NationMaster - Encyclopedia: Quadrature amplitude modulation

AM | SSB | FM | PM | QAM QAM is a three-letter abbreviation with multiple meanings, including: Quadrature amplitude modulation Quality Assurance Management (qam. ... In telecommunications, modulation is the process of varying a periodic waveform, i. ... In telecommunications, modulation is the process of varying a periodic waveform, i. ... Amplitude modulation (AM) is a technique used in electronic communication, most commonly for transmitting information via a radio carrier wave. ... Single-sideband modulation (SSB) is a refinement of the technique of amplitude modulation designed to be more efficient in its use of electrical power and bandwidth. ... In telecommunications, frequency modulation (FM) conveys information over a carrier wave by varying its frequency. ... Phase modulation (PM) is a form of modulation which represents information as variations in the instantaneous phase of a carrier wave. ...

Digital modulation

OOK | ASK | PSK | FSK | MSK | QAM | CPM | TCM | OFDM Digital modulation (also referred to as shift keying) is a modulation in which the modified parameter of the carrier signal can take only discrete values. ... On-off keying (OOK) is a type of modulation that represents digital data as the presence or absence of a carrier wave. ... Amplitude-shift keying (ASK) is a form of modulation which represents digital data as variations in the amplitude of a carrier wave. ... Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). ... It has been suggested that this article or section be merged with audio frequency-shift keying. ... Like the OQPSK modulator (i. ... Continuous phase modulation (CPM) is a method for modulation of data commonly used in wireless modems. ... The introduction to this article provides insufficient context for those unfamiliar with the subject matter. ... Orthogonal Frequency-Division Multiplexing (OFDM) â€” essentially identical to Coded OFDM (COFDM) â€” is a digital multi-carrier modulation scheme, which uses a large number of closely-spaced orthogonal sub-carriers. ...

Spread spectrum

FHSS | DSSS Spread-spectrum telecommunications is a technique in which a signal is transmitted in a bandwidth considerably greater than the frequency content of the original information. ... Frequency-hopping spread spectrum (FHSS) is a spread-spectrum method of transmitting radio signals by rapidly switching a carrier among many frequency channels, using a pseudorandom sequence known to both transmitter and receiver. ... In telecommunications, direct-sequence spread spectrum (DSSS) is a modulation technique. ...

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Quadrature amplitude modulation (QAM) is a modulation scheme which conveys data by changing (modulating) the amplitude of two carrier waves. These two waves, usually sinusoids, are out of phase with each other by 90° and are thus called quadrature carriers—hence the name of the scheme. In telecommunications, modulation is the process of varying a periodic waveform, i. ... For other uses, see Data (disambiguation). ... It has been suggested that pulse amplitude be merged into this article or section. ... This article or section does not adequately cite its references or sources. ... A sine wave or sinusoid is a waveform whose graph is identical to the generalized sine function y = Asin[Ï‰(x âˆ’ Î±)] + C where A is the amplitude, Ï‰ is the angular frequency (2Ï€/P where P is the wavelength), Î± is the phase shift, and C is the vertical offset. ... This article describes the unit of angle. ... Look up quadrature in Wiktionary, the free dictionary. ...

1 Overview
2 Analog QAM
3 Digital QAM
- 3.1 Ideal structure
  - 3.1.1 Transmitter
  - 3.1.2 Receiver
4 Digital QAM performance
- 4.1 Rectangular QAM
  - 4.1.1 Odd-k QAM
- 4.2 Non-rectangular QAM
5 See also
6 External links
7 References

Overview

Like all modulation schemes, QAM conveys data by changing some aspect of a carrier signal, or the carrier wave, (usually a sinusoid) in response to a data signal. In the case of QAM, the amplitude of two waves, 90 degrees out-of-phase with each other (in quadrature) are changed (modulated or keyed) to represent the data signal. In telecommunications, modulation is the process of varying a periodic waveform, i. ... For other uses, see Data (disambiguation). ... This article or section does not adequately cite its references or sources. ... In trigonometry, an ideal sine wave is a waveform whose graph is identical to the generalized sine function y = Asin[ω(x − α)] + C, where A is the amplitude, ω is the angular frequency (2π/P where P is the wavelength), α is the phase shift, and C...

