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8.5 — Satellite and Fibre: The Backbones
Almost every byte you receive from another continent travels through a strand of glass on the seabed. Satellite carries a tiny fraction of the traffic and an enormous fraction of the coverage — the places where cable cannot go.
This chapter is both, and why the division between them is the way it is.
The fibre half of this chapter runs on total internal reflection from Volume IV Chapter 5.1; the satellite half runs on the orbital mechanics of Volume IV Chapter 1.9, which is where the 35 786 km geostationary altitude and its quarter-second round trip come from.
1. Optical fibre
How light stays inside
A fibre is a glass core surrounded by cladding with a slightly lower refractive index.
Snell's law says light bends when crossing a boundary between materials of different index. Beyond a critical angle it does not cross at all — it reflects entirely back into the core:
\theta_c=\arcsin\frac{n_2}{n_1}
Worked example. Core index 1.4675, cladding 1.4625 — a difference of about 0.3%:
\theta_c=\arcsin\frac{1.4625}{1.4675}=\arcsin(0.99659)=85.3°
So light within 4.7° of the axis stays inside, bouncing along the fibre for kilometres with essentially no loss at the boundary.
The numerical aperture describes the acceptance cone:
NA=\sqrt{n_1^2-n_2^2}=\sqrt{1.4675^2-1.4625^2}=\sqrt{0.01465}=0.121
\theta_{max}=\arcsin(0.121)=6.9°
A narrow cone, which is why fibre connectors must be aligned to within a fraction of a micrometre and why a dirty or misaligned connector is the most common fault in any fibre installation.
Single mode and multimode
Multimode fibre has a core 50 or 62.5 µm across — wide enough that light can travel by many distinct paths, or modes.
The problem is that different modes take different path lengths, so a pulse launched together arrives spread out. That is modal dispersion, and it limits multimode fibre to a few hundred metres at gigabit rates.
Graded-index fibre reduces it by grading the refractive index so it falls smoothly from the centre outward. Light travelling a longer path spends more time in the lower-index outer region, where it moves faster — so the transit times partly equalise. It buys about a factor of ten.
Single-mode fibre has a core of only 8 to 10 µm — comparable to the wavelength itself, so only one mode can propagate at all. No modal dispersion.
The trade is entirely practical: single mode reaches thousands of kilometres, and its tiny core needs precise connectors and expensive laser sources. Multimode is cheap, uses LEDs or cheap lasers, and is confined to buildings.
\text{cutoff}: \quad V=\frac{2\pi a}{\lambda}NA \lt 2.405
The 2.405 is the first zero of a Bessel function, the same one that appeared in Chapter 7.2's FM sidebands — the mathematics of a circular waveguide and of frequency modulation share this constant, which is a pleasant coincidence rather than a deep connection.
Loss, and the three windows
Fibre loss comes from two mechanisms with opposite frequency dependence, and their sum creates the usable windows.
Rayleigh scattering off microscopic density variations in the glass, falling as 1/\lambda^4 — so short wavelengths scatter badly.
Infrared absorption by the glass's own molecular vibrations, rising steeply above 1600 nm.
Between them is a minimum, and the practical windows are:
| Wavelength | Loss | Use |
|---|---|---|
| 850 nm | 3 dB/km | multimode, short links |
| 1310 nm | 0.35 dB/km | zero dispersion point |
| 1550 nm | 0.19 dB/km | minimum loss — long haul |
0.19 dB/km is a remarkable number. Over 100 km that is 19 dB — the signal falls to 1.3% of what was launched, which is nothing compared with the 60 dB per 100 m that Chapter 7.7 quoted for coaxial cable at 1 GHz.
Put differently: light entering a fibre travels about 20 km before losing half its power. Glass this transparent would let you see through a window ten kilometres thick.
The old "water peak" at 1383 nm came from hydroxyl ion contamination and blocked a band. Modern low-water-peak fibre eliminates it, opening the whole 1260 to 1625 nm range for WDM.
