Talk:Quadrature amplitude modulation

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Two signals on one line?[edit]

How can you put two signals on a single signal line? I don't get it. How can you double the available data rate?

Thanks, --Abdull 22:03, 17 Jan 2005 (UTC)

This is possible because two independent properties of the carrier wave are being manipulated simultaneously by the transmitter: the amplitude, and the phase. (You could think of plain old amplitude modulation as being a subtype of QAM, where only the carrier's amplitude is varied while its phase is held constant.)
The receiver can also measure these two properties independently, yielding two continuously-variable quantities and, thus, two signals. In its simplest form (2QAM), this can be used either to multiplex two data streams into one transmission, or to send one data stream at twice the effective rate (i.e. two bits per baud).
(At least, this is how I understand it.)
Simon 18:30, 23 Jan 2005 (UTC)
It doesn't really double the maximum available data rate. It merely uses more of it. The maximum possible rate is determined by the Shannon-Hartley theorem, and modulation schemes try to use up as much of it as possible. (Apparently no scheme gets 100%, but some get close.) So QAM enables a higher data rate than a simple amplitude modulation of binary data, but isn't making something out of nothing. It's just using up more of the available theoretical bandwidth. (Right?) - Omegatron 19:42, Jan 23, 2005 (UTC)
Yep, that's right—although from the point of view of a terminal sending data over the line, the available data rate has increased. As you point out, there is a theoretical limit on how high this rate can get (before changes to the channel parameters are needed).
Simon 19:27, 24 Jan 2005 (UTC)
Yeah, that's probably what's confusing. It's the distinction between the maximum bandwidth available from the physical channel and the maximum bandwidth available from the transmission protocol. The transmission protocol can use up all of the channel, and the data being sent can use up all of the protocol. - Omegatron 21:03, Jan 24, 2005 (UTC)
TheOriginalPC (talk) 05:36, 19 March 2009 (UTC) QAM doubles the available data rate over AM. The sine and cosine of the same frequency are orthogonal (a receiver tuned to receive the sine and given a cosine will see nothing, and a receiver tuned to receive the cosine and given a sine will likewise see nothing). This includes modulated sines and modulated cosines. Another example of a modulation scheme that uses orthogonal signals to double the available data rate is OFDM (Orthogonal Frequency Division Multiplexing). An example of a QAM system is : telephone-line modem. This orthogonality is not hard to prove, either by experiment or by simulation.

Dialectic inconsistency[edit]

Hi. Yet another page I want to edit for English usage (my main activity on Wikipedia). I noticed the page uses the word analogue (Commonwealth English spelling) and two words (or forms of words) ending in -ize (American English spelling). The Manual of Style recommends (sensibly) that spelling and usage within an article should be uniform. But I'm not sure which we it should go. It seems that perhaps Commonwealth usage is now dominant, but looking at the page history, I see there were inconsistencies from the beginning. (The very first version has both analog and quantised; perhaps analog is creeping into Commonwealth?) I think at least some comments are necessary before unification is performed. Ddawson 01:10, 26 August 2005 (UTC)

I am the editor who rewrote the article into its current form. I speak British English, being English (and British!). However, I've adopted some Americanis(z)ations owing to the journals I write papers in insisting on American English. So I mix them up. Most of the inconsistencies will be my fault, and I do not mind to which version it is harmonized, but harmonized it certainly should be! Thanks for the vigilance. -Splash 01:25, 26 August 2005 (UTC)

Then I will go with Commonwealth, since it's dominant. Ddawson 03:03, 26 August 2005 (UTC)

-ize can also be used in British English. It's common in British academic publications. SpNeo 02:28, 29 October 2005 (UTC)
Yes, though that is largely (in my personal academic writing experience) because many of those publications are in American journals/conferences and the like. For example, the vast majority of electrical engineering journals are published by IEEE which prefers American English spelling. -Splashtalk 06:32, 29 October 2005 (UTC)

'ize is never wrong' in British English although 'ise' is sometimes wrong - so most sensible writers will always use the 'ize' form. Differential spelling is often useful where an English writer will use American spelling (for example) to distinguish technical or computing items from the 'standard' meanings - eg we can programme the writing of programs or a disk (the device) drive may be made up of a stack of discs (the shape) on a single spindle - SDB51 2006.02.02 @ 21.05 zulu

64 QAM Constellation diagram[edit]

How can i construct a 64 QAM Constellation diagram?

