Satellite Links & Constellation Topologies

A satellite is not merely a tall radio tower. Its range, radial velocity, visibility, and pointing direction change according to orbit; ground terminals see the atmosphere through a varying elevation angle; and traffic may traverse a bent-pipe payload, onboard routing, one or more inter-satellite links, and a distant gateway. The RF calculation and the network topology are therefore one design problem.

Orbit labels—LEO, MEO, GEO—are not service guarantees. Altitude influences delay and footprint, but inclination, eccentricity, antenna pattern, gateway placement, spectrum, payload architecture, and constellation phasing decide whether a particular user has continuous capacity.

One topology diagram hides several links #

Service link

Connects the user terminal to the satellite. User aperture and transmit power are often the tight constraints.

Feeder link

Connects a satellite to a gateway. Large gateways buy antenna gain but can create weather and geographic concentration risk.

Inter-satellite link (ISL)

Moves traffic between spacecraft, reducing dependence on a nearby gateway but adding acquisition, routing, pointing and onboard resource constraints.

Telemetry, tracking and command (TT&C)

The control link that must survive acquisition, safe mode and low-gain antenna states even when the high-rate payload link is unavailable.

A transparent or bent-pipe payload frequency-translates/amplifies the waveform and sends it onward; timing and much protocol processing remain on the ground. A regenerative payload demodulates/decodes and can switch or route onboard. Regeneration can break one noisy end-to-end RF path into separately decoded hops, but introduces onboard state, latency, compatibility, upgrade, and failure-domain decisions.

Orbit geometry creates latency and handover #

For a circular orbit of radius $a=R_E+h$, period is

$$T=2\pi\sqrt{\frac{a^3}{\mu_E}},$$

where $R_E$ is Earth radius and $\mu_E$ its gravitational parameter. With $R_E=6371$ km, $\mu_E=398600.44$ km³/s² and $h=550$ km, $T\approx95.5$ min. A ground terminal therefore sees one LEO satellite for only part of an orbit and must acquire another beam or spacecraft as geometry changes.

Geostationary altitude is about 35 786 km above the equator. An overhead ground-to-GEO propagation leg is

$$\frac{35,786\ \text{km}}{299,792.458\ \text{km/s}}\approx119.37\ \text{ms}.$$

A transparent user → GEO satellite → gateway path uses two such legs: about 238.74 ms one way and 477.48 ms round trip before non-overhead slant range, terrestrial routing, processing, scheduling, and queueing. A 550 km overhead leg is about 1.83 ms, but a practical LEO path may include a slanted service hop, feeder hop, ISLs, and gateway backhaul.

Coverage footprint grows with altitude and minimum elevation angle. Low elevation extends visibility but lengthens slant range, increases atmospheric path, raises blockage probability, and makes terminal antenna patterns and local clutter more important. A coverage map that uses the geometric horizon while operations require 20° elevation is optimistic.

Range dominates free-space loss #

ITU-R P.525-5 gives the free-space basic transmission loss as

$$L_{bf}=32.4+20\log_{10}f_{MHz}+20\log_{10}d_{km}\ \text{dB}.$$

At 20 GHz and overhead geometric range:

The difference is 36.27 dB before atmospheric, polarization, pointing, feeder, and implementation losses. GEO compensates with high-gain antennas, large gateways, more stable pointing geometry, and persistent coverage; it does not evade spreading.

Free-space loss rises with frequency at fixed antenna gain because a fixed-gain receive antenna has effective aperture $A_e=G\lambda^2/(4\pi)$. At fixed physical aperture and efficiency, antenna gain rises as $1/\lambda^2$ and can offset that frequency term. Frequency does not independently “absorb more in vacuum”; it changes aperture, hardware, available bandwidth, pointing, and atmospheric loss.

Link closure uses $C/N_0$, not received power alone #

For one hop, a useful dB form is

$$\frac{C}{N_0}=EIRP+\frac{G}{T}-L_{path}+228.60\qquad\text{dB-Hz},$$

where EIRP is dBW, receive $G/T$ is dB/K, losses are dB, and $228.60=-10\log_{10}k$ for Boltzmann's constant in SI units. Then

$$\frac{E_b}{N_0}=\frac{C}{N_0}-10\log_{10}R_b,$$

for information bit rate $R_b$, provided code-rate and modulation definitions are handled consistently.

The margin is required $E_b/N_0$ subtracted from available $E_b/N_0$ after implementation loss. Availability is not established by one clear-sky margin: rain, gas, cloud, scintillation, polarization, pointing, antenna-temperature, interference, power/thermal state, and geometry vary with time.