Dispersion
Even in single-mode fibre, a pulse spreads.
Chromatic dispersion. A laser is not perfectly monochromatic, and different wavelengths travel at slightly different speeds.
\Delta t=D\cdot L\cdot\Delta\lambda
with D around 17 ps/(nm·km) at 1550 nm.
Worked example. A 100 km link, a laser with 0.1 nm of linewidth:
\Delta t=17\times100\times0.1=170\ \text{ps}
At 10 Gbit/s the bit period is 100 ps, so the pulse has spread beyond its own slot and into the next. Dispersion, not loss, is the limit at high rates.
Three fixes:
- Dispersion-compensating fibre with the opposite sign of D, spliced in periodically to unwind the spreading.
- Dispersion-shifted fibre, engineered to have zero dispersion at 1550 nm rather than 1310. Its drawback is that zero dispersion makes nonlinear mixing between WDM channels much worse, so it is now avoided for WDM systems — a case where fixing one problem created a bigger one.
- Coherent detection with digital signal processing, which measures the phase and undoes the dispersion computationally. This is what all modern long-haul systems do, and it is the same equalisation idea as Chapter 7.3 applied to light.
Polarisation mode dispersion comes from slight asymmetry in the fibre, making the two polarisation states travel at different speeds. It varies randomly with temperature and stress, so it cannot be compensated by a fixed device — only adaptively.
Amplification
Before 1990, every 40 km needed a regenerator: convert light to electricity, reshape and retime the signal, convert back. Expensive, and it fixed the data rate and format of the whole link permanently.
The erbium-doped fibre amplifier, demonstrated in 1987, changed everything. A few metres of fibre doped with erbium ions, pumped by a laser at 980 or 1480 nm. The pump excites the erbium; a passing signal at 1550 nm stimulates emission and is amplified.
Why it mattered so much:
- 20 to 30 dB of gain, so amplifiers can be 80 to 100 km apart.
- It amplifies light directly — no conversion to electricity.
- It amplifies a 30 nm band all at once, so every WDM channel is amplified by one device.
- It is transparent to the data rate and format, so a link can be upgraded from 10 to 100 Gbit/s per channel by changing only the terminal equipment.
That last property is why transatlantic cables laid in the 1990s carry vastly more traffic today than they did when installed — the glass and the amplifiers were never the limit; the electronics at the ends were.
The cost is accumulated noise. Each amplifier adds spontaneous emission, so after a chain of them the optical SNR degrades. The number of spans is limited by noise accumulation, not by loss, and a transoceanic cable with a hundred amplifiers is engineered around that number.
Wavelength division multiplexing
\text{capacity}=N_{channels}\times\text{rate per channel}
Dense WDM packs 80 to 160 channels at 50 or 25 GHz spacing across the amplifier's band.
Worked example. 96 channels at 400 Gbit/s each:
96\times400=38.4\ \text{Tbit/s per fibre pair}
And a cable contains 8 to 24 fibre pairs, so a modern transatlantic cable carries hundreds of terabits per second.
Coherent optical transmission is what pushed per-channel rates this high. Instead of simply switching light on and off, it modulates amplitude and phase in two polarisations, and detects by mixing with a local laser — exactly the superheterodyne principle of Chapter 7.2, at 200 THz. A 400 Gbit/s channel typically uses 16-QAM on two polarisations at 64 GBaud, which is Chapter 7.3's constellation diagram implemented in light.
Submarine cables
About 1.4 million kilometres of cable on the seabed, carrying over 99% of intercontinental data traffic. Satellite carries a fraction of a percent.
Construction: the fibres sit in a steel tube filled with gel, wrapped in steel strength members, a copper conductor and polyethylene insulation. Near shore, armouring is added against anchors and trawlers.
