text{Moon}}^2$. It describes the echo returned toward Earth; it is not the fraction of all incident RF energy reflected. The rough surface spreads the echo in delay and Doppler frequency.

EME Path Loss Calculation

Unlike two-way satellite transponders where path loss increases with the square of distance ($d^2$), EME is governed by the bistatic radar range equation, where received power ($P_r$) decreases with the fourth power of distance ($d^4$):

$$P_r = \frac{P_t G_t G_r\lambda^2\sigma}{(4\pi)^3 d^4}$$

Here both Earth–Moon legs are approximated by distance $d$, $\lambda$ is wavelength, and $\sigma$ is lunar radar cross-section. With unity antenna gains and nominal lunar albedo, the basic path losses are approximately:

• $144\text{ MHz}$ (2m): $\approx 252\text{ dB}$
• $432\text{ MHz}$ (70cm): $\approx 262\text{ dB}$
• $1296\text{ MHz}$ (23cm): $\approx 271\text{ dB}$
• $10\text{ GHz}$ (3cm): $\approx 289\text{ dB}$

Libration Fading

The Moon exhibits slight rocking motions known as libration (apparent orbital wobble caused by lunar orbital eccentricity and inclination). Different craters, mountains, and surface features move with slight relative velocity toward or away from Earth, causing microscopic Doppler shifts between different scattering facets. These multiple reflections interfere constructively and destructively, producing libration fading—rapid signal fluctuations of $10\text{ to }20\text{ dB}$ occurring at rates of several hertz.

Technical Requirements for EME Station Design

To bridge a $252+\text{ dB}$ path loss, an amateur EME station must optimize every component of the RF chain:

1. Transmitter Power: Use enough power for the link while observing the applicable band and emission limits. Under Australia's amateur class licence, ordinary Advanced Table C bands allow $400\text{ W}$ PEP for C3F, J3E and R3E, and $120\text{ W}$ mean power for other emissions, including CW and common digital EME modes.
2. High-Gain Directional Antennas:
   • On $144\text{ MHz}$: Arrays of four, eight, or sixteen long-boom Yagis stacked horizontally and vertically ($> 20\text{ dBi}$ gain).
   • On $1296\text{ MHz}$ and $10\text{ GHz}$: Parabolic dish reflectors of $3\text{ to }6\text{ metres}$ in diameter ($> 30\text{ to }45\text{ dBi}$ gain) with precision computer-controlled Azimuth and Elevation rotators capable of $0.1^\circ$ tracking accuracy.
3. Ultra-Low-Noise Preamplifiers (LNAs): Because incoming echo power is measured in fractions of a femtowatt ($-140\text{ dBm}$), masthead preamplifiers using Gallium Arsenide (GaAs) or pseudomorphic High Electron Mobility Transistors (pHEMT) are mandatory. The preamp is mounted directly at the antenna feed point to bypass feedline loss, achieving noise figures under $0.5\text{ dB}$ ($NF < 0.5\text{ dB}$, equivalent noise temperature $T_e < 35\text{ K}$).
4. Digital Weak-Signal Protocols: Historically, EME required multi-kilowatt transmitters and ears trained to extract sub-audible CW tones. In modern amateur radio, Nobel laureate Joe Taylor (K1JT) revolutionized EME by introducing digital protocols utilizing forward error correction (FEC):
   • JT65 and Q65: Both use MFSK, forward error correction and synchronized transmit/receive sequences. JT65 normally uses one-minute sequences. Q65 offers 15, 30, 60, 120 and 300 second sequences, with several tone spacings. Decoding sensitivity depends on the submode and signal conditions; quoted WSJT-X SNR values use a $2500\text{ Hz}$ reference bandwidth. These techniques allow contacts with much weaker signals than ordinary voice reception.

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Space Communications Mode Comparison