Phase modulation (analog PM) and phase-shift keying (digital PSK) can be regarded as a special case of QAM, where the amplitude of the modulating signal is constant, with only the phase varying. This can also be extended to frequency modulation (FM) and frequency-shift keying (FSK), for these can be regarded a special case of phase modulation. Phase modulation (PM) is a form of modulation which represents information as variations in the instantaneous phase of a carrier wave. ... Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). ... In telecommunications, frequency modulation (FM) conveys information over a carrier wave by varying its frequency. ... It has been suggested that this article or section be merged with audio frequency-shift keying. ...

Analog QAM

Analog QAM: measured PAL colour bar signal on a vector analyser screen.

When transmitting two signals by modulating them with QAM, the transmitted signal will be of the form: Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ...

$s(t) = I (t) cos (2 pi f_0 t) + Q (t) sin (2 pi f_0 t)$ ,

where $I (t)$ and $Q (t)$ are the modulating signals and $f 0$ is the carrier frequency.

At the receiver, these two modulating signals can be demodulated using a coherent demodulator. Such a receiver multiplies the received signal separately with both a cosine and sine signal to produce the received estimates of $I (t)$ and $Q (t)$ respectively. Because of the orthogonality property of the carrier signals, it is possible to detect the modulating signals independently. A demodulator is an electronic circuit used to recover the information content from the carrier wave of a signal. ... A product detector is a type of demodulator used for AM and SSB signals. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... In mathematics, the trigonometric functions are functions of an angle, important when studying triangles and modeling periodic phenomena. ... In mathematics, orthogonal is synonymous with perpendicular when used as a simple adjective that is not part of any longer phrase with a standard definition. ...

In the ideal case $I (t)$ is demodulated by multiplying the transmitted signal with a cosine signal:

$begin{align} r_i(t) = & s(t) cos (2 pi f_0 t) = & I(t) cos (2 pi f_0 t)cos (2 pi f_0 t) + Q(t) sin (2 pi f_0 t)cos (2 pi f_0 t) end{align}$

Using standard trigonometric identities, we can write it as: In mathematics, trigonometric identities are equalities that involve trigonometric functions that are true for all values of the occurring variables. ...

$begin{align} r_i(t) = & frac{1}{2} I(t) left[1 + cos (4 pi f_0 t)right] + frac{1}{2} Q(t) sin (4 pi f_0 t) = & frac{1}{2} I(t) + frac{1}{2} [I(t) cos (4 pi f_0 t) + Q(t) sin (4 pi f_0 t)] end{align}$

Low-pass filtering $r i (t)$ removes the high frequency terms (containing $(4π f 0 t)$ ), leaving only the $I (t)$ term, unaffected by $Q (t)$ . A low-pass filter is a filter that passes low frequencies but attenuates (or reduces) frequencies higher than the cutoff frequency. ...

Similarly, we may multiply $s (t)$ by a sine wave and then low-pass filter to extract $Q (t)$ .

It should be noted that here we assumed that the phase of the received signal is known at the receiver. If the demodulating phase is even a little off, it results in crosstalk between the modulated signals. This issue of carrier synchronization at the receiver must be handled somehow in QAM systems. The coherent demodulator needs to be exactly in phase with the received signal, or otherwise the modulated signals cannot be independently received. For example analog television systems transmit a burst of the transmitting colour subcarrier after each horizontal synchronization pulse for reference. In telecommunication, the term crosstalk (XT) has the following meanings: 1. ... Analog television (or analogue television) encodes television and transports the picture and sound information as an analog signal, that is, by varying the amplitude and/or frequencies of the broadcast signal. ...

Analog QAM is used in NTSC and PAL television systems, where the I- and Q-signals carry the components of chroma (colour) information. "Compatible QAM" or C-QUAM is used in AM stereo radio to carry the stereo difference information. NTSC is the analog television system in use in the United States, Canada, Japan, South Korea, the Philippines, Mexico, and some other countries, mostly in the Americas (see map). ... For other uses, see PAL (disambiguation). ... C-QUAM is the method of AM stereo broadcasting used in Canada, the United States and most other countries. ... AM stereo is any of a number of mutually-incompatible techniques for broadcasting two_channel audio in the mediumwave band in a manner that is compatible with receivers designed for standard amplitude modulation. ...

Digital QAM

Like for many digital modulation schemes, the constellation diagram is a useful representation which is relied upon in this article. A constellation diagram is a representation of a digital modulation scheme in the complex plane. ...

