Data communication

Baseband, and the case for a carrier

Send a signal in its own natural range of frequencies and you are transmitting at baseband. A telephone landline does exactly this, speech from about 300 Hz to 3.4 kHz travelling down a private pair of wires, and on a private wire baseband is fine. Radio has no private wires. Every transmitter shares the same air, and if each station broadcast baseband audio they would all occupy the same few kilohertz and land on top of one another.

There is a second, more physical objection. An efficient aerial needs to be a respectable fraction of a wavelength long, and a 3 kHz radio wave is 100 km long. Nobody builds that aerial. Both problems fall to the same trick: print the programme onto a high-frequency carrier wave. The carrier's short wavelength suits real aerials, and each station is allotted its own carrier frequency, so a tuned circuit at the receiver, resonance from earlier in this unit, can select one station and reject the rest. Printing the programme on is called modulation, and the two classic schemes divide this lesson between them.

Amplitude modulation

Amplitude modulation keeps the carrier frequency f_c$f_{c}$f_c fixed and makes its amplitude follow the programme, loud passages swelling the envelope. The surprise is what this does to the spectrum. Modulate a carrier with a single audio tone of frequency f_M$f_{M}$f_M and you transmit exactly three frequencies, the carrier itself plus two sidebands at f_c + f_M$f_{c} + f_{M}$f_c + f_M and f_c - f_M$f_{c} - f_{M}$f_c - f_M. The audio is not sent at its own frequency; it appears as the pair of new frequencies flanking the carrier.

Real programmes are a band of tones up to some maximum audio frequency f_M$f_{M}$f_M, so each sideband spreads into a band, and the transmission occupies everything from f_c - f_M$f_{c} - f_{M}$f_c - f_M to f_c + f_M$f_{c} + f_{M}$f_c + f_M. The occupied width is the bandwidth:

Frequency modulation

Frequency modulation holds the amplitude constant and swings the carrier's frequency instead, above and below f_c$f_{c}$f_c in step with the programme. Louder audio swings it further; the maximum swing is the frequency deviation Δf$\Delta f$Δf. An FM signal's sidebands in truth trail off indefinitely, so the occupied band is an estimate covering the deviation and the modulating structure on top of it, Carson's rule:

What does 180 kHz achieve? Noise, whether from motors, lightning or distant sparks, adds to a wave's amplitude. An AM receiver reads the amplitude, so it faithfully reproduces the noise. An FM receiver reads only the frequency, and it clips the amplitude flat before detection, removing most amplitude noise; noise that disturbs the wave's apparent frequency or phase survives in smaller measure, and the advantage holds only while the signal stays comfortably above the receiver's working threshold.

FM also carries audio to 15 kHz rather than 4.5, and its constant amplitude lets the transmitter run steadily at full efficiency. AM's advantage is economy, a twentieth of the spectrum per station and receivers simple enough to build with a diode.

Sending numbers instead: sampling and PCM

The last lesson argued that digital signals shrug off noise and can be regenerated without loss. To give an analogue signal those advantages, digitise it. Step one is sampling, measuring the signal's value at regular instants. Sample too rarely and wiggles between samples are missed entirely, and the rule has a sharp edge. The sampling rate must be greater than twice the highest frequency present in the signal. Sampled slower than that, a high frequency masquerades as a low one and the corruption cannot be undone afterwards.

Step two is quantisation. Each sample is rounded to the nearest of 2ⁿ$2^{n}$2^n fixed levels, and the level is named by an n-bit binary code. The rounding error is the quantisation error, shrunk by adding bits, since each extra bit doubles the number of levels and halves the step between them. The stream of codes, sent as pulses, is pulse-code modulation, PCM. From then on the signal enjoys every digital privilege, regeneration included, and noise stops accumulating along the route.

Ground wave, sky wave, space wave

Modulated or digitised, a radio signal still has to get there, and how it travels is decided by its frequency rather than by what is written on it. Below about 2 MHz the wave follows the ground. It induces currents in the conducting surface underneath, and that drag tilts the wavefront so the wave leans round the curve of the Earth, while its long wavelength diffracts it round hills and buildings. Those same induced currents are what attenuate it, since the ground takes energy from the wave, and it takes more the higher the frequency. Long wave reaches a thousand kilometres or so by this ground wave, medium wave a few hundred.