    For the rectangular case, you would just use an 8x8 grid.  —Preceding unsigned comment added by (talk) 05:24, 6 October 2007 (UTC) 
TheOriginalPC (talk) 06:27, 19 March 2009 (UTC)

Use a 14 X 14 grid on graph paper. Pick the center point (0,0) and draw the X and Y axes. At each of the points where odd-numbered lines cross plot a point on the 64QAM constellation, every point from (-7,-7) to (+7,+7) and from (-7,+7) to (+7,-7). For examples, (1,-1) and (-1,3).

Analogue QAM[edit]

Although analogue QAM is possible, this article focuses on digital QAM.

This means there's nowhere obvious on Wikipedia to add information about analogue QAM or QAM in general. Perhaps the bulk of this article can be moved to QAM (digital) and the remainder made more mixed? --Dtcdthingy 01:55, 1 June 2006 (UTC)

If you want to write about analogue QAM, just remove the 'disclaimer', add a new section heading somewhere and dive in. Unless you feel strongly that they should be in different articles. -Splashtalk 01:57, 1 June 2006 (UTC)
The problem is that most of the article has been written as if the page was called Digital QAM. You'd have to put all that under a great big Digital QAM subheading and/or rewrite lots of it to say it only applies to digital. It would be better if we just renamed it, even if that means the article here ends up relatively short. --Dtcdthingy 02:17, 1 June 2006 (UTC)

I've gone halfway and split the article into two big sections. The previous situation of completely dismissing analogue QAM was an embarrassment. --Dtcdthingy 12:42, 8 November 2006 (UTC)

Error in equation for BER of Gray coded M-ary QAM[edit]

There is a mathematical error on this page in the description of the BER of a M-ary QAM signal in AWGN, where M is even. The BER for a gray coded signal can be directly infered from the PAM signal in each quadrature phase, which are independent from each other.

Thus 64-QAM, which can be regarded as two independent 8-PAM streams, has a BER approximated by 1/3 of symbol error rate of a Gray coded 8-PAM symbol stream.

In general, BER=\frac{4}{k}\times \left( 1-\frac{1}{\sqrt{M}} \right) \times Q\left(\sqrt{\frac{E_b}{N_0}\times \frac{3k}{(M-1)}}\right)

Where k=\log_2{M}

Although it is true that both quadrature PAM symbols must be correct for the final QAM symbol to be entirely correct, there is no such dependancy between the bit errors occuring in each quadrature PAM channel of a QAM system!

--Crazzell 23:38, 13 September 2006 (UTC)


Just a word of appreciation for such a lucid presentation.

Use of first person[edit]

To be honest, I don't particularly care either way. But I'm not a fan of changing things for the sake of it (another example would be people who go around Americanising British spellings).

From the MOS:

"It is also acceptable to use “we” in mathematical derivations"

For a few counter-examples to the claim that technical articles don't use "we":

I could easily go on all night finding counter-examples... Oli Filth 23:23, 15 January 2007 (UTC)

Is only the amplitude modified in QAM?[edit]

Throughout the article, there are some unclear places whether in QAM only the amplitude of the both carriers is modulated, or both the amplitude and phase is modulated in both carriers. I believe that only the amplitude is modulated, not the phase of each carrier. In this case, I do not quite understand this sentence:

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.