Uplink and downlink should be budgeted separately. Ground stations can often transmit high EIRP and use large low-noise apertures; a small spacecraft has limited DC power, thermal dissipation, mass, and pointing. Command links may close through a low-gain spacecraft antenna at low rate while high-rate downlink requires precise body or gimbal pointing.

Atmosphere is elevation-, frequency-, and climate-dependent #

ITU-R P.618-14 composes Earth-space propagation effects including atmospheric gases, precipitation/cloud attenuation, scintillation, wavefront incoherence, beam spreading, depolarization, and site diversity. It applies statistical methods, not one global “rain margin.”

Above roughly 10 GHz, rain and hydrometeors can dominate availability in some climates. Gas absorption has frequency structure; cloud liquid water, scintillation, and rain have different time scales and dependencies. A low elevation angle increases path length through the troposphere and often intersects more local clutter.

Mitigations spend different resources:

“Five nines” availability requires the joint probability of all selected hops and failover actions, not five nines assigned separately to each component.

Doppler and delay are time-varying state #

First-order Doppler is

$$f_D\approx\frac{v_r}{c}f_c,$$

where $v_r$ is radial velocity. A LEO orbital speed near 7.6 km/s gives a worst-order scale of about 507 kHz at 20 GHz if the full velocity projected onto the line of sight. Actual radial velocity varies through the pass and goes through zero near closest approach.

The receiver must acquire across frequency uncertainty and track its slope; the transmitter may pre-compensate from ephemeris. Residual Doppler affects carrier recovery and OFDM orthogonality, while Doppler rate can exceed a narrow loop's tracking dynamics even when instantaneous offset is inside its nominal range.

Propagation delay also changes. Random access and timing advance in a terrestrial cell assume a much smaller and more stable range than many satellite paths. 3GPP's NTN work therefore treats satellite ephemeris, timing relationships, frequency pre-compensation, and moving cells as protocol inputs rather than hiding them below an unchanged terrestrial PHY.

Constellations trade satellites against gateways and routing #

A constellation's capacity is not satellite count multiplied by headline throughput. Beams reuse spectrum spatially, but gateways, feeder-link spectrum, onboard switching, ISLs, power, thermal limits, and user distribution create bottlenecks. Coverage and capacity are separate maps.

Constellation phasing and inclination should follow service latitude. Polar or high-inclination shells cover high latitudes but concentrate crossings and handovers differently from lower-inclination shells. Multiple orbital planes reduce coverage gaps but create inter-plane ISL geometry that changes rapidly, especially near seams between counter-rotating or differently phased planes.

Pointing closes a narrow-beam link #

Higher frequency and larger aperture increase gain by narrowing the beam. That improves the RF budget but spends attitude knowledge, control, structural stability, and acquisition time. Pointing loss must be computed from the measured pattern, not a generic Gaussian if sidelobes/nulls matter.

Acquisition often uses a wider search beam or beacon, then hands over to narrow tracking. Optical links push this further: tiny beam divergence can provide enormous link gain and spectrum, while cloud blockage and micro-radian-class pointing become central. NASA's current SmallSat communications survey treats RF and free-space optical terminals as distinct trade spaces rather than one replacing the other universally.

For a phased-array user terminal, scan loss, polarization rotation, element pattern, grating lobes, thermal state, and blockage all vary with look angle. “Electronically steered” removes a mechanical gimbal, not the geometry budget.

End-to-end verification #

Build evidence in the order the real service uses it:

1. propagate orbit/attitude and generate time histories of slant range, elevation, radial velocity, Doppler, Doppler rate, pointing, and visibility;
2. compute separate uplink, downlink, feeder, and ISL budgets with measured directional antenna data and $G/T$;
3. apply current ITU-R propagation models with site climate and elevation, producing availability distributions rather than one attenuation;
4. simulate acquisition over full frequency/time/angle uncertainty and verify handoff before the old path falls below threshold;
5. constrain traffic by actual beam, gateway, feeder, ISL, onboard-processing, and backhaul capacities;
6. inject gateway weather outage, satellite/beam loss, stale ephemeris, blocked terminal view, and failed handover;
7. verify TT&C and safe-mode low-gain paths independently of the payload service;
8. compare predicted $C/N_0$, Doppler, timing, selected route, and decoder margin with telemetry from complete passes.

A satellite system works only when orbit state → geometry → per-hop RF/optical margin → acquisition and handover → routed capacity remains continuous over the declared environment and failures. Closing a single clear-sky link budget is the first calculation, not the proof.