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Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signals, or two digital bit streams, by changing (''modulating'') the amplitudes of two carrier waves, using the amplitude-shift keying (ASK) digital modulation scheme or
amplitude modulation Amplitude modulation (AM) is a modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the amplitude (signal strength) of the wave is varied in proportion to ...
(AM) analog modulation scheme. The two carrier waves are of the same frequency and are out of phase with each other by 90°, a condition known as
orthogonality In mathematics, orthogonality is the generalization of the geometric notion of ''perpendicularity''. By extension, orthogonality is also used to refer to the separation of specific features of a system. The term also has specialized meanings in ...
or quadrature. The transmitted signal is created by adding the two carrier waves together. At the receiver, the two waves can be coherently separated (demodulated) because of their orthogonality property. Another key property is that the modulations are low-frequency/low-bandwidth waveforms compared to the carrier frequency, which is known as the narrowband assumption. Phase modulation (analog PM) and
phase-shift keying Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at a ...
(digital PSK) can be regarded as a special case of QAM, where the amplitude of the transmitted signal is a constant, but its phase varies. This can also be extended to frequency modulation (FM) and
frequency-shift keying Frequency-shift keying (FSK) is a frequency modulation scheme in which digital information is transmitted through discrete frequency changes of a carrier signal. The technology is used for communication systems such as telemetry, weather ball ...
(FSK), for these can be regarded as a special case of phase modulation. QAM is used extensively as a modulation scheme for digital telecommunication systems, such as in 802.11 Wi-Fi standards. Arbitrarily high spectral efficiencies can be achieved with QAM by setting a suitable
constellation A constellation is an area on the celestial sphere in which a group of visible stars forms Asterism (astronomy), a perceived pattern or outline, typically representing an animal, mythological subject, or inanimate object. The origins of the e ...
size, limited only by the noise level and linearity of the communications channel.  QAM is being used in optical fiber systems as bit rates increase; QAM16 and QAM64 can be optically emulated with a 3-path
interferometer Interferometry is a technique which uses the ''interference'' of superimposed waves to extract information. Interferometry typically uses electromagnetic waves and is an important investigative technique in the fields of astronomy, fiber op ...
.


Demodulation of QAM

In a QAM signal, one carrier lags the other by 90°, and its amplitude modulation is customarily referred to as the in-phase component, denoted by The other modulating function is the
quadrature component In electrical engineering, a sinusoid with angle modulation can be decomposed into, or synthesized from, two amplitude-modulated sinusoids that are offset in phase by one-quarter cycle (90 degrees or /2 radians). All three functions have the s ...
, So the composite waveform is mathematically modeled as: :s_s(t) \triangleq \sin(2\pi f_c t) I(t)\ +\ \underbrace_\; Q(t),     or: where is the carrier frequency.  At the receiver, a coherent demodulator multiplies the received signal separately with both a cosine and
sine In mathematics, sine and cosine are trigonometric functions of an angle. The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is oppo ...
signal to produce the received estimates of and . For example: :r(t) \triangleq s_c(t) \cos (2 \pi f_c t) = I(t) \cos (2 \pi f_c t) \cos (2 \pi f_c t) - Q(t) \sin (2 \pi f_c t) \cos (2 \pi f_c t). Using standard trigonometric identities, we can write this as: :\begin r(t) &= \tfrac I(t) \left + \cos (4 \pi f_c t)\right- \tfrac Q(t) \sin (4 \pi f_c t) \\ &= \tfrac I(t) + \tfrac \left (t) \cos (4 \pi f_c t) - Q(t) \sin (4 \pi f_c t)\right \end Low-pass filtering removes the high frequency terms (containing ), leaving only the term. This filtered signal is unaffected by showing that the in-phase component can be received independently of the quadrature component.  Similarly, we can multiply by a sine wave and then low-pass filter to extract The addition of two sinusoids is a linear operation that creates no new frequency components. So the bandwidth of the composite signal is comparable to the bandwidth of the DSB (Double-Sideband) components. Effectively, the spectral redundancy of DSB enables a doubling of the information capacity using this technique. This comes at the expense of demodulation complexity. In particular, a DSB signal has zero-crossings at a regular frequency, which makes it easy to recover the phase of the carrier sinusoid. It is said to be
self-clocking In telecommunications and electronics, a self-clocking signal is one that can be decoded without the need for a separate clock signal or other source of synchronization. This is usually done by including embedded synchronization information withi ...
. But the sender and receiver of a quadrature-modulated signal must share a clock or otherwise send a clock signal. If the clock phases drift apart, the demodulated ''I'' and ''Q'' signals bleed into each other, yielding
crosstalk In electronics, crosstalk is any phenomenon by which a signal transmitted on one circuit or channel of a transmission system creates an undesired effect in another circuit or channel. Crosstalk is usually caused by undesired capacitive, induc ...
. In this context, the clock signal is called a "phase reference". Clock synchronization is typically achieved by transmitting a burst
subcarrier A subcarrier is a sideband of a radio frequency carrier wave, which is modulated to send additional information. Examples include the provision of colour in a black and white television system or the provision of stereo in a monophonic radio broa ...
or a pilot signal. The phase reference for NTSC, for example, is included within its
colorburst Colorburst is an analog video, composite video signal generated by a video-signal generator used to keep the chrominance subcarrier synchronized in a color television signal. By synchronizing an oscillator with the colorburst at the back porc ...
signal. Analog QAM is used in: * NTSC and PAL analog
color television Color television or Colour television is a television transmission technology that includes color information for the picture, so the video image can be displayed in color on the television set. It improves on the monochrome or black-and-white t ...
systems, where the I- and Q-signals carry the components of chroma (colour) information. The QAM carrier phase is recovered from a special colorburst transmitted at the beginning of each scan line. *
C-QUAM C-QUAM (Compatible QUadrature Amplitude Modulation) is the method of AM stereo broadcasting used in Canada, the United States and most other countries. It was invented in 1977 by Norman Parker, Francis Hilbert, and Yoshio Sakaie, and published i ...
("Compatible QAM") is used in AM stereo radio to carry the stereo difference information.