The copper conductor carries power to the amplifiers — up to 15 kV DC, feeding perhaps 150 amplifiers spaced 80 km apart along the cable. A single conductor with the seawater as the return path.
Repairs. A cable ship locates the fault, grapples the cable, hauls it aboard, splices in a new section and lowers it back. Two to four weeks, and there are only about 60 cable ships in the world.
Around 100 to 200 faults occur annually, mostly from fishing gear and anchors in shallow water. The internet keeps working because of route diversity — traffic reroutes over other cables automatically, and the effect is usually invisible except as slightly higher latency.
Latency is set by the speed of light in glass:
v=\frac{c}{1.47}=2.04\times10^8\ \text{m/s}
London to New York, 5,600 km of cable:
t=\frac{5.6\times10^6}{2.04\times10^8}=27.5\ \text{ms one way}
55 ms round trip, and real measurements show 70 to 80 ms because cables do not run in straight lines and routers add delay.
This is why financial firms paid for straighter cables. The Hibernia Express, completed in 2015, cost $300 million to shave about 6 ms off the London-New York round trip, and that was commercially worthwhile for high-frequency trading.
Light does not travel down a fibre in a straight line, and the two ways it can travel instead are what separate the cable running to a house from the cable running under an ocean.
Multi-mode, step index (top). The core is wide — around 50 microns — and light entering at different angles bounces down it by total internal reflection, each angle taking a different path length. A pulse launched as one sharp flash therefore arrives smeared, because the ray that went straight down the middle gets there before the one that zig-zagged. That smearing is called modal dispersion, and it is what limits multi-mode fibre to a few hundred metres.
Multi-mode, graded index (middle). The same idea with a fix: the glass's refractive index falls smoothly from the centre outward, so light straying towards the edge travels through faster glass and catches up. The paths differ in length but not much in time, and the reach improves severalfold.
Single-mode (bottom). The core is shrunk to about 9 microns — only a few wavelengths across — and at that width only one path physically fits. There is nothing to smear, so pulses stay sharp over hundreds of kilometres, and this is what every long-haul and undersea cable uses. The price is that aligning a light source to a 9-micron core is difficult and the connectors are correspondingly expensive.
The narrowing of the core is the same confinement argument as Volume IV Chapter 2.4's string: make the container small enough and only one mode fits.
2. Satellite
The orbits
| Orbit | Altitude | Period | Latency (one way) |
|---|---|---|---|
| LEO | 500–2000 km | 90–120 min | 2–7 ms |
| MEO | 8,000–20,000 km | 6–12 h | 27–67 ms |
| GEO | 35,786 km | 24 h | 119 ms |
Geostationary orbit is at exactly one altitude, because the period must equal one sidereal day:
T=2\pi\sqrt{\frac{r^3}{GM}}=86164\ \text{s} \;\Rightarrow\; r=42{,}164\ \text{km}
Subtracting the earth's radius gives 35,786 km.
A GEO satellite appears motionless from the ground, so a dish can be aimed once and bolted down. That single property is why GEO dominated satellite broadcasting for fifty years.
The cost is latency. 35,786 km up and the same down is 71,572 km:
t=\frac{71{,}572\times10^3}{3\times10^8}=239\ \text{ms one way}
478 ms round trip minimum, before any processing. This is why satellite internet felt broken for interactive use — every click had half a second of unavoidable delay, and TCP's acknowledgement round trips made it worse.
GEO also cannot serve high latitudes. From above 70° the satellite is below the horizon.
LEO constellations solve latency by being 60 times closer, at the cost of needing hundreds or thousands of satellites, since each is visible for only a few minutes and covers a small area.
Starlink: thousands of satellites at 550 km, giving 20 to 40 ms latency. The user terminal is a phased array (Chapter 7.6) that electronically tracks satellites as they cross and hands over between them without moving.
