Amplitude-shift_keying

# Amplitude-shift keying **Amplitude-shift keying** is a digital modulation method that carries data by switching the amplitude of a fixed-frequency carrier wave between two or more discrete levels, leaving its phase and frequency unchanged. In the most common form, one level is switched off entirely, so a symbol is either "carrier present" or "carrier absent," a scheme usually called on-off keying. The microsim on this page lets the reader push the modulation depth toward that on-off extreme, add channel noise, and watch a simple envelope detector's recovered waveform close in on, and eventually cross, the threshold that separates a correctly decoded bit from a wrong one. ASK is the amplitude-based counterpart to [[Frequency-shift_keying|frequency-shift keying]] and [[Phase-shift_keying|phase-shift keying]], the other two classical ways of keying a sinusoidal carrier, and it is the oldest of the three: the earliest practical radiotelegraphy, keying a spark-gap or continuous-wave transmitter fully on and off in Morse code, is on-off keying in its simplest possible form. Because the information rides entirely in the envelope, a receiver can recover it with a diode and a low-pass filter rather than a coherent [[Phase-locked_loop|phase-locked loop]], which keeps ASK receivers inexpensive even though the scheme gives up performance for that simplicity. That performance gap is the subject of the second half of this article: switching a carrier fully off wastes no power sending a "0," but it also means that symbol carries no [[Signal-to-noise_ratio|signal-to-noise ratio]] margin of its own, a cost that other forms of [[Signal_modulation|digital carrier modulation]] do not have to pay in the same way. ## Method An ASK transmitter builds its signal as `s(t) = A(t) * cos(2*pi*fc*t)`, where the carrier frequency `fc` and phase never move and all of the information sits in the envelope `A(t)`, which switches between a low level `A0` and a high level `A1` as the bit stream calls for a 0 or a 1. The depth of modulation, `depth = 1 - A0/A1`, describes how far apart the two levels sit: at depth 0 the two symbols are identical and no information gets through at all, and at depth 1 the low level disappears entirely, which is the special case called on-off keying (OOK). ASK is, in this sense, ordinary [[Amplitude_modulation|amplitude modulation]] restricted to a small number of discrete levels rather than a continuously varying message, the same restriction that let the earliest spark-gap and continuous-wave radiotelegraphy transmitters send Morse code simply by switching fully on and off.[^cn-history] Because the data lives entirely in the envelope, a receiver can recover it non-coherently with an envelope detector — a rectifier followed by a low-pass filter that tracks the envelope's slower variation and discards the fast carrier oscillation underneath it — and then a simple voltage comparison against a threshold set halfway between the two levels, `threshold = (A0 + A1) / 2`. This is about the cheapest possible digital receiver: it needs no local oscillator locked to the incoming carrier's phase and no [[Phase-locked_loop|phase-locked loop]], only a diode-like nonlinearity and a filter. A coherent receiver can also be built, multiplying the incoming signal against a locally generated, phase-matched copy of the carrier before filtering and thresholding, and it performs somewhat better in noise, but at the cost of the carrier-recovery circuitry ASK is usually chosen specifically to avoid. The gap between the two levels, `A1 - A0`, is the "eye opening" that noise has to close before a bit flips, and it is the single number that governs how forgiving the link is: a deep modulation index opens that eye wide and is easy to detect but wastes no energy sending a 0, so half the transmitted symbols carry no signal at all to fight the [[Noise_(electronics)|noise]] floor with. A shallow modulation index keeps some energy in every symbol at the cost of a narrower eye and a link more sensitive to any drift in the receiver's threshold. Multilevel ASK generalises the same idea to more than two amplitudes, carrying `log2 M` bits per symbol at the cost of packing the levels closer together on a fixed power budget; modulating both the amplitude and the phase of the same carrier at once — the strategy behind quadrature amplitude modulation — packs in still more bits per symbol by treating the constellation as a two-dimensional grid rather than a single ring. Because an envelope detector is so simple to build, ASK and on-off keying turn up wherever the receiver, not the transmitter, has to stay cheap. Optical fibre links overwhelmingly use on-off keying of a laser's intensity, since a photodiode is naturally a square-law envelope detector and needs no separate optical phase reference to recover a bit; short-range radio-frequency identification tags and simple remote controls for garage doors and similar consumer devices use ASK or OOK for the same reason, trading the deep-fade vulnerability that comes from carrying data in amplitude for a receiver a battery-powered tag can afford. Near-field contactless cards and tags typically use ASK in both directions of a single link — a strong, deeply modulated signal from the reader to power and address the tag, and a much shallower, load-modulated echo from the tag back