Fourier analysis of QAM

In the frequency domain, QAM has a similar spectral pattern to
DSB-SC Double-sideband suppressed-carrier transmission (DSB-SC) is transmission in which frequencies produced by amplitude modulation (AM) are symmetrically spaced above and below the carrier frequency and the carrier level is reduced to the lowest pra ...
modulation. Applying Euler's formula to the sinusoids in , the positive-frequency portion of (or
analytic representation In mathematics and signal processing, an analytic signal is a complex-valued function that has no negative frequency components.  The real and imaginary parts of an analytic signal are real-valued functions related to each other by the Hilber ...
) is: : s_c(t)_+ = \tfrac e^ (t) + i Q(t) \quad\stackrel\quad \tfrac\left widehat(f - f_c) + e^ \widehat Q(f - f_c)\right where \mathcal denotes the Fourier transform, and and are the transforms of and This result represents the sum of two DSB-SC signals with the same center frequency. The factor of represents the 90° phase shift that enables their individual demodulations.


Digital QAM

As in many digital modulation schemes, the constellation diagram is useful for QAM. In QAM, the constellation points are usually arranged in a square grid with equal vertical and horizontal spacing, although other configurations are possible (e.g. a hexagonal or triangular grid). In digital telecommunications the data is usually binary, so the number of points in the grid is typically a power of 2 (2, 4, 8, …), corresponding to the number of bits per symbol. The simplest and most commonly used QAM constellations consist of points arranged in a square, i.e. 16-QAM, 64-QAM and 256-QAM (even powers of two). Non-square constellations, such as Cross-QAM, can offer greater efficiency but are rarely used because of the cost of increased modem complexity. By moving to a higher-order constellation, it is possible to transmit more bits per
symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different conc ...
. However, if the mean energy of the constellation is to remain the same (by way of making a fair comparison), the points must be closer together and are thus more susceptible to noise and other corruption; this results in a higher bit error rate and so higher-order QAM can deliver more data less reliably than lower-order QAM, for constant mean constellation energy. Using higher-order QAM without increasing the bit error rate requires a higher
signal-to-noise ratio Signal-to-noise ratio (SNR or S/N) is a measure used in science and engineering that compares the level of a desired signal to the level of background noise. SNR is defined as the ratio of signal power to the noise power, often expressed in deci ...
(SNR) by increasing signal energy, reducing noise, or both. If data-rates beyond those offered by 8- PSK are required, it is more usual to move to QAM since it achieves a greater distance between adjacent points in the I-Q plane by distributing the points more evenly. The complicating factor is that the points are no longer all the same amplitude and so the
demodulator Demodulation is extracting the original information-bearing signal from a carrier wave. A demodulator is an electronic circuit (or computer program in a software-defined radio) that is used to recover the information content from the modulated ...
must now correctly detect both
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform * Phase space, a mathematic ...
and amplitude, rather than just phase. 64-QAM and 256-QAM are often used in
digital cable Digital cable is the distribution of cable television using digital data and video compression. The technology was first developed by General Instrument. By 2000, most cable companies offered digital features, eventually replacing their previou ...
television and
cable modem A cable modem is a type of network bridge that provides bi-directional data communication via radio frequency channels on a hybrid fibre-coaxial (HFC), radio frequency over glass (RFoG) and coaxial cable infrastructure. Cable modems are primaril ...
applications. In the United States, 64-QAM and 256-QAM are the mandated modulation schemes for
digital cable Digital cable is the distribution of cable television using digital data and video compression. The technology was first developed by General Instrument. By 2000, most cable companies offered digital features, eventually replacing their previou ...
(see QAM tuner) as standardised by the
SCTE The Society of Cable Telecommunications Engineers or SCTE is a non-profit professional association for the advancement of technology, standards and workforce education related to cable telecommunications engineering. Founded in 1969 as The Societ ...
in the standar
ANSI/SCTE 07 2013
Note that many marketing people will refer to these as QAM-64 and QAM-256. In the UK, 64-QAM is used for digital terrestrial television (
Freeview Freeview may refer to: *Freeview (Australia), the marketing name for the digital terrestrial television platform in Australia *Freeview (New Zealand), a digital satellite and digital terrestrial television platform in New Zealand *Freeview (UK), a ...
) whilst 256-QAM is used for Freeview-HD. Communication systems designed to achieve very high levels of spectral efficiency usually employ very dense QAM constellations. For example, current Homeplug AV2 500-Mbit/s powerline Ethernet devices use 1024-QAM and 4096-QAM, as well as future devices using ITU-T
G.hn G.hn is a specification for home networking with data rates up to 2 Gbit/s and operation over four types of legacy wires: telephone wiring, coaxial cables, power lines and plastic optical fiber. A single G.hn semiconductor device is able to net ...
standard for networking over existing home wiring (
coaxial cable Coaxial cable, or coax (pronounced ) is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric ( insulating material); many coaxial cables also have a p ...
,
phone line A telephone line or telephone circuit (or just line or circuit industrywide) is a single-user circuit on a telephone communication system. It is designed to reproduce speech of a quality that is understandable. It is the physical wire or ot ...
s and power lines); 4096-QAM provides 12 bits/symbol. Another example is ADSL technology for copper twisted pairs, whose constellation size goes up to 32768-QAM (in ADSL terminology this is referred to as bit-loading, or bit per tone, 32768-QAM being equivalent to 15 bits per tone). Ultra-high capacity Microwave Backhaul Systems also use 1024-QAM.http://www.trangosys.com/products/point-to-point-wireless-backhaul/licensed-wireless/trangolink-apex-orion.shtml A Apex Orion With 1024-QAM,
adaptive coding and modulation Link adaptation, comprising adaptive coding and modulation (ACM) and others (such as Power Control), is a term used in wireless communications to denote the matching of the modulation, coding and other signal and protocol parameters to the conditio ...
(ACM) and XPIC, vendors can obtain gigabit capacity in a single 56 MHz channel.


