Editing Signal modulation (section)

==Digital modulation methods==
<!-- This section is linked from [[Phase-shift keying]] -->

In [[Digital data|digital]] modulation, an analog carrier signal is modulated by a discrete signal. Digital modulation methods can be considered as digital-to-analog conversion and the corresponding [[demodulation]] or detection as analog-to-digital conversion. The changes in the carrier signal are chosen from a finite number of M alternative symbols (the ''modulation alphabet'').

[[File:baud.svg|thumb|right|200px|Schematic of 4 baud, 8 bit/s data link containing arbitrarily chosen values]]

<blockquote>'''A simple example:''' A telephone line is designed for transferring audible sounds, for example, tones, and not digital bits (zeros and ones). Computers may, however, communicate over a telephone line by means of modems, which are representing the digital bits by tones, called symbols. If there are four alternative symbols (corresponding to a musical instrument that can generate four different tones, one at a time), the first symbol may represent the bit sequence 00, the second 01, the third 10 and the fourth 11. If the modem plays a melody consisting of 1000 tones per second, the [[symbol rate]] is 1000 symbols/second, or 1000 [[baud]]. Since each tone (i.e., symbol) represents a message consisting of two digital bits in this example, the [[bit rate]] is twice the symbol rate, i.e. 2000 bits per second.</blockquote>

According to one definition of [[digital signal]],<ref>{{Cite web|title=Modulation Methods {{!}} Electronics Basics {{!}} ROHM|url=https://www.rohm.com/electronics-basics/wireless/modulation-methods|website=www.rohm.com|access-date=2020-05-15}}</ref> the modulated signal is a digital signal. According to another definition, the modulation is a form of [[digital-to-analog conversion]]. Most textbooks would consider digital modulation schemes as a form of [[digital transmission]], synonymous to data transmission; very few would consider it as [[analog transmission]].{{cn|date=September 2024}}

===Fundamental digital modulation methods===
The most fundamental digital modulation techniques are based on [[keying (telecommunications)|keying]]:
* [[Phase-shift keying|PSK (phase-shift keying)]]: a finite number of phases are used.
* [[Frequency-shift keying|FSK (frequency-shift keying)]]: a finite number of frequencies are used.
* [[Amplitude-shift keying|ASK (amplitude-shift keying)]]: a finite number of amplitudes are used.
* [[Quadrature amplitude modulation|QAM (quadrature amplitude modulation)]]: a finite number of at least two phases and at least two amplitudes are used.

In QAM, an in-phase signal (or I, with one example being a cosine waveform) and a quadrature phase signal (or Q, with an example being a sine wave) are amplitude modulated with a finite number of amplitudes and then summed. It can be seen as a two-channel system, each channel using ASK. The resulting signal is equivalent to a combination of PSK and ASK.

In all of the above methods, each of these phases, frequencies or amplitudes are assigned a unique pattern of [[Binary numeral system|binary]] [[bit]]s. Usually, each phase, frequency or amplitude encodes an equal number of bits. This number of bits comprises the ''symbol'' that is represented by the particular phase, frequency or amplitude.

If the alphabet consists of <math>M = 2^N </math> alternative symbols, each symbol represents a message consisting of ''N'' bits. If the [[symbol rate]] (also known as the [[baud rate]]) is <math>f_{S}</math> symbols/second (or [[baud]]), the data rate is <math>N f_{S}</math> bit/second.

For example, with an alphabet consisting of 16 alternative symbols, each symbol represents 4 bits. Thus, the data rate is four times the baud rate.

In the case of PSK, ASK or QAM, where the carrier frequency of the modulated signal is constant, the modulation alphabet is often conveniently represented on a [[constellation diagram]], showing the amplitude of the I signal at the x-axis, and the amplitude of the Q signal at the y-axis, for each symbol.

===Modulator and detector principles of operation===
PSK and ASK, and sometimes also FSK, are often generated and detected using the principle of QAM. The I and Q signals can be combined into a [[complex-valued]] signal ''I''+''jQ'' (where ''j'' is the [[imaginary unit]]). The resulting so called [[equivalent lowpass signal]] or [[equivalent baseband signal]] is a complex-valued representation of the [[real-valued]] modulated physical signal (the so-called [[passband signal]] or [[RF signal]]).

