Talk:Phase-shift keying

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Ham radio applications[edit]

There uld be some mention of use in ham radio, described here in at least these two almost-stubs: PSK31 and PSK63. Jonadair 02:26, 22 December 2006 (UTC)

Good start[edit]

However, remember that we already have modulation and that the info on how to transmit a signal isn't unique to PSK, so probably belongs elsewhere. Also, I made the lead-section a paragraph or two, since that is what Wikipedia:Lead section asks for. The tutorial part is also requested by Wikipedia:Lead section. -Splash 01:07, 22 August 2005 (UTC)

Just feel free to revert if it's easier to do...I actually wanted to put DPSK somewhere there, but when I moved it I couldn't find it in the article. As for the lead, just change it back to what it was before if you feel that is better. I like the introduction with ASK, FSK and PSK all together since it provides a bit more context regarding how PSK is related to thse other implementations. --HappyCamper 01:24, 22 August 2005 (UTC)
Yes, I like the broader intro. It gives more context. I'm not just going to revert you! -Splash 01:27, 22 August 2005 (UTC)

Agreed. Very good start, specially when compared to Amplitude-shift keying. Sohaibafzal (talk) 13:17, 14 July 2011 (UTC)

Lead paragraph[edit]

Uh, the paragraph you just moved to differential encoding actually describes DPSK (not the same thing). Per having a tutorial lead-in and not making the DPSK section repetitive, at least some of it shoudl go back up top. -Splash 01:19, 22 August 2005 (UTC)

Yes, when I moved that section I couldn't find it, so placed it somewhere temporarily and expecting to move it later. I'll try and fix it up. --HappyCamper 01:31, 22 August 2005 (UTC)

Numbered lists at top[edit]

OK, how about I make a diagram for those numbered lists and include them in Modulation? Will keep the generic stuff in one place. -Splash 01:22, 22 August 2005 (UTC)

Okay, that sounds good too. --HappyCamper 01:26, 22 August 2005 (UTC)
Okay, they're at modulation now... --HappyCamper 01:41, 22 August 2005 (UTC)


I use of rowspan). I had originally done that, but an anon removed them without comment and I didn't put them back in. I don't actually get any problem when I look at the page, but there's an example table in the Higher-order section; does that break too? -Splash 03:29, 22 August 2005 (UTC)

Let me get someone from the help desk to help out...I specialized in LaTeX not WikiTable markup lately... --HappyCamper 03:40, 22 August 2005 (UTC)
I asked for some help at the help desk. Maybe a kind Wikipedian will come by and help us out! --HappyCamper 03:45, 22 August 2005 (UTC)

Timing diagram[edit]

I added a timing diagram for BPSK, in the implementation section and some blurb to go with it. What do you think? I do not plan to make another one for QPSK since it would just be two of the same and a third to add them together, which wouldn't seem to add much that a brief sentence wouldn't cover. However, I think for Offset QPSK a timing diagram might be useful since the two carriers are not keyed together. What think you? -Splash 01:43, 23 August 2005 (UTC)

That sounds reasonable. I would like to see one for QPSK though :-) But I guess it really isn't so important for the article. I think OQPSK would be an excellent addition. --HappyCamper 02:33, 23 August 2005 (UTC)
Ok, I'll see what I can knock up! Though now I think the other way: would it be better to have just the QPSK one and, in the BPSK section refer to it? The other reviewer at WP:PR wants the article refactoring so that the math is away from the non-math. I was thinking that, if we do that (and it wouldn't be hard) then the QPSK diag would certainly suffice for both. -Splash 02:40, 23 August 2005 (UTC)
Yes, I read about that refactoring. I'm a bit weary of that though, since it may risk oversimplification. In my opinion, digital communications as a whole is a complicated concept to fully appreciate, and this is one reason why it is often introduced late into curricula at many undergraduate institutions. Why not just keep both images in the article anyway? --HappyCamper 02:29, 24 August 2005 (UTC)
The timing waveforms are great - I wish someone could go and do the same for some of the other digital articles, like QAM, etc... -Russvdw 15:44, 2 June 2006 (UTC)
The timing diagrams as drawn represent the special case where the symbol rate is exactly half the carrier frequency and synchronous with it. In practice this is not likely to be the case. (talk) 12:29, 4 January 2009 (UTC)

Angles correct?[edit]

Hello, I believe that the constellation diagram for QPSK normally includes angles of 0,90,180,270, not 45, 135, 225, 315. (See, for example, Proakis). I realize that the BER performance is the same, but the diagram for QPSK should either be labelled as 4-QAM, or modified. IMO --kaczor47 04:29, 10 November 2005 (UTC)

I have to think about this...I think we used those angles so that it would be easier to draw the timing diagram. --HappyCamper 01:33, 11 November 2005 (UTC)


Oh, noise is always so confusing. I was using Proakis which appears to use , whereas now I look in Haykin, where the basis functions I guess are from, he uses just . Right? So is my change to the basis functions correct, or did I do it upside down or something?