As said earlier, no change to the phase of either carrier is done. Why should a demodulator need to detect the phase? Paluchpeter 13:14, 20 July 2007 (UTC)

By altering the amplitudes of the I and Q components, the phase of the overall signal is altered. Oli Filth 13:25, 20 July 2007 (UTC)
Of course, but the phase of the combined signal is not relevant as I understand it. After receiving the combined signal and multiplying it with either sine or cosine signal and filtering the result with a low-pass filter, we will extract the corresponding I or Q component, without paying attention to the phase of the combined signal. Perhaps I am missing something... Paluchpeter 14:59, 20 July 2007 (UTC)
The phase is relevant. QAM demodulation requires a phase reference, i.e. it can only be demodulated coherently. Also, it is susceptible to phase noise. Neither of these apply to simple AM. Oli Filth 16:34, 20 July 2007 (UTC)
The phase is relevant but not because is required as phase reference for coherent demodulation, but because it actually carries information. And that is why it must be demodulated coherently, because only detecting the envelope would not result in anything (the two modulating signals are merged in the envelope and in the phase).
And regarding to simple AM, I don't understand what you say about they don't apply. Because it is possible to detect the "simple AM" (I guess AM-DSB/SSB-LC) with coherent detection rather than envelope detection, and the Rx should also be in sync with the carrier's frequency and is susceptible to phase and frequency errors as well.--Dhcpy 04:51, 1 December 2007 (UTC)

The previous comment is dead on. Regular AM can be demodulated with simple noncoherent envelope detection, but QAM requires coherent demodulation, i.e. a phase reference is required. Mathematically speaking, sine and cosine (the two orthogonal carriers that define the quadrature) are just phase-delayed (or equivalently, time-delayed) versions of each other. The receiver must somehow synchronize (typically via a phase reference) its own local oscillator so that it matches that of the transmitter. This is necessary because the signal undergoes an unknown time delay (e.g. phase delay) in the channel, and arrives at the receiver with an (at least initially) unknown phase offset (with respect to it's own local oscillator). Any non-zero phase offset (between the transmitter and receiver local oscillators) will rotate the constellation correspondingly. For instance, a rotation of 90 degrees corresponds to a misidentification (a swapping) of the sine and cosine components, which, in general, would yield a catastrophically high bit error probability, near 1/2. This requirement for phase synchronization is exactly the same as PSK, and for the same reason. In fact, the simplest way to view QAM is as a generalization of PSK, e.g. PSK without a constant envelope requirement. —Preceding unsigned comment added by (talk) 06:28, 6 October 2007 (UTC)
Both of the carriers are only amplitude modulated, and no phase modulation is normally performed for the carriers. However, phase is still relevant at reception (although not the phase of the total signal). The receiver must synchronize to the carrier phase, beacuse the carriers can be only demodulated using coherent demodulation. Alinja 10:56, 8 October 2007 (UTC)

This is how I understand it:
If you take a look at the block diagram of the analogue QAM you'll see that modulating signal I(t) multiplies cosine and modulating signal Q(t) multiplies the sine. Those I and Q are two different signals from, lets say, two different voice channels.
At this point, the 2 resulting signals I(t)cos(wc.t) & Q(t)sin(wc.t) are, as you say, Amplitude Modulated signals, the phase of the carriers isn't changed.
But, when they are added, at that point they merge into a complex signal that varies amplitude AND phase. That can be easily shown by writing this complex signal in the "module and argument form" .
By writing the QAM signal that way, you'll see that the envelope (amplitude) varies and the phase varies as well.--Dhcpy 04:51, 1 December 2007 (UTC)

Amplitude modulating two carrier waves in quadrature is identical to amplitude and phase modulating a single carrier wave; the two are a trigonometric identity. -Dawn McGatney —Preceding unsigned comment added by McGatney (talkcontribs) 06:31, 17 January 2008 (UTC)

Time domain signal[edit]

A signal in the time domain demonstrating the transmitted signal and how its formed from its data carrying components would be really useful. ~RayLast «Talk!» 18:15, 4 April 2008 (UTC)

TheOriginalPC (talk) 07:58, 19 March 2009 (UTC)

A QAM digital waveform is a series of analog pulses spaced evenly in time at the symbol rate. The envelope of the prototype pulse is a special function called a ZI (zero intersymbol interference) function which is time-symmetrical and has nulls in its value at the symbol rate except at ZI(0) = 1. All ZI functions are constructed by multiplying the SINC [needs reference] function by some time-even time-constrained function g(t) with g(0) = 1. One commonly-used g(t) = e^(-at^2).

The reason for selecting this function is the presence of time-nulls as well as the narrow resulting filter bandwidth, which by duality is the filter function of the SINC function (the narrowest possible filter) convolved with the filter function G(w) of the time-constrained function.

