Satellite & Non-Terrestrial Networks (NTN) Engineering

Orbital Mechanics & Geometric Link Architecture

The architecture of satellite communications and 3GPP 5G Non-Terrestrial Networks (NTN) is fundamentally constrained by Keplerian orbital mechanics and the geometry of curved space-to-ground propagation. A satellite in a circular orbit around Earth experiences an exact balance between gravitational attraction and centripetal acceleration:

where the standard gravitational parameter of Earth is $\mu = G \cdot M_E = 398,600.4418\text{ km}^3/\text{s}^2$, the mean equatorial radius of Earth is $R_E = 6,378.137\text{ km}$, and $h$ is the orbital altitude above mean sea level.

Orbital altitude dictates every physical parameter of the communications link:

• Low Earth Orbit (LEO, $300\text{ to }2,000\text{ km}$): Satellites travel at immense velocities ($7.2\text{ to }7.8\text{ km/s}$), completing a full orbit in $90\text{ to }120\text{ minutes}$. While one-way propagation latency is ultra-low ($1.5\text{ to }10\text{ ms}$), the satellite traverses a ground station’s field of view in only $5\text{ to }12\text{ minutes}$. This demands fast antenna tracking and rapid inter-satellite handovers.
• Medium Earth Orbit (MEO, $2,000\text{ to }35,786\text{ km}$): Exemplified by GPS, Galileo, and SES O3b mPOWER ($8,062\text{ km}$). MEO provides broad regional beam footprints with intermediate one-way latencies ($25\text{ to }70\text{ ms}$) and moderate Doppler dynamics.
• Geostationary Earth Orbit (GEO, $35,786\text{ km}$): At exactly $35,786\text{ km}$ above the equator, the orbital period perfectly synchronizes with Earth’s sidereal rotation ($23\text{h }56\text{m }04\text{s}$). The satellite appears stationary in the sky, allowing fixed parabolic dish alignment with zero Doppler frequency shift. However, one-way propagation latency jumps to $120\text{ to }140\text{ ms}$ ($240\text{ to }280\text{ ms}$ round-trip time).

Spherical Trigonometry of Satellite Look Angles

To establish an RF link, an earth station must orient its antenna reflector or steer its phased-array beam toward the satellite. For a geostationary satellite positioned at longitude $\Lambda_s$, observed from an earth station at geodetic latitude $\phi_e$ and longitude $\Lambda_e$, the true Azimuth ($Az$) and Elevation ($El$) angles are computed using spherical trigonometry.

First, the central Earth angle ($\gamma$) between the earth station and the sub-satellite point is derived:

The true geometric Elevation angle ($El$) above the local horizontal tangent plane is given by:

The true Azimuth angle ($Az$) is measured clockwise from True North:

In addition, linearly polarized feeds require polarization skew adjustment ($\psi_{\text{pol}}$) to align with the satellite’s equatorial plane, preventing cross-polarization interference (XPI) penalties exceeding $20\text{ to }30\text{ dB}$.

Slant Range & Free Space Path Loss (FSPL) Dynamics

The line-of-sight distance separating an earth station from an orbital satellite is known as the slant range ($d$). Slant range is not constant during a non-GEO pass: it contracts to a minimum at the point of closest approach (nadir elevation, $\theta = 90^\circ$, where $d = h$) and expands to a maximum when the satellite dips toward the operational horizon ($\theta = 5^\circ\text{ to }10^\circ$).

Applying the law of cosines to the Earth-center, earth-station, and satellite triangle yields:

Because electromagnetic energy radiates outward in a spherical wavefront, the received power density diminishes according to the inverse-square law. Free Space Path Loss ($\text{FSPL}$) is quantified as:

During a single LEO satellite pass at $600\text{ km}$ altitude, slant range varies from $600\text{ km}$ (overhead) to $1,932\text{ km}$ ($5^\circ$ elevation). This dynamic variation introduces a $10.1\text{ dB}$ free-space path loss swing and a propagation delay variation from $2.0\text{ ms}$ to $6.4\text{ ms}$, requiring 3GPP 5G NTN gNodeBs to deploy continuous, dynamic timing advance (TA) adjustments.

Doppler Shift Physics in Non-Geostationary Networks

When a satellite moves relative to a stationary ground terminal with relative velocity vector $\vec{v}_{\text{rel}}$, the transmitted RF carrier undergoes a relativistic Doppler frequency shift:

In LEO constellations operating at orbital speeds near $7.6\text{ km/s}$, the maximum Doppler shift at low elevation angles reaches approximately:

Furthermore, the rate of change of frequency (Doppler rate, $\mathrm{d}f/\mathrm{d}t$) reaches its sharpest peak precisely at the Time of Closest Approach (TCA), exceeding $1.5\text{ kHz/s}$ in Ka-band. To prevent inter-carrier interference (ICI) in 5G NR Orthogonal Frequency Division Multiplexing (OFDM) waveforms, 3GPP Release 17 NTN standards mandate GNSS-assisted autonomous terminal pre-compensation, where user equipment (UE) pre-shifts its uplink transmission to arrive at the gNodeB satellite receiver with near-zero residual Doppler offset.

Ground Station Figure of Merit (G/T) & System Noise Temperature

The receiving performance of an earth station is universally characterized by its Gain-to-Noise-Temperature ratio ($G/T$), expressed in decibels per Kelvin ($\text{dB/K}$):

The total system noise temperature ($T_{\text{sys}}$) referenced to the Low Noise Amplifier (LNA) input flange accounts for multiple cascaded thermal noise contributors:

1. Antenna Noise Temperature ($T_{\text{ant}}$): Comprises cosmic microwave background radiation ($2.7\text{ K}$), atmospheric gas absorption, hydrometeor rain attenuation, and ground thermal noise ($290\text{ K}$) coupled through antenna sidelobes and backlobes.
2. Waveguide Feed Losses ($L_{\text{feed}}$): Physical waveguide attenuation dissipates signal power while generating thermal Johnson-Nyquist noise ($T_{\text{feed}} = (L_{\text{feed}} - 1) \cdot 290\text{ K}$).
3. LNA / LNB Noise Temperature ($T_{\text{LNA}}$): Active solid-state amplifier noise ($T_{\text{LNA}} = 290 \cdot (10^{\text{NF}/10} - 1)$), which dominates downstream receiver noise in accordance with Friis’ formula for cascaded stages.

Orbital Class Comparison & RF Transmission Benchmark

The reference table below compares the foundational physical and RF propagation characteristics across standard orbital regimes from Very Low Earth Orbit (VLEO) to Geostationary Earth Orbit (GEO).