Also, I took out the sentence about the noise spectral density. This is partly because some phrasing that introduces fewer one-time-only symbols would be better and mainly because I'm not sure which the correct expression is. One-sided, two-sided? -Splash 01:46, 23 August 2005 (UTC)

You have access to Haykin's book? I'm pretty sure he consistently uses , see for example the the bottom page 68. Check also page 558 in appendix D where he specifies that "...the factor 1/2 has been included to indicate that half the power is associated with positive frequencies and half with negative frequencies." The basis functions are based on material in chapter 7 of that book. --HappyCamper 02:15, 23 August 2005 (UTC)
Yeah, these factors are getting to be a bit confusing for me too...Would it be beneficial to draw out a little diagram illustrating the symbol and bit duration? I think the problem right now is that we don't have other good digital communications articles to support the material that's here... --HappyCamper 02:15, 23 August 2005 (UTC)
I do have Haykin, yes. I got myself confused up top: Proakis appears to use and yes, Haykin halves it. So...I think we're ok. E.g. in the BPSK BER equation, Haykin doesn't have the 2 on top: this checks with him only having half the noise. As for the picture, well, yes, we could use with the article signal noise or maybe somewhere else doing the job properly. I think adding it here would be too much since we've a lot of ground to cover already. A one-sentence definition with a wikilink to a good-ish article would be better. Before we can make this an FA, we anyway need to make sure that the one-click-away bluelinks are all decent. Which is not a huge amount of work, but it is some since, as you point out, so many of the basic articles are rather poor. Now, I'm going to find my lecture notes from years ago and work this out. -Splash 02:28, 23 August 2005 (UTC)
No, I don't think the change back to 2's is right. Remember that I've changed the definition of noise to be N0 everywhere. Consider that as unity. Then, Haykin's halving puts a 2 on top (as 1/0.5), but with the Proakis definition of noise, which I used everywhere else (and in other modulation articles), there's no 0.5, so no 2 either. -Splash 02:51, 23 August 2005 (UTC)
Oh yeah, what was I thinking? Years and years of "factors of 1/2" brainwash ones mind... --HappyCamper 02:54, 23 August 2005 (UTC)
Hmmm...after some more thinking, I still think there should be an extra 2. The 2 there is not due to the noise, but rather the normalization of the basis function so that it has unit energy. What do you think? --HappyCamper 02:31, 24 August 2005 (UTC)
Having revisited Haykin, and done the integrations for myself, I've concluded that you were right all along. The basis functions need their 2's, as you say. Elsewhere, though, the definition of the noise doesn't need changing. I've been taking a break from this article today, just for variety's sake, but I'll make the rest of the pictures I promised tomorrow. By the way, did you see the other peer-reviews? I'm in two minds about carving this up into several much shorter articles. We should think hard before doing that. -Splash 03:06, 24 August 2005 (UTC)
Yes, I've read through those other comments, but I refrained from commenting since I wasn't sure if you wanted to respond to them first. It's great to see all this nice feedback! I don't remember the last time when peer review supplied such a rich set of comments. I haven't put much thought into splitting the article yet. I think it's best to keep it large, and then split it up. Right now, I think it's best to aim for an article which is of "course note quality". If I gave this page to a group of undergraduates studying PSK with the right background, I hope that this would convey all the essential fundamentals to them in a clear and concise way. At least, this is the sort of vision I have when I'm editing articles like this. I think making it more accessible can be done easily once all the bread and butter is placed on the table. --HappyCamper 03:15, 24 August 2005 (UTC)
Yes, feedback is a considerable oxygen. So is collaboration! You articulate exactly the sort of article I had in mind when I was originally rewriting the (excuse for an) article. And once we have everything here and are sure that's what we want to say, yes, that would probably be the best time to think about splitting it. We might not be too far from having all the material, once I make the remaining timing diagrams and a block-diagram of a PSK modulator (to show how the basis functions get used, per the second reviewer). My concern in splitting it up is what I said in response to the third reviewer: articles weak on context repeating introductory material and none of them FA'able.-Splash 03:36, 24 August 2005 (UTC)

By the way, I don't fully understand your "coincidence" sentence. (Note that my choice of bit sequence isn't quite the same as Haykin's — I wanted to use all 4 symbols.) -Splash 03:36, 24 August 2005 (UTC)

Ah, yes, I see (though it's only the first 4 bits in this case matching I). I might upload an alternative where this pattern doesn't exhibit. -Splash 03:58, 24 August 2005 (UTC)

Unit energy basis function for BPSK[edit]

For Wikipedians visiting, here is a check to make sure that needs a "2" in the square root to normalize its energy in BPSK

Hence, the energy of the signal will be given as

Now, the quantity:

is always chosen so that:
the integral over cosine is zero.


