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Massive MIMO Goes to Orbit

Massive MIMO was conceived, and has been almost entirely deployed, as a terrestrial technology: the base station sits on a rooftop or a tower, the users move at walking or driving speed, and the channel varies over milliseconds. Non-terrestrial networks (NTN) break all three assumptions at once. The "base station" is a satellite moving at $7.5$ km/s. The user terminal is stationary from its own perspective, but its apparent relative velocity is enormous. And the channel — now a free-space LEO link — varies over tens of microseconds at Ka band. Re-doing the design from these physical constraints is the purpose of this chapter, and the surprising punchline of Part V is that the cell-free and user-centric ideas of Part III translate naturally to the orbital regime. Each visible LEO becomes an access point; the user-centric cluster is a set of simultaneously visible satellites; handover is cluster reselection.

The CommIT contribution by Buzzi, Caire, and Colavolpe shows how macro- diversity across multiple simultaneously visible satellites recovers what the single-satellite link cannot: reliable service at low elevation angles, robustness to rain fade, and graceful handover. We build the machinery step by step, starting with the geometry of orbits and coverage.

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Definition:
Orbital Classes for Satellite Communications

Three altitude regimes dominate modern satcom deployments:

Low Earth Orbit (LEO): altitude $h \in [500, 2000]$ km. Orbital period $\approx 90$ – $120$ min. Velocity $\approx 7.5$ km/s. Footprint radius a few hundred to a thousand km. A given satellite is visible to any fixed terminal for only $5$ – $15$ minutes per pass, so continuous coverage requires a constellation of hundreds to tens of thousands of satellites. Starlink, OneWeb, Kuiper, Telesat Lightspeed.
Medium Earth Orbit (MEO): $h \in [8000, 20000]$ km. Example: GNSS systems (GPS, Galileo, GLONASS) at $\approx 20{,}200$ km. O3b mPOWER at $\approx 8000$ km for broadband. Smaller constellations ( $\approx 20$ – $80$ satellites), longer visibility windows ( $\approx 1$ – $4$ hours per pass), larger delays.
Geostationary Orbit (GEO): $h \approx 35{,}786$ km. The satellite appears fixed above the equator, so a single GEO craft with a wide beam covers roughly one-third of the Earth. No handover, no Doppler (by design), but one-way delay $\approx 120$ ms and massive path loss.

For the massive-MIMO-adapted-to-NTN problem this chapter treats, LEO is both the most relevant and the most challenging: it is the only regime where the Doppler and visibility-window dynamics force a genuine rework of the signal-processing stack.

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Low Earth Orbit (LEO)

The altitude band $h \in [500, 2000]$ km. LEO satellites orbit at $\approx 7.5$ km/s, have a $\approx 90$ – $120$ -minute period, and pass over any given terminal for only $5$ – $15$ minutes. Continuous coverage requires a constellation of hundreds to tens of thousands of craft (Starlink, OneWeb, Kuiper). LEO minimizes propagation delay ( $5$ – $20$ ms one-way) and path loss relative to GEO but introduces the largest Doppler shifts and the most frequent handovers of any satellite regime.

Non-Terrestrial Network (NTN)

A 3GPP umbrella term for radio access networks whose base stations are not on the ground. Includes LEO, MEO, GEO satellites, as well as high-altitude platform stations (HAPS) and airborne platforms. 3GPP Release 17 (2022) introduced the first NTN normative support in 5G NR, covering the adapted timing, Doppler, and scheduling procedures that make the air interface work through a moving overhead node.

Definition:
Slant Range and One-Way Delay

Consider a satellite at altitude $h$ above a spherical Earth of radius $R_E$ , seen from a ground terminal at elevation angle $\theta_{\text{el}}$ . From the law of cosines in the Earth–satellite triangle,

$d_{\text{slant}}(h, \theta_{\text{el}}) = \sqrt{R_E^2 \sin^2\theta_{\text{el}} + 2 R_E h + h^2} - R_E \sin\theta_{\text{el}}.$

The corresponding one-way propagation delay is $\tau_{\text{prop}} = d_{\text{slant}} / c$ . Two useful limits:

Overhead zenith pass ( $\theta_{\text{el}} = 90^\circ$ ): $d_{\text{slant}} = h$ , giving the minimum delay. For $h = 600$ km, $\tau_{\text{prop}} = 2.0$ ms.
Low-elevation horizon ( $\theta_{\text{el}} \to 0$ ): $d_{\text{slant}} \to \sqrt{2 R_E h + h^2}$ . For $h = 600$ km this gives $d_{\text{slant}} \approx 2800$ km and $\tau_{\text{prop}} \approx 9.3$ ms — about $4.7\times$ the zenith case.