Interference and noise

In moving to a higher order QAM constellation (higher data rate and mode) in hostile RF/ microwave QAM application environments, such as in broadcasting or telecommunications, multipath interference typically increases. There is a spreading of the spots in the constellation, decreasing the separation between adjacent states, making it difficult for the receiver to decode the signal appropriately. In other words, there is reduced noise immunity. There are several test parameter measurements which help determine an optimal QAM mode for a specific operating environment. The following three are most significant: *
Carrier Carrier may refer to: Entertainment * ''Carrier'' (album), a 2013 album by The Dodos * ''Carrier'' (board game), a South Pacific World War II board game * ''Carrier'' (TV series), a ten-part documentary miniseries that aired on PBS in April 20 ...
/interference ratio *
Carrier-to-noise ratio In telecommunications, the carrier-to-noise ratio, often written CNR or ''C/N'', is the signal-to-noise ratio (SNR) of a modulated signal. The term is used to distinguish the CNR of the radio frequency passband signal from the SNR of an analog ba ...
* Threshold-to-noise ratio


See also

*
Amplitude and phase-shift keying Amplitude and phase-shift keying (APSK) is a digital modulation scheme that conveys data by modulating both the amplitude and the phase of a carrier wave. In other words, it combines both amplitude-shift keying (ASK) and phase-shift keying (PSK) ...
or
asymmetric phase-shift keying Amplitude and phase-shift keying (APSK) is a digital modulation scheme that conveys data by modulating both the amplitude and the phase of a carrier wave. In other words, it combines both amplitude-shift keying (ASK) and phase-shift keying (P ...
(APSK) *
Carrierless amplitude phase modulation Carrierless amplitude phase modulation (CAP) is a variant of quadrature amplitude modulation (QAM). Instead of modulating the amplitude of two carrier waves, CAP generates a QAM signal by combining two PAM signals filtered through two filters desig ...
(CAP) * * In-phase and quadrature components *
Modulation In electronics and telecommunications, modulation is the process of varying one or more properties of a periodic waveform, called the ''carrier signal'', with a separate signal called the ''modulation signal'' that typically contains informatio ...
for other examples of modulation techniques *
Phase-shift keying Phase-shift keying (PSK) is a digital modulation process which conveys data by changing (modulating) the phase of a constant frequency reference signal (the carrier wave). The modulation is accomplished by varying the sine and cosine inputs at a ...
* QAM tuner for HDTV *
Random modulation In the theories of modulation and of stochastic processes, random modulation is the creation of a new signal from two other signals by the process of quadrature amplitude modulation. In particular, the two signals are considered as being random proc ...


References


Further reading

*Jonqyin (Russell) Sun "Linear diversity analysis for QAM in Rician fading channels", IEEE WOCC 2014 *''John G. Proakis'', "''Digital Communications, 3rd Edition''"


External links


QAM Demodulation

Interactive webdemo of QAM constellation with additive noise
Institute of Telecommunicatons, University of Stuttgart
QAM bit error rate for AWGN channel – online experiment

How imperfections affect QAM constellation

Microwave Phase Shifters
Overview by Herley General Microwave
Simulation of dual-polarization QPSK (DP-QPSK) for 100G optical transmission
{{DEFAULTSORT:Quadrature Amplitude Modulation Radio modulation modes Data transmission