to the reader — because a coil that can only load or not load the reader's own field has no other convenient way to answer. That fade vulnerability is ASK's characteristic weakness: any part of the channel that attenuates the signal unevenly, which a multipath radio channel or a bent, aging fibre both do, moves the received amplitude around in exactly the dimension the data is encoded in, in a way a frequency- or phase-based scheme does not share. Sharper transitions between `A0` and `A1` also spread more energy into a wider band, so practical designs round off the switch between levels over some fraction of a symbol rather than switching instantly, trading a slightly slower transition for a narrower occupied spectrum. ## Probability of error On-off keying detected coherently has bit-error probability `P_b = Q(sqrt(Eb/N0))`, the same functional form as [[Phase-shift_keying|BPSK]]'s formula but needing twice the energy per bit — 3 dB more [[Signal-to-noise_ratio|signal-to-noise ratio]] — to hold the same error rate, because half of OOK's symbols spend no energy at all and so contribute nothing to the average while still being counted in it.[^ell148] Detected non-coherently, with an envelope detector rather than a phase-locked receiver, on-off keying's bit-error probability becomes `P_b = (1/2)*exp(-Eb/(2*N0))`, a curve that costs only about another decibel beyond the coherent case[^ell150] — a small enough penalty that almost no OOK system pays the much higher price of coherent detection just to recover it. That roughly one-decibel gap between coherent and non-coherent detection is the number this article's probability curves are really built around: it is why on-off keying is normally built as the cheapest possible receiver rather than as a coherent one, since the benefit on offer from adding a [[Phase-locked_loop|phase-locked loop]] is small next to what depth and noise are already costing the link. Multilevel ASK extends the same error analysis to more than two amplitude levels, with a closed-form bit-error probability of its own;[^ell152] as with higher-order PSK, packing more levels into the same power budget crowds them together and demands more signal-to-noise ratio for the same reliability, so ASK's headline weakness — no energy at all on its lowest symbol — only gets worse as more levels are added, never better, which is why a real M-ASK design pairs the amplitude axis with forward error correction far more readily than a comparable M-PSK design does. The same one-decibel gap is why cheap consumer ASK devices almost always choose the non-coherent receiver: coherent detection's advantage is real but small, and it is easily swamped by exactly the deep, amplitude-domain fades a real channel introduces, and that a phase- or frequency-based [[Signal_modulation|modulation]] would ride through untouched. ## Microsims The primary microsim plots the modulated carrier and its recovered envelope on one time axis, with the decoded bit stream below it. **DEPTH** sets how far the low level sits below the high one, from no modulation at all up to full on-off keying; **CYCLES/BIT** sets how many carrier cycles fill one symbol; **NOISE** adds Gaussian noise to the carrier before it is rectified and smoothed into an envelope. A "randomize bits" button refills the bit pattern, and an "animate" toggle drifts the carrier's phase slowly so the noisy trace keeps moving instead of sitting still. The recovered bit stream is drawn under the waveform with any bit that crosses the threshold on the wrong side of its intended level marked in a different colour, so pushing depth toward its maximum while raising noise visibly narrows the eye until decoded bits start flipping. A three.js companion renders the same on-off-keyed signal as two points on the in-phase axis of a [[Constellation_diagram|constellation]]. *Try:* Set DEPTH to its maximum, on-off keying, then raise NOISE until the recovered bit stream starts showing errors — watch that the errors appear on the low-amplitude symbols first, where the eye is narrowest. ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Amplitude-shift_keying) : [Wikitube](https://en.wikitube.io/wiki/Amplitude-shift_keying) Skeleton mirrored at revision 1374492652. Prose, emphasis and the microsims are Wikitube's own. ## See also - [[Constellation_diagram]] - [[Amplitude_modulation]] - [[Frequency-shift_keying]] - [[Phase-shift_keying]] - [[Phase-locked_loop]] - [[Signal-to-noise_ratio]] - [[Signal_modulation]] ## References [^ell148]: Ellingson, S. *Radio Systems Engineering – Revised First Edition*. 2023, pp. 148–149 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^ell150]: Ellingson, S. *Radio Systems Engineering – Revised First Edition*. 2023, p. 150 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^ell152]: Ellingson, S. *Radio Systems Engineering – Revised First Edition*. 2023, p. 152 (PDF pages). Open Textbook Library: https://open.umn.edu/opentextbooks/textbooks/radio-systems-engineering . CC BY-NC. [^cn-history]: Citation needed: a primary source (inventor, publication or patent, and date) for the earliest on-off-keyed continuous-wave or spark-gap radiotelegraphy. ## External links - [Amplitude-shift keying (live sketch)](https://editor.p5js.org/sciencenibber/full/-MG6jnt4_) - [Amplitude-shift keying (editor)](https://editor.p5js.org/sciencenibber/sketches/-MG6jnt4_)