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. Cross-QAM). Since in digital telecommunications the data is usually binary, the number of points in the grid is usually a power of 2 (2,4,8...). Since QAM is usually square, some of these are rare—the most common forms are 16-QAM, 64-QAM, 128-QAM and 256-QAM. By moving to a higher-order constellation, it is possible to transmit more bits per symbol. 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. Telecommunication involves the transmission of signals over a distance for the purpose of communication. ... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... This article is about the unit of information. ... For the Irish mythological figure, see Naoise. ... In telecommunication, an error ratio is the ratio of the number of bits, elements, characters, or blocks incorrectly received to the total number of bits, elements, characters, or blocks sent during a specified time interval. ...

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 must now correctly detect both phase and amplitude, rather than just phase. Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). ... A demodulator is an electronic circuit used to recover the information content from the carrier wave of a signal. ... This article is about a portion of a periodic process. ... It has been suggested that pulse amplitude be merged into this article or section. ...

64-QAM and 256-QAM are often used in digital cable television and cable modem applications. In the US, 64-QAM and 256-QAM are the mandated modulation schemes for digital cable (see QAM tuner) as standardised by the SCTE in the standard ANSI/SCTE 07 2000. Note that many marketing people will refer to these as QAM-64 and QAM-256. In the UK, 16-QAM and 64-QAM are currently used for digital terrestrial television (Freeview and Top Up TV). Digital cable is a term for a type of cable digital television that delivers more channels than possible with analog cable by using digital video compression. ... Motorola Surfboard cable modem A cable modem is a type of modem that provides access to a data signal sent over the cable television infrastructure. ... Motto: (Out Of Many, One) (traditional) In God We Trust (1956 to date) Anthem: The Star-Spangled Banner Capital Washington D.C. Largest city New York City None at federal level (English de facto) Government Federal constitutional republic - President George Walker Bush (R) - Vice President Dick Cheney (R) Independence from... Digital cable is a term for a type of cable digital television that delivers more channels than possible with analog cable by using digital video compression. ... It has been suggested that this article or section be merged with Quadrature amplitude modulation. ... The Society of Cable Telecommunications Engineers (SCTE) is an organization that develops training for cable television installers and engineers; in this role it is analogous to the Society of Broadcast Engineers for broadcast television. ... Digital Terrestrial Television (DTTV or DTT) is an implementation of digital technology to provide a greater number of channels and/or better quality of picture and sound using aerial broadcasts to a conventional antenna (or aerial) instead of a satellite dish or cable connection. ... This article is about the United Kingdom digital terrestrial television service. ... Top Up TV is a pay TV service provided in the United Kingdom. ...

Ideal structure

Transmitter

The following picture shows the ideal structure of a QAM transmitter, with a carrier frequency $f 0$ and $H t$ the frequency response of the transmitter's filter: Carrier frequency is the fundamental frequency used in both amplitude modulation and frequency modulation i. ...

First the flow of bits to be transmitted is split into two equal parts: this process generates two independent signals to be transmitted. They are encoded separately just like they were in an amplitude-shift keying (ASK) modulator. Then one channel (the one "in phase") is multiplied by a cosine, while the other channel ("in quadrature") is multiplied by a sine. This way there is a phase of 90° between them. They are simply added one to the other and sent through the real channel. Image File history File links QAM_transmitter. ... Amplitude-shift keying (ASK) is a form of modulation which represents digital data as variations in the amplitude of a carrier wave. ...

The sent signal can be expressed in the form:

$s(t) = sum_{n=-infty}^{infty} left[ v_c [n] cdot h_t (t - n T_s) cos (2 pi f_0 t) - v_s [n] cdot h_t (t - n T_s) sin (2 pi f_0 t) right],$

where $v c [n]$ and $v s [n]$ are the voltages applied in response to the $n$ ^th symbol to the cosine and sine waves respectively.

Receiver

The receiver simply performs the inverse process of the transmitter. Its ideal structure is shown in the picture below with $H r$ the receive filter's frequency response:

Multiplying by a cosine (or a sine) and by a low-pass filter it is possible to extract the component in phase (or in quadrature). Then there is only an ASK demodulator and the two flows of data are merged back. Image File history File links QAM_receiver. ... Amplitude-shift keying (ASK) is a form of modulation which represents digital data as variations in the amplitude of a carrier wave. ...

In any application, the low-pass filter will be within h_r (t): here it was shown just to be clearer.

Digital QAM performance

The following definitions are needed in determining error rates:

$M$ = Number of symbols in modulation constellation
$E b$ = Energy-per-bit
$E s$ = Energy-per-symbol = $k E b$ with k bits per symbol
$N 0$ = Noise power spectral density (W/Hz)
$P b$ = Probability of bit-error
$P b c$ = Probability of bit-error per carrier
$P s$ = Probability of symbol-error
$P s c$ = Probability of symbol-error per carrier
$Q(x) = frac{1}{sqrt{2pi}}int_{x}^{infty}e^{-t^{2}/2}dt, xgeq{}0$ .