Hence is normalized to unit energy as given. --HappyCamper 12:41, 24 August 2005 (UTC)

Duplicate sections[edit]

The "Ideal structure" section directly duplicates the "Implementation section". Could these be merged? -Splashtalk 12:20, 9 December 2005 (UTC)

It's not really a duplicate, but there is some redundancy for sure: The "ideal structure" section is simpler and more generic (according to me). In the "Implementation section" there are more data, but the first time I read it I found it quite confusing. I agree with merging them (but I'm not skilled enough to do it). Alessio Damato 10:09, 11 December 2005 (UTC)

I think they should stay separate. It seems PSK is an extensive enough topic to write that huge article on it. Perhaps better thing to do would be to separate all the different variations of PSK, much like this one.

figures with weird phase ?[edit]

I'm not an expert, but the BPSK figure shows "1" at theta=0 and "0" at theta=pi, but the description explains that "0" is theta=0 and "1" is theta=pi. I realize at differential encodings, it's all relative, but it has me a bit confused as I try to learn about PSK in general. Does this have to do some weird convention in EE with their j's that is different from the mathematical/physics i's imaginary axis?

Toslink does not utilize PSK[edit]

I removed the line "This technology is used in the optical in/out ports of some sound cards" because it is not true. Optical Toslink/SPDIF utilizes a biphase-mark-code modulation which is very different than PSK. In fact optical SPDIF uses the same coding that wired SPDIF uses. (Requestion 23:49, 27 April 2007 (UTC))

Channel Capacity Plots[edit]

Channel capacity for complex constellations.svg

Here is a plot of all of the different common modulation techniques and their shannon capacity limits vs SNR. I'm kind of surprised no one has posted this yet. Its pretty important. The reason the lines are not perfectly smooth is because they were generated from simulation. There are no closed form equations for them. —The preceding unsigned comment was added by Speedplane (talkcontribs) 09:37, 15 May 2007 (UTC). Speedplane 09:38, 15 May 2007 (UTC)

I guess one of the difficulties is explaining what these plots mean. It would require not only mentioning the Shannon limit in general, but also how this is applied to particular modulation schemes to obtain these curves, and also what this means in practice, i.e. only obtainable with the "perfect" code, asymptotic limit, etc. If we can find a suitable way to explain all of this, then I'm all for putting these curves in. Oli Filth 10:43, 15 May 2007 (UTC)

Point taken... but if you look at all of the different modulation techniques there is no visual clear way of clearly comparing them. There is the BER plot towards the bottom of the page. But that plot suggests that BPSK/QPSK is 'better' than the other modulation techniques. The value of this graph is that is shows that at for a given rate at low SNRs it doesn't matter which modulation to choose, and at higher SNRs the more complex the better (but harder to implement). 05:55, 16 May 2007 (UTC)
I agree about introducing the plot as well Alessio Damato 12:46, 17 May 2007 (UTC)
I've added the graph, plus a brief remark about it. Alas, I fear that remark is either incomprehensible, or self-evidently obvious -- feel free to replace it with a more useful remark. -- (talk) 06:52, 6 December 2007 (UTC)
I replaced the graph with a more numerically stable one. I also rephrased the text by substituting the word capacity with the more appropriate Mutual Information, since the capacity is the supremum among all possible symbol distributions. Paolostar (talk) 17:34, 29 December 2016 (UTC)

Nice Work[edit]

Hi I think this is a nice article. It's more comprehensive than the other articles about digital modulation techniques. Especially the signal graphs are usefull.