Why now and not in the 1990s. Iridium and Globalstar tried in the 1990s and went bankrupt. Three things changed: launch cost fell by an order of magnitude with reusable rockets, satellites became mass-manufacturable rather than bespoke, and phased arrays became cheap enough for consumers.
The link
The bands, and their trade:
| Band | Frequency | Character |
|---|---|---|
| L | 1–2 GHz | small antennas, low rate, rain-immune |
| C | 4–8 GHz | rain-resistant, large dishes |
| Ku | 12–18 GHz | small dishes, some rain fade |
| Ka | 26–40 GHz | high capacity, significant rain fade |
Rain fade is the dominant operational issue above about 10 GHz. Raindrops are comparable in size to the wavelength and absorb strongly.
Worked example. Ka band at 30 GHz, heavy rain at 25 mm/hour, through a 5 km rain cell:
\text{specific attenuation}\approx4\ \text{dB/km} \;\Rightarrow\; 20\ \text{dB}
Twenty decibels is a factor of 100. The link budget must carry that margin, or the service must degrade gracefully.
Adaptive coding and modulation is the standard answer (Chapter 7.3): in clear sky, use 32-APSK with light coding; in heavy rain, drop to QPSK with rate-1/4 coding. The rate falls by a factor of six and the link stays up, which is far better than a fixed scheme that either wastes capacity or fails.
Uplink power control helps the earth-to-space direction, where the earth station has power available. It cannot help the downlink, since the satellite's power is fixed.
The transponder
A GEO communications satellite carries 24 to 100 transponders, each a receive-amplify-shift-retransmit chain for one block of spectrum.
Bent pipe — the traditional design. Receive at one frequency, amplify, shift to another frequency, retransmit. The satellite understands nothing about the signal, so it works with any modulation and any protocol, and can be upgraded from the ground indefinitely.
Regenerative — demodulate, decode, re-encode, retransmit. Better performance, because noise does not accumulate through the satellite, and it enables onboard switching between beams. The cost is that the satellite is locked to one standard for its fifteen-year life, which is a serious commitment.
Spot beams replaced the old continent-wide coverage. A satellite with 100 narrow beams reuses the same frequency in every non-adjacent beam, multiplying capacity many-fold — the identical argument as cellular frequency reuse in Chapter 8.1, applied from orbit.
Power and lifetime
Solar panels supplying 5 to 20 kW, with batteries for the eclipse periods around the equinoxes when the earth's shadow crosses the satellite.
Station keeping. A GEO satellite drifts from the pull of the sun and moon and from the earth's slight non-sphericity. Thrusters correct it a few times a month, and the fuel supply determines the satellite's life — typically 15 years, ending not because anything has failed but because there is nothing left to manoeuvre with.
At end of life the satellite is boosted to a graveyard orbit 300 km above GEO, because the geostationary belt is a finite and irreplaceable resource.
3. Choosing between them
| Fibre | GEO satellite | LEO satellite | |
|---|---|---|---|
| Latency | lowest | 480 ms round trip | 40–80 ms |
| Capacity | enormous | moderate | moderate per user |
| Cost per bit | lowest | high | medium |
| Coverage | where cable runs | continental | global |
| Deployment | months to years | one launch | many launches |
| Broadcast | poor | excellent | moderate |
Fibre wins wherever it can be laid, on every measure except coverage and broadcast.
Satellite wins for three things and they are genuine:
Places cable cannot reach — ships, aircraft, remote regions, disaster areas where the terrestrial infrastructure is destroyed.
Broadcast. One satellite transmission reaches millions of receivers at no extra cost per receiver. Sending the same television channel to ten million homes over fibre requires ten million streams. This is the one application where the economics are decisively in satellite's favour, and it is why direct-to-home television is still satellite-delivered.
Rapid deployment. A satellite terminal works within hours of arriving.
The honest summary. Fibre carries the traffic; satellite carries the coverage. Over 99% of intercontinental data goes through glass on the seabed, and the popular impression that international communication is a satellite business has been wrong since about 1990.