These are the general steps used by the [[modulator]] to transmit data:
# Group the incoming data bits into codewords, one for each symbol that will be transmitted.
# Map the codewords to attributes, for example, amplitudes of the I and Q signals (the equivalent low pass signal), or frequency or phase values.
# Adapt [[pulse shaping]] or some other filtering to limit the bandwidth and form the spectrum of the equivalent low pass signal, typically using digital signal processing.
# Perform digital to analog conversion (DAC) of the I and Q signals (since today all of the above is normally achieved using [[digital signal processing]], DSP).
# Generate a high-frequency sine carrier waveform, and perhaps also a cosine quadrature component. Carry out the modulation, for example by multiplying the sine and cosine waveform with the I and Q signals, resulting in the equivalent low pass signal being frequency shifted to the modulated [[passband signal]] or RF signal. Sometimes this is achieved using DSP technology, for example [[direct digital synthesis]] using a [[waveform table]], instead of analog signal processing. In that case, the above DAC step should be done after this step.
# Amplification and analog bandpass filtering to avoid harmonic distortion and periodic spectrum.

At the receiver side, the [[demodulator]] typically performs:
# Bandpass filtering.
# [[Automatic gain control]], AGC (to compensate for [[attenuation]], for example [[fading]]).
# Frequency shifting of the RF signal to the equivalent baseband I and Q signals, or to an intermediate frequency (IF) signal, by multiplying the RF signal with a local oscillator sine wave and cosine wave frequency (see the [[superheterodyne receiver]] principle).
# Sampling and analog-to-digital conversion (ADC) (sometimes before or instead of the above point, for example by means of [[undersampling]]).
# Equalization filtering, for example, a [[matched filter]], compensation for multipath propagation, time spreading, phase distortion and frequency selective fading, to avoid [[intersymbol interference]] and symbol distortion.
# Detection of the amplitudes of the I and Q signals, or the frequency or phase of the IF signal.
# Quantization of the amplitudes, frequencies or phases to the nearest allowed symbol values.
# Mapping of the quantized amplitudes, frequencies or phases to codewords (bit groups).
# Parallel-to-serial conversion of the codewords into a bit stream.
# Pass the resultant bit stream on for further processing such as removal of any error-correcting codes.

As is common to all digital communication systems, the design of both the modulator and demodulator must be done simultaneously. Digital modulation schemes are possible because the transmitter-receiver pair has prior knowledge of how data is encoded and represented in the communications system. In all digital communication systems, both the modulator at the transmitter and the demodulator at the receiver are structured so that they perform inverse operations.

Asynchronous methods do not require a receiver reference clock signal that is [[phase synchronisation|phase synchronized]] with the sender [[carrier signal]]. In this case, modulation symbols (rather than bits, characters, or data packets) are [[asynchronous communication|asynchronously]] transferred. The opposite is [[Bit-synchronous operation|synchronous modulation]].

===List of common digital modulation techniques===
The most common digital modulation techniques are:
* [[Phase-shift keying]] (PSK)
** Binary PSK (BPSK), using M=2 symbols
** Quadrature PSK (QPSK), using M=4 symbols
** 8PSK, using M=8 symbols
** 16PSK, using M=16 symbols
** Differential PSK (DPSK)
** Differential QPSK (DQPSK)
** Offset QPSK ([[OQPSK]])
** π/4–QPSK
* [[Frequency-shift keying]] (FSK)
** [[Audio frequency-shift keying]] (AFSK)
** [[Multi-frequency shift keying]] (M-ary FSK or MFSK)
** [[Dual-tone multi-frequency signaling]] (DTMF)
* [[Amplitude-shift keying]] (ASK)
* [[On-off keying]] (OOK), the most common ASK form
** M-ary [[vestigial sideband modulation]], for example [[8VSB]]
* [[Quadrature amplitude modulation]] (QAM), a combination of PSK and ASK
** [[Polar modulation]] like QAM a combination of PSK and ASK{{Citation needed|date=October 2008}}
* [[Continuous phase modulation]] (CPM) methods
** [[Minimum-shift keying]] (MSK)
** [[Gaussian minimum-shift keying]] (GMSK)
** [[Continuous-phase frequency-shift keying]] (CPFSK)
* [[Orthogonal frequency-division multiplexing]] (OFDM) modulation
** [[Discrete multitone]] (DMT), including adaptive modulation and bit-loading
* [[Wavelet modulation]]
* [[Trellis coded modulation]] (TCM), also known as [[Trellis modulation]]
* [[Spread spectrum]] techniques
** [[Direct-sequence spread spectrum]] (DSSS)
** [[Chirp spread spectrum]] (CSS) according to IEEE 802.15.4a CSS uses pseudo-stochastic coding
** [[Frequency-hopping spread spectrum]] (FHSS) applies a special scheme for channel release