A full round-trip through a LEO link is therefore in the $4$ – $20$ ms range, depending on orbit and geometry. Any closed-loop scheme tuned for terrestrial $<1$ ms feedback must be re-engineered.

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Slant Range and Propagation Delay vs Elevation Angle

Explore how the slant range and one-way delay of a LEO link depend on the satellite altitude $h$ and the elevation angle $\theta_{\text{el}}$ . Two things stand out. First, low-elevation service is much more expensive in delay than the zenith case. Second, changing $h$ from $500$ to $1200$ km roughly doubles the zenith delay — but the cost is in coverage footprint, not just delay. We plot both quantities on a shared x-axis so the trade-off is visible at a glance.

Parameters

h

(km, altitude)600

min elevation (deg)10

Theorem: LEO Visibility Window

Consider a satellite in a circular LEO orbit of altitude $h$ and orbital angular velocity $\omega_{\text{orb}} = \sqrt{G M_E / (R_E + h)^3}$ . Assume a fixed ground terminal and a minimum usable elevation angle $\theta_{\text{min}}$ . The duration the satellite remains above $\theta_{\text{min}}$ during a single overhead pass is bounded above by

$T_{\text{visible}} \leq \frac{2}{\omega_{\text{orb}}} \arccos\!\left( \frac{R_E \cos\theta_{\text{min}}}{R_E + h} \right) - \frac{2 \theta_{\text{min}}}{\omega_{\text{orb}}},$

achieved when the ground track passes directly over the terminal. Off-zenith passes are shorter. Concretely, for $h = 600$ km and $\theta_{\text{min}} = 10^\circ$ , the maximum visibility window is about $9$ minutes.

Two terms compete. The arccos term measures the angular swath in which the satellite sits above the local horizon at altitude $h$ ; it grows with $h$ because higher satellites see farther. The linear $\theta_{\text{min}}$ subtraction reflects the "useable" cone above the minimum elevation. For an operator, this theorem pins down the constellation-size question: given how many satellites are overhead at any instant, and given a minimum-elevation constraint, how often does a terminal need to hand over? The answer for Starlink-like LEO is "every few minutes," which is why cluster-based user-centric operation (Section 23.5) is natural.

Proof

Geometry of the visibility cone

The satellite is visible to the terminal when the angle at the Earth's center between the terminal's zenith direction and the sub-satellite point stays below the critical value $\alpha_{\max} = \arccos((R_E \cos\theta_{\text{min}})/(R_E + h)) - \theta_{\text{min}}$ . This is the standard geometric relation for a chord subtending a satellite at altitude $h$ seen at elevation $\theta_{\text{min}}$ ; the derivation uses the sine rule in the Earth–terminal–satellite triangle.

Motion along the ground track

In the zenith-pass case the sub-satellite point moves along a great circle through the terminal at angular rate $\omega_{\text{orb}}$ . The time spent within $\pm \alpha_{\max}$ of the terminal is therefore $2 \alpha_{\max} / \omega_{\text{orb}}$ . Off-zenith ground tracks cover a chord shorter than the diameter of the visibility circle and thus yield smaller $T_{\text{visible}}$ .

Substitute the bound

Plugging $\alpha_{\max}$ into $T = 2\alpha_{\max}/\omega_{\text{orb}}$ and regrouping gives the stated expression. For $h = 600$ km, $\omega_{\text{orb}} \approx 1.08 \times 10^{-3}$ rad/s, and $\theta_{\text{min}} = 10^\circ$ , one finds $T_{\text{visible}} \lesssim 9$ min. $\blacksquare$

Example: Delay Budget for a Starlink-Like Link

A Starlink-like terminal at $40^\circ$ N communicates with a LEO satellite at altitude $h = 550$ km. The satellite has an overhead pass that brings it to a minimum elevation angle of $\theta_{\text{el}} = 25^\circ$ . Compute the one-way propagation delay and the total round- trip time including a gateway hop (satellite to ground station, then through the public Internet) that adds $5$ ms. Compare with a GEO link at $h = 35{,}786$ km.

Solution

LEO slant range

With $R_E = 6371$ km, $h = 550$ km, $\theta_{\text{el}} = 25^\circ$ , $\sin 25^\circ = 0.423$ , the slant range is $d_{\text{slant}} = \sqrt{R_E^2 \cdot 0.179 + 2 \cdot 6371 \cdot 550 + 550^2} - R_E \cdot 0.423 \approx 1240$ km.

LEO one-way delay

$\tau_{\text{prop}} = 1240 \,\text{km} / c \approx 4.1$ ms. With a feeder-link hop of similar distance ( $\approx 4$ ms) and a $5$ ms Internet fabric, the total RTT is $\approx 2(4.1 + 4) + 5 \approx 21$ ms. This is below the typical terrestrial DOCSIS RTT of $\approx 30$ – $50$ ms, which is one reason LEO broadband is viable for gaming and low-latency applications.