Chapter 8.6 closes Part 8 with the history that produced all of it, from a device that could barely carry a voice across a room to the network that carries everything.
Every formula above, built from scratch
None of the results in this chapter are worth memorising, because each one can be rebuilt in under a minute from something simpler. What follows is that rebuilding, one result at a time, so the formula and the reason for it sit on the same page as the explanation that needed them.
Fibre
Critical angle and total internal reflection:
\theta_c=\arcsin\frac{n_2}{n_1}
Numerical aperture:
NA=\sqrt{n_1^2-n_2^2}, \qquad \theta_{max}=\arcsin(NA)
For n_1=1.4675, n_2=1.4625: NA = 0.121, acceptance half-angle 6.9°.
Single-mode cutoff:
V=\frac{2\pi a}{\lambda}NA\lt2.405
The 2.405 is the first zero of the Bessel function J_0 — the same constant that gives the FM carrier null in Chapter 7.2.
Loss windows:
| \lambda | Loss |
|---|---|
| 850 nm | 3 dB/km |
| 1310 nm | 0.35 dB/km |
| 1550 nm | 0.19 dB/km |
Rayleigh scattering falls as 1/\lambda^4; infrared absorption rises steeply above 1600 nm. The windows are where their sum is smallest.
At 0.19 dB/km, light travels about 20 km before losing half its power.
Chromatic dispersion:
\Delta t=D\cdot L\cdot\Delta\lambda, \qquad D\approx17\ \text{ps/(nm·km)} \text{ at 1550 nm}
Worked: 100 km, 0.1 nm linewidth gives 170 ps — beyond the 100 ps bit period at 10 Gbit/s, so dispersion, not loss, limits high-rate links.
Propagation speed and latency:
v=\frac{c}{n}=\frac{3\times10^8}{1.47}=2.04\times10^8\ \text{m/s}
London to New York, 5600 km: 27.5 ms one way, 55 ms round trip minimum.
WDM capacity:
C=N_{channels}\times R_{channel}\times N_{fibre\ pairs}
96 channels × 400 Gbit/s = 38.4 Tbit/s per fibre pair.
Satellite
Orbital period:
T=2\pi\sqrt{\frac{r^3}{GM}}, \qquad GM=3.986\times10^{14}\ \text{m}^3/\text{s}^2
Geostationary: T=86{,}164 s (one sidereal day) gives r=42{,}164 km, so altitude 35,786 km.
GEO latency:
t=\frac{2\times35{,}786\times10^3}{3\times10^8}=239\ \text{ms one way}, \qquad 478\ \text{ms round trip}
Slant range from a ground station at elevation angle \varepsilon:
d=\sqrt{R_e^2\sin^2\varepsilon+2R_eh+h^2}-R_e\sin\varepsilon
Free space loss at GEO, 12 GHz:
L=32.4+20\log_{10}(35{,}786)+20\log_{10}(12{,}000)=32.4+91.1+81.6=205\ \text{dB}
Rain attenuation:
A=\gamma_R\times L_{eff}
with specific attenuation \gamma_R in dB/km. At 30 GHz in 25 mm/h rain, roughly 4 dB/km, so a 5 km rain cell costs 20 dB.
Adaptive coding and modulation absorbs it by dropping from 32-APSK with light coding to QPSK with rate-1/4 — a sixfold rate reduction that keeps the link alive.
G/T, the receiver figure of merit:
\frac{G}{T}=G_{antenna}-10\log_{10}(T_{system}) \ \text{dB/K}
Carrier to noise density:
\frac{C}{N_0}=EIRP-L_{path}+\frac GT-10\log_{10}k
with -10\log_{10}k=228.6 dB.
What the next chapter fixes
Chapter 8.6 closes the Part with the system all of this replaced, because the constraints that shaped the telephone network still shape what a voice call sounds like today — including why it sounds worse than the music on the same phone.