ZI(t-nT) * (I[n]*SIN (W t) + Q[n]*COS(W t))

Note that the sinusoid is not centered in the shaping pulse function. In fact, the sinusoid frequency and the baud rate are independent. However, for easier drawing you can pick any value for T and W you want.

Only at the instants t=mT can you see values for I[m] and Q[m]. The signal is constantly in transit from one such instant to the next. A picture of the aggregate waveform would be very unenlightening. Pictures of the separate I and Q waveforms are called "eye diagrams" and are much more intuitive. QAM test sets commonly display eye diagrams.

True, that's the ideal situation. Many QAM systems though work without ideal equalization, so there may be some inter-symbol interference, rather than ZI functions. But this is no different from ordinary AM digital channels, BPSK, etc. If you start by viewing I and Q as piecewise-constant baseband signals (NRZ-like), then you can get to your idealized case, or close to it, by appropriate filtering. Dicklyon (talk) 04:59, 20 March 2009 (UTC)

How the signals look like?[edit]

I have a question, how the signals look like in the transmitter, the I and the Q signal? Do they look like sine and cosine wave with varying amplitude (amplitude of 1 and 3) and phase (either 0 or 180)? Something like this ?

And how does the receiver "read" the phase? How will the signal look like in the receiver after being filtered by the low-pass filter? Will it be a signal that has a frequency nearly 0Hz, so basically, will it be a constant signal of amplitude -3, -1, 1 or 3? Thank you in advance. WielkiZielonyMelon (talk) 21:12, 5 February 2009 (UTC)

Yes, sort of like that. Each of the I and Q channels looks like a piece of sine wave (I) or cosine wave (Q) of different amplitudes and polarities. Their sum can therefore have a few more phases and amplitudes. To demodulate, each is synchronously downconverted to baseband by mixing with a corresponding local oscillator synced to the appropriate I and Q carrier phases, so the two resulting channels looks like baseband signals, and they don't interfere with each other since each channel's signal is orthogonal to the other's local oscillator or recovered carrier. The only tricky part is how to make a carrier PLL to sync up with something like that. For that, you need an elaborated Costas loop or something; I don't recall exactly. Dicklyon (talk) 06:05, 19 March 2009 (UTC)

Too Technical[edit]

This article, along with nearly all the articles in the "Modulation techniques" category fail to meet Wikipedia guidelines, specifically those on making articles accessible: Wikipedia:Make technical articles accessible. These articles are almost entirely composed of mathematical formulas and technical terms. Most visitors will be expecting information relevant to common consumer devices, not text resembling a physics textbook. Focus should be put on making the introductions readable to the layman. —Preceding unsigned comment added by (talk) 04:15, 19 November 2009 (UTC)

Added link at the top to the more relevant article, I think the rest of the articles could use similar attention. —Preceding unsigned comment added by (talk) 04:31, 19 November 2009 (UTC)

I am in the "People who have studied related subjects in college" category mentioned in WP:TECHNICAL. I have reviewed the article and do not see how this subject can be simplified more. There are certain concepts that need to be understood before anyone can understand QAM. The leading paragraph does a decent job of pointing those topics out. You seem to be confused about what you're looking for. You mention consumer devices. Maybe you're looking for QAM tuner? The QAM tuner page (mentioned in the header of this article, in See Also, and in the Quantized QAM section) does a good job of explaining QAM as it relates to set-top boxes and TV. I am removing the Technical tag for the above reasons. --Littleman_TAMU (talk) 18:59, 8 December 2009 (UTC)
An example of the use of QAM in consumer devices is in cable modems and cable television as briefly mentioned in this article. It is also used in fax transmissions, as briefly mentioned in that article.
What makes this article seem so technical is that only technical information is included; any information useful to a layman is either missing, abbreviated, or hopelessly buried in the article: Who developed the technique, when and where it was developed, how, where, and why it is used, what it accomplishes, what standards are applied to it, who regulates the standards, etc. Downstrike (talk) 19:04, 6 September 2010 (UTC)

Copyright problem removed[edit]