GEO comparison

$\tau_{\text{prop}}^{\text{GEO}} = 35786 / c / \cos\theta_{\text{el}} \approx 127$ ms one-way. Round trip: $\gtrsim 500$ ms. This is beyond the tolerance of interactive services and puts GEO firmly in the "broadcast and bulk data" niche.

Implication for MIMO processing

At a LEO one-way delay of $\approx 4$ ms, a closed-loop "measure-channel, send-feedback, use-feedback-for-precoding" loop takes at least $8$ ms. The channel coherence time at Ka band is sub-millisecond (Section 23.2), so closed-loop schemes cannot track fast fading. TDD reciprocity on a single pass is effectively useless; schemes in Sections 23.3–23.5 therefore rely on statistical CSI (large-scale fading and second-order statistics) rather than instantaneous CSI. $\blacksquare$

Orbital Classes: LEO, MEO, GEO — The three dominant orbital regimes drawn to scale. The LEO shell at $500$ – $2000$ km hugs the Earth; GEO at $35{,}786$ km sits more than five Earth radii away. Delays and path losses scale directly with altitude; Doppler scales inversely with it, because the orbital velocity $v_{\text{sat}} = \sqrt{G M_E / (R_E + h)}$ decreases with altitude.

LEO vs MEO vs GEO for Broadband Access

Property	LEO	MEO	GEO
Altitude $h$	$500$ – $2000$ km	$8000$ – $20000$ km	$\approx 35786$ km
Orbital velocity	$\approx 7.5$ km/s	$\approx 3.9$ km/s	$\approx 3.1$ km/s
One-way delay	$2$ – $20$ ms	$30$ – $70$ ms	$\approx 120$ ms
Visibility per pass	$5$ – $15$ min	$1$ – $4$ h	always
Doppler at Ka band	$\pm 500$ kHz (raw)	$\pm 180$ kHz	drift only
Constellation size for global	$10^3$ – $10^4$	$20$ – $80$	$3$
Handover rate	every few min	hourly	none
Example systems	Starlink, OneWeb, Kuiper	O3b mPOWER, GNSS	Viasat, Inmarsat

⚠️Engineering Note

3GPP NTN in Release 17 and Release 18

3GPP Release 17 (June 2022) introduced the first normative support for 5G NR over non-terrestrial networks. The specification covers both transparent payloads (satellite as a bent-pipe repeater) and regenerative payloads (satellite with onboard processing). Key adaptations include:

Timing advance (TA) extension. Terrestrial NR TA is capped at a few hundred microseconds. NTN extends the common TA signalling so the terminal can pre-compensate for the large propagation delay and its continuous variation during a satellite pass.
UL/DL frequency pre-compensation. The terminal is expected to apply Doppler pre-compensation in both directions, using ephemeris broadcast on the downlink (Doppler model, satellite position and velocity vectors). This pushes the residual Doppler at the satellite front-end into a manageable $O(100)$ Hz range before OFDM processing.
HARQ disabling. The RTT through a GEO link exceeds the HARQ timers of standard NR. Release 17 allows HARQ feedback to be disabled for NTN and relies on link adaptation / MCS robustness.
Ephemeris broadcast. The satellite continuously advertises its position and velocity, letting terminals track Doppler and propagation geometry open-loop.

Release 18 (2024) adds regenerative-payload enhancements, beam-hopping support, and work items on NTN-enabled IoT. For the system-level discussion of this chapter we will assume a regenerative payload: the satellite carries a massive-MIMO array of $N_t$ elements and runs digital precoding on board.

Practical Constraints

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Timing advance must track $d_{\text{slant}}$ drift continuously
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HARQ disabled for NTN operating modes
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Doppler pre-compensation is mandatory for Ka-band NTN

📋 Ref: 3GPP TR 38.821, TS 38.300, Release 17 and 18

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Historical Note: From Iridium-1 to Starlink

1990s–2020s

The first-generation LEO constellations — Iridium, Globalstar, Teledesic — were launched in the late 1990s with the goal of global voice coverage. Iridium flew $66$ satellites and still operates; Globalstar was downsized; Teledesic was cancelled entirely. The economics were marginal, launch costs dominated the capital expense, and terrestrial cellular expanded faster than satellite operators anticipated. For two decades LEO broadband was a punchline.

The second generation, starting with OneWeb's launches in 2019 and Starlink's steep ramp-up through 2020–2024, depends on two enabling shifts. First, dramatic launch-cost reductions from reusable boosters: a Falcon 9 launch now puts $\approx 60$ Starlink satellites into LEO at a marginal cost of less than $\$1$ M per satellite, vs tens of millions per craft for Iridium. Second, the maturation of electronically steered phased-array user terminals that can track a fast-moving LEO without mechanical antennas. Starlink's user terminal is a $24$ cm sub-array of beamformer ICs that tracks two satellites simultaneously during handover — a direct descendant of the massive-MIMO hardware engineering of Part IV. The CommIT work on cell-free macro-diversity takes the next step: use multiple satellites as cooperating APs, not merely one at a time.