Small Corrections[edit]

I have corrected some minor errors. I also have a suggestion regarding the QPSK-transmitter Image: it would be a good idea to draw square-waves at the output lines of the NRZ encoder, instead of numbers. I think this is more intuitive. Jd185152

please sign your posts. I wouldn't replace the numbers with square waves, we can use both: draw the square wave with numbers on it. Alessio Damato (Talk) 19:55, 4 July 2007 (UTC)
Hello, i modified the image. It is now called QPSK_Transmitter_2.PNG. If you dont like it feel free to revert to the previous version. PS: How does signature work? --Jd185152 09:09, 5 July 2007 (UTC)

Example of Sound[edit]

I would like to have an example of sound put onto the page. I am a am listner of the lower end bands, I get this signal that I cant seem to decode. So an example of sound would be helpfull. I know the sound I pick up is not RTTY or SSTV or WXFAX or CW. —Preceding unsigned comment added by Rippey574 (talkcontribs) 17:22, 15 April 2008 (UTC)

I'm not sure what the point would be. Modulation methods aren't designed to be listened to, so I'm not sure what information this would impart to the user. What's more, with iid data, PSK will sound exactly the same as QAM and ASK, all other things being equal. I would imagine that what's far important to the sound is the bandwidth (i.e. bit-rate) and pulse-shaping, and even more importantly, the protocol running over the top.Oli Filth(talk) 19:42, 15 April 2008 (UTC)
Their is many diffrent ways to transmit RTTY and SSTV, but they all have examples of sound. As for my listing it appears to hav 8 diffrent bumps and probly square wave. Judging buy software from my comp, MMTTY and MMSSTV. Rippey574 (talk) 17:14, 16 April 2008 (UTC)
Also im not to fam with QuAM and ASK. But I do belive each one would have a distinked sound to the transmit. I am aware its not desinged to be listend to, but refrance to the sound so you can determin what to use to decode is always helpfull. Do they all realy have the have the same puls sound and bit depth? The only way to decode is to know exactly what it is they are transmiting at? I do not see ham radio having this set up like that. RTTY and SSTV have an easly distink sound to them and I would think that is on purpuse so other hams can talk to each other. Sorry if stuff is misspelled and cut up, on a labtop that keeps on jumpin sections while typein, good thing im not editng! Rippey574 (talk) 06:38, 19 April 2008 (UTC)
As I said above, the examples of QAM, ASK and PSK will all sound identical with the same symbol rate and data distribution; their spectra are identical. RTTY and SSTV are both protocols, they're likely to sound different to each other. PSK is not a protocol, it's a modulation scheme; on its own, it will just sound like filtered white noise, like most other modulation schemes. Oli Filth(talk) 19:50, 20 April 2008 (UTC)
Well could you recomend a freeware program that could decode all 3 of them? Rippey574 (talk) 04:07, 21 April 2008 (UTC)

Question agian[edit]

I seen something said vandalism and that it either was from me or was revertad to an older state that i was the last person to edit. Can some one clafiy this to me? Rippey574 (talk) 01:27, 12 May 2008 (UTC) —Preceding unsigned comment added by Rippey574 (talkcontribs) 01:22, 12 May 2008 (UTC)

By the way where is a section of which products need 8psk and why? —Preceding unsigned comment added by (talk) 21:35, 6 April 2011 (UTC)

Higher-order PSK Section missing a differential[edit]

In the section where some expressions are given for how to calculate the BER/SER for higher-order PSK, the integral given has no differential in it, i.e. no dV, dTheta, dWhatever. I'm not sure by looking at the equation what the "d" should be, by guess would be dV. —Preceding unsigned comment added by Rajb245 (talkcontribs) 18:37, 26 March 2009 (UTC) Rajb245 (talk) 18:38, 26 March 2009 (UTC)

Fixed. Oli Filth(talk|contribs) 19:08, 26 March 2009 (UTC)

What means DQPSK?[edit]

What does "DQPSK" mean? Can anybody ad the meaning of the abreviations used? (talk) 14:21, 17 April 2008 (UTC)

DQPSK is "Differentially-encoded QPSK". It's described in the page. (OK, the term is used before definition, but it can be found later in the text.)AleyCZ (talk) 15:07, 12 November 2010 (UTC)

Diagrams overlap in my browser[edit] The constellation diagrams overlap the trext on my browswer (Internet Explorer)

That's odd. I wrote in Mozilla Firefox, but it uses tables so all browsers ought to behave with it. I also just tried turning my screen resolution down to 800x600 and it still had no problems, though admittedly the pics are a bit big at that level. There is an option in 'Preference->Recent changes' which allows you set a max. image size, but you'll need to register to able to do that. You can also seek help in the Village pump. Splash 15:43, Jun 16, 2005 (UTC)


Today I'm reading a paper by Martin Hoch ("Comparison of PLC G3 and PRIME".) which mentions "t-DPSK" and "f-DPSK".

I came to this Wikipedia article (and others) looking for a better explanation of "f-DPSK" and "t-DPSK". Dear Wikipedia editors, if you know what these things are, please add them to this article. --DavidCary (talk) 16:18, 19 January 2013 (UTC)

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