One or more portions of this article duplicated other source(s). The material was copied from: Infringing material has been rewritten or removed and must not be restored, unless it is duly released under a compatible license. (For more information, please see "using copyrighted works from others" if you are not the copyright holder of this material, or "donating copyrighted materials" if you are.) For legal reasons, we cannot accept copyrighted text or images borrowed from other web sites or published material; such additions will be deleted. Contributors may use copyrighted publications as a source of information, but not as a source of sentences or phrases. Accordingly, the material may be rewritten, but only if it does not infringe on the copyright of the original or plagiarize from that source. Please see our guideline on non-free text for how to properly implement limited quotations of copyrighted text. Wikipedia takes copyright violations very seriously, and persistent violators will be blocked from editing. While we appreciate contributions, we must require all contributors to understand and comply with these policies. Thank you. Ozob (talk) 00:28, 23 December 2009 (UTC)

It's not clear why you removed as much as you did; yes the definitions are very close to what's in that cited source, and perhaps should be paraphrased more or rewritten in light of other sources. I'm going to put back the main paragraph, and try to make a sensible section heading. Dicklyon (talk) 08:06, 23 December 2009 (UTC)

Split analog and digital QAM[edit]

The analog and digital cases are not same. I suggest to split this article into 2. `a5b (talk) 21:46, 12 September 2010 (UTC)

What great differences would suggest a need for separate articles? Dicklyon (talk) 04:26, 13 September 2010 (UTC)

Should the first section named "Digital" ?[edit]

Is the first section, named "Digital QAM", describing digital modulation? It is talking about QAM generally, or even some about analog QAM. Why is it named "Digital"? As far as I know, "digital" means discrete in time domain and quantized in amplitude. Is that right? —Preceding unsigned comment added by Zhaixm (talkcontribs) 13:16, 28 November 2010 (UTC)

Sign convention[edit]

A QAM-modulated signal has the form

I(t) \cos(2 \pi f_0 t) \pm Q(t) \sin(2 \pi f_0 t)

where sign before Q(t) seems to be a matter of convention. The section Analog QAM states it's a +. However, in the same article, the figures showing the structure of the transmitter and the receiver imply it's a −. I guess I prefer a −, because this makes I and Q be the real an imaginary part of the complex amplitude. I am however not an expert, and I've seen both sighs used on the web:

Now, my question to those working in the field: is there is a preferred, or more commonly accepted sign convention?

--Edgar.bonet (talk) 17:19, 3 February 2012 (UTC)

The correct sign convention is with a minus sign. There are other problems with notational convention. Capital letters should be used for the Fourier or Laplace transform of time-domain signals. As long as LaTeX is here to be used, then subscripts should be used. I would suggest:
Signal(s) with information:
 x(t) = x_i(t) + j x_q(t) \    where  j^2 = -1 \
Transmitted signal (carrier with information-bearing signals):
 y(t) & = \Re \left\{ x(t) e^{j 2 \pi f_0 t} \right\} \\
 & =  x_i(t) \cos(2 \pi f_0 t) -  x_q(t) \sin(2 \pi f_0 t)  \\
The notation should be like that and build on that convention for the whole article. (talk) 16:53, 4 June 2012 (UTC)

OK, since there seems to be no disagreement, I went on and changed the sign convention in the article. I did not change the other notations though. --Edgar.bonet (talk) 11:42, 18 June 2012 (UTC)

VDSL2 does not use QAM[edit]

The line about VDSL2 using 32768-QAM needs to be removed. VDSL2 only uses DMT line code. VDSL1 gave the option of using QAM or DMT but it was removed in the later VDSL2 specification. An article that backs up the removal of QAM from the spec: scroll down to: VDSL2 Band Plan and Profiles — Preceding unsigned comment added by (talk) 17:18, 20 March 2014 (UTC)

I find this statements about QAM vs. DMT confusing. DMT is not a modulation scheme: it's a multiplexing scheme, i.e. a way to split the channel into several subchannels. You still need a modulation scheme in those subchannels, which may be QAM or another. Does anyone have some information about the modulation used in VDSL2? —Edgar.bonet (talk) 19:35, 20 March 2014 (UTC)