Between roughly 3 MHz and 30 MHz the wave leaves the ground and meets the ionosphere, layers of gas that solar ultraviolet has ionised from about 60 km upward. The free electrons there lower the refractive index, and since the ionisation increases with height the wave is refracted progressively, bending further and further until it is turned back towards the ground. It lands hundreds or thousands of kilometres away, and can reflect off the ground for a second hop. That is the sky wave, and it is how short wave crosses an ocean with no repeater in between.

Two consequences follow from where the sky wave comes from. The ionosphere is made by sunlight, so it thins at night and shifts with the solar cycle, and the frequency a station can use moves with it. And between the range where the ground wave fades out and the point where the sky wave first comes back down lies a skip zone that hears nothing at all.

Above about 30 MHz the ionosphere no longer bends the wave enough to return it and the ground wave has long since given up, so what is left travels in a nearly straight line from one aerial to the other. That is the space wave, and the horizon is its limit. Height is the only way to extend it, which is why television and FM masts stand on hills and why a hand-held marine radio reaches tens of kilometres and no further. The failure to be turned back is also the opportunity: a wave the ionosphere cannot hold on to is a wave that can be sent straight out to a satellite.

Up to the satellite and back down

A communications satellite is a repeater in orbit. The earth station transmits on the uplink frequency, the satellite's transponder amplifies what it hears, shifts it to a different downlink frequency and sends it back, and both are far above 30 MHz so that the ionosphere lets them through rather than turning them round. Typical pairs are 6 GHz up with 4 GHz down, or 14 GHz up with 11 GHz down.

The two frequencies have to differ, and the reason is plain enough. The satellite receives microwatts and transmits watts from the same small structure, so if it retransmitted on the frequency it was listening to, its own output would swamp its own receiver and the transponder would howl like a microphone held in front of its loudspeaker.

Which of the two is made the lower is a separate decision, and power settles it. Atmospheric attenuation depends on the band, and across the microwave bands these links use it worsens towards higher frequency, rain fade above all, while the satellite runs its transmitter on whatever its solar panels supply and the earth station can afford a large dish and a kilowatt. The weaker end of the link, the downlink, is therefore given the lower and less attenuated frequency.

Sharing the channel, choosing the medium

One cable or one band is always shared, and there are two ways to slice it. Frequency-division multiplexing gives each user a permanent slice of the spectrum, every broadcaster transmitting continuously on its own carrier, which is precisely how the radio dial works. Time-division multiplexing gives each user the whole channel for a brief repeating time slot. Digital signals suit TDM perfectly: each user is assigned a short repeating slot in a fixed frame, the calls take strict turns on the one channel, and because digital samples compress into brief bursts, thirty phone calls interleave without colliding.

The comparison that scores is argued through attenuation and bandwidth. Fibre loses least per kilometre, so its repeaters are furthest apart; it carries the most, and being an insulator carrying light it ignores electrical interference completely. Copper is the cheap incumbent for the last mile. Radio is the only choice when the receiver moves, and the drawback is a shared, weather-dependent medium in which whatever you transmit can be received by anyone.

Who else is listening

Radio does not choose its audience. Everything transmitted arrives at every receiver in range, a shared cable can be tapped anywhere along its length, and fibre, the hardest of the three to intercept, is only hard rather than impossible. Since no medium can be trusted to keep a secret, the protection has to travel inside the data.

Encryption is the first half of it. Before transmission the bit stream is combined with a key by a reversible rule, and what goes out carries the same information in a form that nobody without the key can read. The receiver holds the matching key and undoes the operation exactly, so the message arrives intact while an interceptor collects every bit and learns nothing from any of them. The security sits in the secrecy of the key, and the method itself is assumed to be public knowledge, since a rule kept secret only stays secret until somebody takes a receiver apart.

Authentication is the other half, and it answers a different question. Encryption stops an eavesdropper reading the traffic; it does nothing to stop somebody transmitting a message of their own and claiming to be you. So the sender computes a short check value from the whole message together with a secret key and sends it alongside, and the receiver recomputes it from what arrived. A match says two things at once: the message came from a holder of that key, and not one bit of it was altered on the way. A mismatch means one of those has failed, and the receiver throws the block away instead of acting on it.

Keep both apart from error checking. A parity bit or a checksum catches the accidental corruption a noisy channel causes, and it is designed to be easy to recompute, so anyone who deliberately alters the message simply recomputes the checksum to match. Only a key nobody else holds makes the check unforgeable, which is the difference between detecting an accident and defeating an opponent.