$Q (x)$ is related to the complementary Gaussian error function by: $Q(x) = frac{1}{2}operatorname{erfc}left(frac{x}{sqrt{2}}right)$ , which is the probability that x will be under the tail of the Gaussian PDF towards positive infinity. This article is about the unit of information. ... In science, and especially in physics and telecommunication, noise is fluctuations in and the addition of external factors to the stream of target information (signal) being received at a detector. ... In physics, the spectral density, or more correctly the power spectral density (PSD) of a given bandwidth of electromagnetic radiation is the total power in this bandwidth divided by the specified bandwidth. ... For other uses, see Watt (disambiguation). ... MHZ redirects here. ... Probability is the likelihood that something is the case or will happen. ... Plot of the error function In mathematics, the error function (also called the Gauss error function) is a non-elementary function which occurs in probability, statistics and partial differential equations. ... In mathematics, a probability density function (pdf) is a function that represents a probability distribution in terms of integrals. ... The infinity symbol âˆž in several typefaces. ...

The error-rates quoted here are those in additive white Gaussian noise (AWGN). ]] selectivity, interference, nonlinearity or dispersion. ... Calculated spectrum of a generated approximation of white noise White noise is a random signal (or process) with a flat power spectral density. ... Gaussian noise is noise that has a probability density function (pdf) of the normal distribution (a. ... In communications, the additive white Gaussian noise (AWGN) channel is one in which the only impairment is the linear addition of wideband Gaussian noise with a constant spectral density (expressed as watts per hertz of bandwidth). ...

Where coordinates for constellation points are given in this article, note that they represent a non-normalised constellation. That is, if a particular mean average energy were required (e.g. unit average energy), the constellation would need to be linearly scaled. See Cartesian coordinate system or Coordinates (elementary mathematics) for a more elementary introduction to this topic. ...

Rectangular QAM

Constellation diagram for rectangular 16-QAM.

Rectangular QAM constellations are, in general, sub-optimal in the sense that they do not maximally space the constellation points for a given energy. However, they have the considerable advantage that they may be easily transmitted as two pulse amplitude modulation (PAM) signals on quadrature carriers, and can be easily demodulated. The non-square constellations, dealt with below, achieve marginally better bit-error rate (BER) but are harder to modulate and demodulate. Image File history File links 16QAM_Gray_Coded. ... Image File history File links 16QAM_Gray_Coded. ... A constellation diagram is a representation of a digital modulation scheme in the complex plane. ... Pulse-amplitude modulation, acronym PAM, is a form of signal modulation where the message information is encoded in the amplitude of a series of signal pulses. ...

The first rectangular QAM constellation usually encountered is 16-QAM, the constellation diagram for which is shown here. A Gray coded bit-assignment is also given. The reason that 16-QAM is usually the first is that a brief consideration reveals that 2-QAM and 4-QAM are in fact binary phase-shift keying (BPSK) and quadrature phase-shift keying (QPSK), respectively. Also, the error-rate performance of 8-QAM is close to that of 16-QAM (only about 0.5dB better), but its data rate is only three-quarters that of 16-QAM. The reflected binary code, also known as Gray code after Frank Gray, is a binary numeral system where two successive values differ in only one digit. ... Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). ... Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). ...

Expressions for the symbol error-rate of rectangular QAM are not hard to derive but yield rather unpleasant expressions. For an even number of bits per symbol, $k$ , exact expressions are available. They are most easily expressed in a per carrier sense:

$P_{sc} = 2left(1 - frac{1}{sqrt M}right)Qleft(sqrt{frac{3}{M-1}frac{E_s}{N_0}}right)$ ,

$,P_s = 1 - left(1 - P_{sc}right)^2$ .

The bit-error rate will depend on the exact assignment of bits to symbols, but for a Gray-coded assignment with equal bits per carrier:

$P_{bc} = frac{4}{k}left(1 - frac{1}{sqrt M}right)Qleft(sqrt{frac{3k}{M-1}frac{E_b}{N_0}}right)$ ,

$,P_b = 1 - left(1 - P_{bc}right)^2$ .

Odd- $k$ QAM

For odd $k$ , such as 8-QAM ( $k = 3$ ) it is harder to obtain symbol-error rates, but a tight upper bound is:

$P_s leq{} 4Qleft(sqrt{frac{3kE_b}{(M-1)N_0}}right)$ .

