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Frequency offset compensation for 802.15.4 (ZigBee-MSK)

Started by tarikkazaz October 2, 2015
On Tue, 6 Oct 2015 00:47:20 +0000 (UTC), spope33@speedymail.org (Steve
Pope) wrote:

>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: > >>On Mon, 5 Oct 2015 20:17:57 +0000 (UTC), spope33@speedymail.org (Steve > >>>But more importantly thinking of MSK as a type of FM signal can add >>>some insight into what you're working with (examples below). > >>In my experience thinking of MSK as CPM with no filtering is good for >>evaluating how it fits within performance tradeoff spaces. > >Thanks, an interesting perspective. > >(Tangentially, 2-MSK can be either continuous phase, or non-continuous >phase. However, only the continuous phase sub-category of 2-MSK is >equivalent to OQPSK with the right filtering (or the right pulse >shape, take your pick). So we're talking about a form of modulation >that is both MSK and CPM.)
That's what I've been saying all along: MSK is CPM with no phase filter. MSK is a limiting case of FSK. MSK is also a special case of OQPSK with half-sine pulse shaping. It is all these things.
>> It's an oddball in that there are multiple ways of thinking >> about it, but if you only think about it as FSK you may miss >> opportunities to make a much more flexible system. > >I'm not suggesting excluding other perspectives, just that >the perspective of MSK (or FSK) being a form of frequency modulation >is useful.
I never claimed otherwise.
>>>>>2-MSK is OQPSK with filtering, I think we can agree. > >>>>Not really. > >>>It's amazing how we can look at the same set of facts yet come up >>>with diametrically opposite statements. > >>>If you apply a filter with a half-sine response to an OQPSK >>>signal whose pulse shape is an impulse (that is, a delta function), >>>you get MSK. Therefore MSK is OQPSK with filtering. > >>MSK is OQPSK *only* in the case where the OQPSK pulse shape is a >>half-sine. > >Correct > >OQPSK with any other pulse shape is not MSK. > >Correct > >> So I would disagree with your description above. > >Ah. The disconnect here is as follows: > >English often is ambiguous between whether a statement involves >the general case or a specific case. > >"MSK is OQPSK with filtering" might mean, "there exists a filter such >that applying that filter to OQPSK results in MSK". > >Or it might (much less likely, in my opinion) mean "for any filter, >applying the filter to OQPSK results in MSK". > >I meant the first of these two, whereas the second is clearly false >(trivial example, suppose the filter is H(t) = 0). > >But I'll allow that my statement was technically ambiguous. > >I hope this clears at least that much up. > >>>> With MSK you can't control the spectral occupancy, and the >>>> main lobe of the frequency response is much wider >>>> than a filtered OQPSK signal. > >>>Okay. Sorta. There's nothing fundamentally preventing anyone >>>from applying filtering to an MSK signal in a similar fashion >>>as is commonly practiced with PSK / QAM signals. But the results are >>>not going to work out as well. > >>If it changes the pulse shape, it is no longer MSK. If it changes >>the phase trajectory, it is no longer MSK. > >>>The reason it is not going to work out as well is that MSK is a >>>type of frequency modulation, > >>Or it is CPM. Or it is OQPSK with a half-sine pulse shape. > >>>[...] MSK is a type of frequency modulation, therefore it has >>>sidelobes (defined by Bessel functions) and, those sidelobes >>>carry significant information necessary for signal fidelity -- >>>I really do think there's insight to be gained by recognizing >>>that MSK is a subcategory of FM. > >> You don't have to think of it that way to get the full benefit of MSK. > >You don't *have* to think of it that way, but thinking of it that way >provides some immediate insight into the problem...that there >are information-containing sidelobes (perhaps more correctly, sidebands) >as there are in any form of frequency modulation. > >>Limiting the conceptual view to FSK with h = 1/2 is...limiting. > >I am not suggesting this, just to be clear. It is most effective >to have multiple conceptual views on this problem (and many >other problems). > >>>And, FM being non-linear creates an opportunity in the MSK case to add >>>filtering ahead of the modulator and obtain a different (and it turns >>>out, desirable) effect distinct from filtering the output of the >>>modulator. > >>If you filter the phase trajectory by filtering prior to the >>modulator, it is no longer MSK. e.g., If you apply a Gaussian filter >>to the phase trajectory, it is GMSK. > >(See my comment upthread about whether GMSK is MSK.) > >>>>If you apply any kind of filtering to MSK, it's not MSK any more. > >>> True. The exact same could be said about PSK. > >> Definitively not true. > >(I think we might have to disagree on this.) > >> [...] So, filtered or unfiltered or any kind of filter you want, it's >> still PSK. > >> MSK is an oddball because it is a specific limiting case, and it is >> defined as such. Changing it moves it out of the definition of what >> MSK is. > >I will counter by saying that, in the general case, filtering >a phase-modulated signal will add amplitude modulation, thereby moving it >outside of the definition of being purely phase modulated.
Bullshit. While it is possible to be incompetent and expect a miracle with an inappropriate application of a filter, PSK is still PSK when it is filtered, which it almost always is. There is no form of QPSK that does not have amplitude changes, including the drastic one of a 180-degree transition that goes straight through the origin. That occurs even in the NRZ case. With any filtering the 180-degree transition still occurs with a big amplitude change and potentially a lot of overshoot between symbols. This is the reason OQPSK exists, to eliminate that transition through the origin and reduce the PAPR. How can BPSK exist in any form without the transition through the origin? Is BPSK never really BPSK because it changes amplitude to make the phase transition? Come on... I've never before heard anybody claim that PSK ceases to be PSK, or purely phase modulated, when filtering is applied. The vast majority of practical PSK applications are filtered, some heavily with only 5-10% excess bandwidth that adds a lot of amplitude changes between symbols and increases PAPR. It's still PSK because the "modulation", i.e., the sliced constellation points that carry the information, do not vary in amplitude. The "modulation" is a phase change ONLY, but what the signal does to transition between the modulated constellation points may include, likely will include, and may HAVE to include, something other than just phase transitions. Like the transitions through the origin. This can easily be seen on an eye diagram, like here: http://www.dsprelated.com/showarticle/60.php See Figure 7 and Table 1. A filter that adds undesired amplitude changes to full-response PSK constellation modulation points is likely just a crappy filter or part of a bad system design. And for CPM systems the phase filter adds no amplitude changes at all to the signal, so even in that case a filter is applied to a truly constant-envelope signal, without affecting that property of the signal.
>As an example, apply the filter 1 + D to QPSK. The magnitude of the >resulting symbols might be 0, sqrt(2), or 2. The signal is no longer >purely phase modulated, it is also amplitude modulated. You >end up with a QAM constellation with nine points.
It is very easy, common practice, and covered in many textbooks, to add useful filtering to QPSKthat results in zero ISI without adding amplitude changes to the constellation points. This helps control spectral occupancy by adjusting the rolloff of the signal spectral energy to adjust the required guardband size.
>In general, filtering a modulated signal will distort it such >that it might no longer meet the constraints that define >the underlying modulation. MSK and PSK both equally fall into this >category.
In general if you have no idea what you're doing, I suppose you're right. You could put a 10MHz signal through a 5MHz-wide filter and distort it pretty badly. Yes, it is possible to screw up modulation. That really applies to just about anything, though. Comm systems are not unique in that regard. It is, however, possible to apply an infinite variety of filter shapes to PSK and NOT distort the modulated constellation, in either amplitude or phase. Or to add a phase filter to a CPM system and not add any amplitude changes to the signal at all. This is done routinely. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Eric Jacobsen <eric.jacobsen@ieee.org> wrote:

>On Tue, 6 Oct 2015 00:47:20 +0000 (UTC), spope33@speedymail.org (Steve
>>>>>If you apply any kind of filtering to MSK, it's not MSK any more.
>>>> True. The exact same could be said about PSK.
>>> Definitively not true.
>>(I think we might have to disagree on this.)
I definitely think we will have to disagree on this. Really it comes down to your being willing to call distorted PSK "PSK", but unwilling to call distorted MSK "MSK". If this distinction happens to help you organize your thoughts on the subject that is a good thing for you. But were I to think this way, I would view it as inconsistent thinking on my part ... it would not be helpful to understanding, and I would refine my thinking to something clearer. (I somewhat feel like I'm being accused of a thought crime, as opposed to having written anything technically incorrect in this thread that justifies rebuke, which seems to be your angle.) Steve
eric.jacobsen@ieee.org (Eric Jacobsen) writes:

> On Tue, 6 Oct 2015 00:47:20 +0000 (UTC), spope33@speedymail.org (Steve > Pope) wrote: > >>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: >> >>>On Mon, 5 Oct 2015 20:17:57 +0000 (UTC), spope33@speedymail.org (Steve >> >>>>But more importantly thinking of MSK as a type of FM signal can add >>>>some insight into what you're working with (examples below). >> >>>In my experience thinking of MSK as CPM with no filtering is good for >>>evaluating how it fits within performance tradeoff spaces. >> >>Thanks, an interesting perspective. >> >>(Tangentially, 2-MSK can be either continuous phase, or non-continuous >>phase. However, only the continuous phase sub-category of 2-MSK is >>equivalent to OQPSK with the right filtering (or the right pulse >>shape, take your pick). So we're talking about a form of modulation >>that is both MSK and CPM.) > > That's what I've been saying all along: MSK is CPM with no phase > filter. MSK is a limiting case of FSK. MSK is also a special case > of OQPSK with half-sine pulse shaping. It is all these things. > >>> It's an oddball in that there are multiple ways of thinking >>> about it, but if you only think about it as FSK you may miss >>> opportunities to make a much more flexible system. >> >>I'm not suggesting excluding other perspectives, just that >>the perspective of MSK (or FSK) being a form of frequency modulation >>is useful. > > I never claimed otherwise.
Yes you did, Eric. Here is the entire post, indented for quotation: On Sat, 03 Oct 2015 07:54:15 -0400, Randy Yates <yates@digitalsignallabs.com> wrote: >"tarikkazaz" <50642@DSPRelated> writes: > >> Hi all, >> >> I am working on implementation of zigbee device on FPGA. Till now I have >> made Tx which is compatible with commercial devices. Also I have Rx which >> is working with my own Tx, but does not work with commercial devices. >> Major reason why my receiver can not decode signals from commercial >> devices is frequency offset. So far I tried to apply zero crossing >> approach to decode signal, but that does not help >> (http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1615158&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D1615158). >> Previously I have been doing correlation of known chips with received >> signal (on that way I was able to decode signals from my own Tx). >> >> Because now I am planning to start with implementation of frequency offset >> compensation for my receiver, I would like to get advice. Which estimator >> do you suggest me to use? Or maybe I could use some simplified method, as >> zigbee has known preamble of 256 chips, which is 128 chips in I branch, >> and 128 chips in Q branch. Sampling rate of my ADC is 64Msps, and I was >> doing down sapling to 4Msps. > >Hi, > >MSK is FM, right? No, MSK is not FM. It is essentially OQPSK with crappy filtering. >Why not compute the phase of the IQ stream over some >computationally-convenient block and then simply do a least-squares fit >of a straight line? The slope of that line is then your frequency >offset. This assumes there is an even number of ones and zeros. And the >longer the block, the better the estimate via averaging. > >I would think this could at least give you a coarse frequency offset >estimation. >-- >Randy Yates >Digital Signal Labs >http://www.digitalsignallabs.com Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
On Tue, 06 Oct 2015 12:19:11 -0400, Randy Yates
<yates@digitalsignallabs.com> wrote:

>eric.jacobsen@ieee.org (Eric Jacobsen) writes: > >> On Tue, 6 Oct 2015 00:47:20 +0000 (UTC), spope33@speedymail.org (Steve >> Pope) wrote: >> >>>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: >>> >>>>On Mon, 5 Oct 2015 20:17:57 +0000 (UTC), spope33@speedymail.org (Steve >>> >>>>>But more importantly thinking of MSK as a type of FM signal can add >>>>>some insight into what you're working with (examples below). >>> >>>>In my experience thinking of MSK as CPM with no filtering is good for >>>>evaluating how it fits within performance tradeoff spaces. >>> >>>Thanks, an interesting perspective. >>> >>>(Tangentially, 2-MSK can be either continuous phase, or non-continuous >>>phase. However, only the continuous phase sub-category of 2-MSK is >>>equivalent to OQPSK with the right filtering (or the right pulse >>>shape, take your pick). So we're talking about a form of modulation >>>that is both MSK and CPM.) >> >> That's what I've been saying all along: MSK is CPM with no phase >> filter. MSK is a limiting case of FSK. MSK is also a special case >> of OQPSK with half-sine pulse shaping. It is all these things. >> >>>> It's an oddball in that there are multiple ways of thinking >>>> about it, but if you only think about it as FSK you may miss >>>> opportunities to make a much more flexible system. >>> >>>I'm not suggesting excluding other perspectives, just that >>>the perspective of MSK (or FSK) being a form of frequency modulation >>>is useful. >> >> I never claimed otherwise. > >Yes you did, Eric. Here is the entire post, indented for quotation:
No, because I think the terminology of FM = FSK is very misleading and creates more confusion than clarity. I already explained that. MSK is FSK with h = 1/2. It's just a nomenclature overload thing. I try to reserve FM for analog, which still gets used a lot. There are disingenuous vendors out that that claim they're selling you a "digital FM" link, but it's analog FM with an ADC in the receiver or something similarly suboptimal. So, sorry if my deprecation of "FM" as a digital methodology caused confusion.
> > On Sat, 03 Oct 2015 07:54:15 -0400, Randy Yates > <yates@digitalsignallabs.com> wrote: > > >"tarikkazaz" <50642@DSPRelated> writes: > > > >> Hi all, > >> > >> I am working on implementation of zigbee device on FPGA. Till now I have > >> made Tx which is compatible with commercial devices. Also I have Rx which > >> is working with my own Tx, but does not work with commercial devices. > >> Major reason why my receiver can not decode signals from commercial > >> devices is frequency offset. So far I tried to apply zero crossing > >> approach to decode signal, but that does not help > >> (http://ieeexplore.ieee.org/xpl/login.jsp?tp=&arnumber=1615158&url=http%3A%2F%2Fieeexplore.ieee.org%2Fxpls%2Fabs_all.jsp%3Farnumber%3D1615158). > >> Previously I have been doing correlation of known chips with received > >> signal (on that way I was able to decode signals from my own Tx). > >> > >> Because now I am planning to start with implementation of frequency offset > >> compensation for my receiver, I would like to get advice. Which estimator > >> do you suggest me to use? Or maybe I could use some simplified method, as > >> zigbee has known preamble of 256 chips, which is 128 chips in I branch, > >> and 128 chips in Q branch. Sampling rate of my ADC is 64Msps, and I was > >> doing down sapling to 4Msps. > > > >Hi, > > > >MSK is FM, right? > > No, MSK is not FM. It is essentially OQPSK with crappy filtering. > > >Why not compute the phase of the IQ stream over some > >computationally-convenient block and then simply do a least-squares fit > >of a straight line? The slope of that line is then your frequency > >offset. This assumes there is an even number of ones and zeros. And the > >longer the block, the better the estimate via averaging. > > > >I would think this could at least give you a coarse frequency offset > >estimation. > >-- > >Randy Yates > >Digital Signal Labs > >http://www.digitalsignallabs.com > > Eric Jacobsen > Anchor Hill Communications > http://www.anchorhill.com > >-- >Randy Yates >Digital Signal Labs >http://www.digitalsignallabs.com
Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
On Tue, 6 Oct 2015 03:34:48 +0000 (UTC), spope33@speedymail.org (Steve
Pope) wrote:

>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: > >>On Tue, 6 Oct 2015 00:47:20 +0000 (UTC), spope33@speedymail.org (Steve > >>>>>>If you apply any kind of filtering to MSK, it's not MSK any more. > >>>>> True. The exact same could be said about PSK. > >>>> Definitively not true. > >>>(I think we might have to disagree on this.) > >I definitely think we will have to disagree on this. > >Really it comes down to your being willing to call distorted >PSK "PSK", but unwilling to call distorted MSK "MSK".
Seriously, I can't sort out where you're coming from. You're really not making much sense to me here. Proper filtering doesn't "distort" PSK. This is what pulse shaping and matched filtering is all about, so there's no ISI, specifically no distortion, in the receiver. That allows bandlimiting without removing information. Do you mean some other kind of distortion? You've not been clear. What "distortion" of MSK are you talking about?
>If this distinction happens to help you organize your >thoughts on the subject that is a good thing for you.
I'm just trying to clarify your misconceptions.
>But were I to think this way, I would view it as inconsistent >thinking on my part ... it would not be helpful to understanding, >and I would refine my thinking to something clearer.
>(I somewhat feel like I'm being accused of a thought crime, >as opposed to having written anything technically incorrect >in this thread that justifies rebuke, which seems to be >your angle.)
Sorry if it came across that way, but you've been stating some things as facts that simply aren't. These really aren't odd or difficult concepts, I don't know what the difficulty is here. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
On Tue, 06 Oct 2015 18:22:27 GMT, eric.jacobsen@ieee.org (Eric
Jacobsen) wrote:

>On Tue, 06 Oct 2015 12:19:11 -0400, Randy Yates ><yates@digitalsignallabs.com> wrote: > >>eric.jacobsen@ieee.org (Eric Jacobsen) writes: >> >>> On Tue, 6 Oct 2015 00:47:20 +0000 (UTC), spope33@speedymail.org (Steve >>> Pope) wrote: >>> >>>>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: >>>> >>>>>On Mon, 5 Oct 2015 20:17:57 +0000 (UTC), spope33@speedymail.org (Steve >>>> >>>>>>But more importantly thinking of MSK as a type of FM signal can add >>>>>>some insight into what you're working with (examples below). >>>> >>>>>In my experience thinking of MSK as CPM with no filtering is good for >>>>>evaluating how it fits within performance tradeoff spaces. >>>> >>>>Thanks, an interesting perspective. >>>> >>>>(Tangentially, 2-MSK can be either continuous phase, or non-continuous >>>>phase. However, only the continuous phase sub-category of 2-MSK is >>>>equivalent to OQPSK with the right filtering (or the right pulse >>>>shape, take your pick). So we're talking about a form of modulation >>>>that is both MSK and CPM.) >>> >>> That's what I've been saying all along: MSK is CPM with no phase >>> filter. MSK is a limiting case of FSK. MSK is also a special case >>> of OQPSK with half-sine pulse shaping. It is all these things. >>> >>>>> It's an oddball in that there are multiple ways of thinking >>>>> about it, but if you only think about it as FSK you may miss >>>>> opportunities to make a much more flexible system. >>>> >>>>I'm not suggesting excluding other perspectives, just that >>>>the perspective of MSK (or FSK) being a form of frequency modulation >>>>is useful. >>> >>> I never claimed otherwise. >> >>Yes you did, Eric. Here is the entire post, indented for quotation: > >No, because I think the terminology of FM = FSK is very misleading and >creates more confusion than clarity. I already explained that. > >MSK is FSK with h = 1/2. > >It's just a nomenclature overload thing. I try to reserve FM for >analog, which still gets used a lot. There are disingenuous vendors >out that that claim they're selling you a "digital FM" link, but it's >analog FM with an ADC in the receiver or something similarly >suboptimal. > >So, sorry if my deprecation of "FM" as a digital methodology caused >confusion. >
To clarify slightly more, my original comment that MSK is not FM, but OQPSK with crappy filtering, was made partly in jest. From my perspective it is true, but I fully appreciate that many folks consider FSK to be FM, and it is not incorrect to do so. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Eric Jacobsen <eric.jacobsen@ieee.org> wrote:

> On Tue, 6 Oct 2015 03:34:48 +0000 (UTC), spope33@speedymail.org (Steve
>> Eric Jacobsen <eric.jacobsen@ieee.org> wrote:
>>> If you apply any kind of filtering to MSK, it's not MSK any more.
>> Really it comes down to your being willing to call distorted >> PSK "PSK", but unwilling to call distorted MSK "MSK".
> What "distortion" of MSK are you talking about?
Exactly what you described above.
> you've been stating some things as facts that simply aren't.
If I have stated anything non-factual, I will correct it, but right now I don't believe there are any instances of such. If I have said anything unclear, I will clarify it. Steve
eric.jacobsen@ieee.org (Eric Jacobsen) writes:

> On Tue, 06 Oct 2015 12:19:11 -0400, Randy Yates > <yates@digitalsignallabs.com> wrote: > >>eric.jacobsen@ieee.org (Eric Jacobsen) writes: >> >>> On Tue, 6 Oct 2015 00:47:20 +0000 (UTC), spope33@speedymail.org (Steve >>> Pope) wrote: >>> >>>>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: >>>> >>>>>On Mon, 5 Oct 2015 20:17:57 +0000 (UTC), spope33@speedymail.org (Steve >>>> >>>>>>But more importantly thinking of MSK as a type of FM signal can add >>>>>>some insight into what you're working with (examples below). >>>> >>>>>In my experience thinking of MSK as CPM with no filtering is good for >>>>>evaluating how it fits within performance tradeoff spaces. >>>> >>>>Thanks, an interesting perspective. >>>> >>>>(Tangentially, 2-MSK can be either continuous phase, or non-continuous >>>>phase. However, only the continuous phase sub-category of 2-MSK is >>>>equivalent to OQPSK with the right filtering (or the right pulse >>>>shape, take your pick). So we're talking about a form of modulation >>>>that is both MSK and CPM.) >>> >>> That's what I've been saying all along: MSK is CPM with no phase >>> filter. MSK is a limiting case of FSK. MSK is also a special case >>> of OQPSK with half-sine pulse shaping. It is all these things. >>> >>>>> It's an oddball in that there are multiple ways of thinking >>>>> about it, but if you only think about it as FSK you may miss >>>>> opportunities to make a much more flexible system. >>>> >>>>I'm not suggesting excluding other perspectives, just that >>>>the perspective of MSK (or FSK) being a form of frequency modulation >>>>is useful. >>> >>> I never claimed otherwise. >> >>Yes you did, Eric. Here is the entire post, indented for quotation: > > No, because I think the terminology of FM = FSK is very misleading and > creates more confusion than clarity. I already explained that. > > MSK is FSK with h = 1/2. > > It's just a nomenclature overload thing. I try to reserve FM for > analog, which still gets used a lot. There are disingenuous vendors > out that that claim they're selling you a "digital FM" link, but it's > analog FM with an ADC in the receiver or something similarly > suboptimal. > > So, sorry if my deprecation of "FM" as a digital methodology caused > confusion.
Fair enough. Peace, brother! --Randy -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Randy Yates  <yates@digitalsignallabs.com> wrote:

>eric.jacobsen@ieee.org (Eric Jacobsen) writes:
>> It's just a nomenclature overload thing. I try to reserve FM for >> analog, which still gets used a lot. There are disingenuous vendors >> out that that claim they're selling you a "digital FM" link, but it's >> analog FM with an ADC in the receiver or something similarly >> suboptimal.
>> So, sorry if my deprecation of "FM" as a digital methodology caused >> confusion.
>Fair enough. Peace, brother!
And there is precedent; I remember when PacBell described its PCS services as "not cellular". Steve
On Tue, 6 Oct 2015 20:14:18 +0000 (UTC), spope33@speedymail.org (Steve
Pope) wrote:

>Eric Jacobsen <eric.jacobsen@ieee.org> wrote: > >> On Tue, 6 Oct 2015 03:34:48 +0000 (UTC), spope33@speedymail.org (Steve > >>> Eric Jacobsen <eric.jacobsen@ieee.org> wrote: > >>>> If you apply any kind of filtering to MSK, it's not MSK any more. > >>> Really it comes down to your being willing to call distorted >>> PSK "PSK", but unwilling to call distorted MSK "MSK". > >> What "distortion" of MSK are you talking about? > >Exactly what you described above.
Are you disagreeing that adding a filter that changes an MSK waveform makes it deviate from being MSK? If it can change, how much can it change before it's not MSK?
>> you've been stating some things as facts that simply aren't. > >If I have stated anything non-factual, I will correct it, but >right now I don't believe there are any instances of such.
You seem to be claiming that filtering PSK makes it not PSK. Filters are integral parts of PSK systems to achieve matched filtering performance. How do you reconcile that? You also claimed that adding a filter to a phase modulated signal adds amplitude distortion. Here is the received constellation of a heavily-filtered 8PSK signal: http://www.ericjacobsen.org/Files/8PSKconstellation.jpg There is no amplitude distortion. How do explain that? Can you discern what sort of filter was used, or not used, by the lack of distortion?
>If I have said anything unclear, I will clarify it. > >Steve
Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com