The previous lesson made the case for going digital. This one answers the practical question it left open: once the message is a stream of bits, how do you actually put them on a radio carrier? A sine wave has exactly three properties you can change — its amplitude, its frequency, and its phase. Switch any one of them between discrete states, one state per symbol, and you have a digital modulation. Those three choices give the three foundational schemes: ASK, FSK, and PSK. Everything more advanced — QAM in the next lessons, the schemes inside WiFi and 5G — is built from them.
In AM and FM (Modules 3 and 4) the carrier property varied continuously, tracking an analog message instant by instant. Digital modulation instead switches the carrier between a small, fixed set of states — one state held for the duration of each symbol. That switching gives these schemes the name keying, from telegraph keys: amplitude-shift keying, frequency-shift keying, phase-shift keying. For a binary scheme there are two states, so each symbol carries exactly one bit.
The simplest idea: send the carrier at one amplitude for a 1 and a different amplitude for a 0. The extreme case turns the carrier fully off for a 0 — On-Off Keying (OOK), the most common form of ASK:
That simplicity is ASK’s whole appeal: it is cheap to build and cheap to receive. But it inherits AM’s fatal weakness (Lesson 3.4): noise arrives as an amplitude disturbance, and ASK’s message is an amplitude, so noise attacks the information directly. It is also non-constant-envelope, which forces a linear power amplifier — less efficient than the class-C amplifiers FM enjoyed. ASK survives where those costs do not matter: infrared remote controls, passive RFID tags, garage-door openers, and simple on-off optical fiber links.
Keep the amplitude fixed and switch the frequency instead: a high tone for a 1, a low tone for a 0. Because the amplitude never changes, FSK is a constant-envelope signal — and that single fact carries most of its advantages. A constant envelope can be pushed through an efficient, non-linear class-C amplifier without distortion, and it is immune to amplitude noise and to the amplitude-fading that plagues ASK.
The price is bandwidth: FSK occupies at least the span between its two tones plus the sidebands of each, so it is wider than ASK or PSK carrying the same bit rate. A Carson-style estimate gives roughly 2Δf + 2Rb, where Δf is the tone separation. Smoothing the frequency transitions with a Gaussian filter (GFSK) tightens the spectrum; that is the flavour Bluetooth uses. FSK also appears in pagers, caller-ID, low-cost ISM-band sensors, and the earliest telephone modems.
Hold both amplitude and frequency constant and switch the phase. The binary case, BPSK, flips the carrier 180° between symbols — a 1 is the cosine, a 0 is its exact negative:
Like FSK, BPSK is constant-envelope. Unlike FSK, it is also bandwidth-thrifty and has the best noise performance of any binary scheme — the two facts that make phase the property modern systems key most often.
Nothing says a phase has to flip only between two values. QPSK uses four phases, 90° apart, and so carries two bits per symbol. The reward is decisive: with Gray coding (Lesson 5.4), QPSK has the same bit-error rate as BPSK at the same energy per bit, yet sends each bit in half the symbols — so it needs half the bandwidth for the same bit rate. That free doubling of spectral efficiency is why QPSK, not BPSK, is the workhorse of satellite links, WiFi, and cellular control channels.
The fair way to compare schemes is by bit-error rate (BER) against Eb/N0 — the energy spent per bit divided by the noise power spectral density. With coherent detection over an AWGN channel, the results collapse into two families:
Because the factor of 2 lives inside the square root, BPSK/QPSK reach any target BER at half the Eb/N0 that ASK or FSK need — a 3 dB advantage (Lesson 2.4: halving a ratio is −3 dB). Put plainly: to hit a one-in-a-million error rate, PSK needs roughly 3 dB less signal power than the other two. That is the quantitative reason phase keying dominates.
| Scheme | Keys | Bits / symbol | Envelope | BER (coherent) | Null-to-null BW | Typical use |
|---|---|---|---|---|---|---|
| ASK / OOK | Amplitude | 1 | Varies | Q(√(E⃗/N₀)) | 2R⃗ | RFID, IR remotes, optical on-off |
| BFSK | Frequency | 1 | Constant | Q(√(E⃗/N₀)) | > 2R⃗ | Bluetooth (GFSK), pagers, caller-ID |
| BPSK | Phase | 1 | Constant | Q(√(2E⃗/N₀)) | 2R⃗ | GPS, deep-space, control channels |
| QPSK | Phase | 2 | Constant | Q(√(2E⃗/N₀)) | R⃗ | Satellite, WiFi, LTE/5G |
Bandwidths are null-to-null main-lobe widths for rectangular pulses, with Rb the bit rate; pulse shaping (Lesson 6.2) narrows them all. FSK’s width grows with the tone separation Δf.
Why “constant envelope” keeps appearing. FSK, BPSK, and QPSK all hold their amplitude fixed. That lets the transmitter use a class-C power amplifier at ~70% efficiency — the same efficiency win FM claimed over AM in Lesson 4.4 — because there is no amplitude information to distort. ASK cannot; its amplitude is the message. In battery-powered radios that efficiency often matters more than the raw BER.