Two rectangular 8-QAM constellations are shown below without bit assignments. These both have the same minimum distance between symbol points, and thus the same symbol-error rate (to a first approximation).

The exact bit-error rate, $P b$ will depend on the bit-assignment.

Note that neither of these constellations are used in practice, as the non-rectangular version of 8-QAM is optimal.

Constellation diagram for rectangular 8-QAM. Image File history File links Constellation diagram for rectangular 8-QAM. File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... A constellation diagram is a representation of a digital modulation scheme in the complex plane. ...

Alternative constellation diagram for rectangular 8-QAM. Image File history File links Alternative constellation diagram for rectangular 8-QAM. File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... A constellation diagram is a representation of a digital modulation scheme in the complex plane. ...

Non-rectangular QAM

Constellation diagram for circular 8-QAM.

Constellation diagram for circular 16-QAM.

It is the nature of QAM that most orders of constellations can be constructed in many different ways and it is neither possible nor instructive to cover them all here. This article instead presents two, lower-order constellations. Image File history File links Constellation diagram for optimum circular 8-QAM. File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Constellation diagram for optimum circular 8-QAM. File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... A constellation diagram is a representation of a digital modulation scheme in the complex plane. ... Image File history File links Constellation diagram for circular 16-QAM. File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... Image File history File links Constellation diagram for circular 16-QAM. File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ... A constellation diagram is a representation of a digital modulation scheme in the complex plane. ...

Two diagrams of circular QAM constellation are shown, for 8-QAM and 16-QAM. The circular 8-QAM constellation is known to be the optimal 8-QAM constellation in the sense of requiring the least mean power for a given minimum Euclidean distance. The 16-QAM constellation is suboptimal although the optimal one may be constructed along the same lines as the 8-QAM constellation. The circular constellation highlights the relationship between QAM and PSK. Other orders of constellation may be constructed along similar (or very different) lines. It is consequently hard to establish expressions for the error-rates of non-rectangular QAM since it necessarily depends on the constellation. Nevertheless, an obvious upper bound to the rate is related to the minimum Euclidean distance of the constellation (the shortest straight-line distance between two points): Phase-shift keying (PSK) is a digital modulation scheme that conveys data by changing, or modulating, the phase of a reference signal (the carrier wave). ... In mathematics, the Euclidean distance or Euclidean metric is the ordinary distance between two points that one would measure with a ruler, which can be proven by repeated application of the Pythagorean theorem. ...

$P_s < (M-1)Qleft(sqrt{d_{min}^{2}/2N_0}right)$ .

Again, the bit-error rate will depend on the assignment of bits to symbols.

Although, in general, there is a non-rectangular constellation that is optimal for a particular $M$ , they are not often used since the rectangular QAMs are much easier to modulate and demodulate.

External links

How imperfections affect QAM constellation

References

These results can be found in any good communications textbook, but the notation used here has mainly (but not exclusively) been taken from:

John G. Proakis, "Digital Communications, 3rd Edition", McGraw-Hill Book Co., 1995. ISBN 0-07-113814-5
Leon W. Couch III, "Digital and Analog Communication Systems, 6th Edition", Prentice-Hall, Inc., 2001. ISBN 0-13-081223-4

Categories: Radio modulation modes | Data transmission

Results from FactBites:

BIGpedia - Quadrature amplitude modulation - Encyclopedia and Dictionary Online (368 words)
	Quadrature Amplitude Modulation (QAM) is the encoding of information into a carrier wave by variation of the amplitude of both the carrier wave and a 'quadrature' carrier that is 90° out of phase with the main carrier in accordance with two input signals.
	Phase modulation can also be regarded as a special case of quadrature amplitude modulation, where the amplitude of the modulating signal is constant, with only the phase varying.
	QAM is used in NTSC and PAL television systems, where the in-phase and 90° components carry the components of chroma (colour) information.

What is Quadrature Amplitude Modulation? (516 words)
	More technically, quadrature amplitude modulation is a system of modulation in which data is transferred by modulating the amplitude of two separate carrier waves, mostly sinusoidal, which are out of phase by 90 degrees (sine and cosine).
	In quadrature amplitude modulation, a signal obtained by summing the amplitude and phase modulation of a carrier signal (a modulated sine and cosine wave or quadrature waves) is used for the data transfer.
	Incidentally, rectangular quadrature amplitude modulations are preferred to non-rectangular quadrature amplitude modulations as the former is easier to modulate and demodulate.

More results at FactBites »

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