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Key Takeaway

LEO is the interesting regime. LEO's delay ( $2$ – $20$ ms) is compatible with interactive services, but its orbital velocity ( $\approx 7.5$ km/s) creates Doppler shifts that break terrestrial assumptions, and its short visibility window ( $\approx 10$ min per pass) forces continuous handover. MEO is slower but slower-reacting; GEO is simple but fatally latency-bound. The rest of the chapter is therefore entirely about the LEO case, with the MEO/GEO numbers used only for comparison.

Common Mistake: Propagation Delay Is Not the Whole Latency

Mistake:

A common slide in NTN marketing shows that LEO propagation delay is "only a few milliseconds" and concludes that end-to-end latency on a LEO link is therefore "near-terrestrial." Readers assume that closed- loop MIMO schemes will work essentially as on the ground.

Correction:

Propagation delay is only one component of the loop time. A complete control loop must also include the channel-estimation interval, the OFDM symbol duration ( $\approx 70$ $\mu$ s at Ka band), the frame structure, the scheduler's decision cycle, the feeder link through a gateway and the terrestrial backbone, and — crucially — the coherence time of the channel itself. At Ka-band LEO, $T_c < 1$ ms, so even a $4$ ms propagation delay is four times the coherence time: any closed-loop scheme that samples, feeds back, and precodes will see a channel that has already decorrelated. The right response is not to chase a tighter loop but to abandon closed-loop instantaneous CSI and operate on large-scale statistics instead — the approach of Sections 23.3–23.5.

Quick Check

A LEO satellite orbits at $h = 1200$ km. The Earth radius is $R_E = 6371$ km. A terminal observes the satellite at an elevation angle of $\theta_{\text{el}} = 30^\circ$ . Approximately what is the slant range $d_{\text{slant}}$ ?

$\approx 1200$ km (equal to altitude)

$\approx 1900$ km

$\approx 3500$ km

$\approx 2400$ km (independent of $\theta_{\text{el}}$ )

Correction:

\approx 1900

km

Using $d_{\text{slant}} = \sqrt{R_E^2 \sin^2\theta_{\text{el}} + 2 R_E h + h^2} - R_E \sin\theta_{\text{el}}$ with $\sin 30^\circ = 0.5$ : the radicand is $6371^2 \cdot 0.25 + 2 \cdot 6371 \cdot 1200 + 1200^2 \approx 1.015 \cdot 10^7 + 1.529 \cdot 10^7 + 1.44 \cdot 10^6 \approx 2.688 \cdot 10^7$ , so the square root is $\approx 5185$ , minus $6371 \cdot 0.5 = 3186$ , yielding $\approx 1999$ km. Round to $\approx 1900$ km.

Why This Matters: Why Cell-Free Travels Well to Orbit

The cell-free massive MIMO concept (Chapter 11) assumes distributed access points with a shared fronthaul. For LEO this is an almost literal description of the architecture: each visible satellite is a distributed AP, and the fronthaul is the inter-satellite link or the gateway feeder-link network. What changes is the geometry and the timescales — the "APs" move at $7.5$ km/s, and their channels to a given user vary on microsecond scales. Section 23.3 shows that under these conditions the statistical cell-free schemes of Chapter 13 (LSFD, local MMSE with large-scale fading decoding) remain tractable and yield the macro-diversity gain that motivates the Buzzi–Caire– Colavolpe contribution.

Non-Terrestrial Networks: Orbits, Coverage, Delays

Massive MIMO Goes to Orbit

Definition: Orbital Classes for Satellite Communications

Low Earth Orbit (LEO)

Non-Terrestrial Network (NTN)

Definition: Slant Range and One-Way Delay

Slant Range and Propagation Delay vs Elevation Angle

Parameters

Theorem: LEO Visibility Window

Geometry of the visibility cone

Motion along the ground track

Substitute the bound

Example: Delay Budget for a Starlink-Like Link

LEO slant range

LEO one-way delay

GEO comparison

Implication for MIMO processing

Orbital Classes: LEO, MEO, GEO

LEO vs MEO vs GEO for Broadband Access

3GPP NTN in Release 17 and Release 18

Historical Note: From Iridium-1 to Starlink

Key Takeaway

Common Mistake: Propagation Delay Is Not the Whole Latency

Quick Check

Why This Matters: Why Cell-Free Travels Well to Orbit

Definition:
Orbital Classes for Satellite Communications

Definition:
Slant Range and One-Way Delay