[[Minimum-shift keying|MSK]] and [[GMSK]] are particular cases of continuous phase modulation. Indeed, MSK is a particular case of the sub-family of CPM known as [[continuous-phase frequency-shift keying]] (CPFSK) which is defined by a rectangular frequency pulse (i.e. a linearly increasing phase pulse) of one-symbol-time duration (total response signaling).

[[OFDM]] is based on the idea of [[frequency-division multiplexing]] (FDM), but the multiplexed streams are all parts of a single original stream. The bit stream is split into several parallel data streams, each transferred over its own sub-carrier using some conventional digital modulation scheme. The modulated sub-carriers are summed to form an OFDM signal. This dividing and recombining help with handling channel impairments. OFDM is considered as a modulation technique rather than a multiplex technique since it transfers one bit stream over one communication channel using one sequence of so-called OFDM symbols. OFDM can be extended to multi-user [[channel access method]] in the [[orthogonal frequency-division multiple access]] (OFDMA) and [[multi-carrier code-division multiple access]] (MC-CDMA) schemes, allowing several users to share the same physical medium by giving different sub-carriers or [[spreading code]]s to different users.

Of the two kinds of [[RF power amplifier]], [[switching amplifier]]s ([[Class D amplifier]]s) cost less and use less battery power than [[linear amplifier]]s of the same output power. However, they only work with relatively constant-amplitude-modulation signals such as angle modulation (FSK or PSK) and [[CDMA]], but not with QAM and OFDM. Nevertheless, even though switching amplifiers are completely unsuitable for normal QAM constellations, often the QAM modulation principle are used to drive switching amplifiers with these FM and other waveforms, and sometimes QAM demodulators are used to receive the signals put out by these switching amplifiers.

===Automatic digital modulation recognition (ADMR)===
Automatic digital modulation recognition in intelligent communication systems is one of the most important issues in [[software-defined radio]] and [[cognitive radio]]. According to incremental expanse of intelligent receivers, automatic modulation recognition becomes a challenging topic in telecommunication systems and computer engineering. Such systems have many civil and military applications. Moreover, blind recognition of modulation type is an important problem in commercial systems, especially in [[software-defined radio]]. Usually in such systems, there are some extra information for system configuration, but considering blind approaches in intelligent receivers, we can reduce information overload and increase transmission performance. Obviously, with no knowledge of the transmitted data and many unknown parameters at the receiver, such as the signal power, carrier frequency and phase offsets, timing information, etc., blind identification of the modulation is made fairly difficult. This becomes even more challenging in real-world scenarios with multipath fading, frequency-selective and time-varying channels.<ref>
{{cite journal
 | title = Survey of automatic modulation classification techniques: classical approaches and new trends
 | author = Dobre, Octavia A., Ali Abdi, Yeheskel Bar-Ness, and Wei Su. Communications, IET 1, no. 2 (2007): 137–156.
 | journal= IET Communications
 | volume = 1
 | issue = 2
 | year = 2007
 | pages = 137–156
 | url = http://web.njit.edu/~abdi/IEE_COM0176_WithFigures.pdf
 | doi = 10.1049/iet-com:20050176
 }}</ref>

There are two main approaches to automatic modulation recognition. The first approach uses likelihood-based methods to assign an input signal to a proper class. Another recent approach is based on feature extraction.

===Digital baseband modulation===
Digital baseband modulation changes the characteristics of a baseband signal, i.e., one without a carrier at a higher frequency.

This can be used as equivalent signal to be later [[Frequency mixer|frequency-converted]] to a carrier frequency, or for direct communication in baseband. The latter methods both involve relatively simple [[line code]]s, as often used in local buses, and complicated baseband signalling schemes such as used in [[DSL]].