Reply by Christian SC May 18, 20162016-05-18
>>On Mon, 03 Jun 2013 06:48:26 -0500, DougB wrote: >> >>>>>Only a fractionally spaced equalizer will resolve timing phase. If >you >>> use >>>>>a T spaced equalizer you had better have good symbol timing recovery >>> prior >>>>>to the equalizer. Carrier reference can be resolved after >equalization >>>>>unless the frequency offset is large in which case you can split the >>> loop >>>>>and recover frequency prior to the equalizer and phase/remaining >>> frequency >>>>>after the equalizer. >>>>>-Doug >>>> >>>> >>>>One of the disadvantages of using the EQ to correct timing is that it >>>>consumes degrees of freedom usually intended for combating the
channel
>>>>distortion. Those degrees of freedom cost complexity, and usually
the
>>>>complexity of the EQ is much greater than the complexity of a decent >>>>timing recovery system. So, in my experience, the systems that try
to
>>>>use the EQ for synchronization or to aid in synchronization wind up >with >>>>a heavier complexity load than alternative methods. Separating the
two
>>>>tasks can be advantageous for the performance of both the EQ and the >>>>timing recovery as well as complexity. >>>> >>>> >>>> >>>>Eric Jacobsen >>>>Anchor Hill Communications >>>>http://www.anchorhill.com >>>> >>>> >>> That's true, but if the channel highly distorted, there is no TED
that
>>> is going to give you the optimum timing phase - that can only be
gotten
>>> from a fractionally spaced equalizer. Still use timing recovery as >>> normal, but let the FSE optimize the timing phase - it can synthesize >>> the proper fractional delay. >> >>I considered just letting the equalizer take care of delay. It would >>certainly make my life easier in many respects. >> >>My problem with this system is that I can't count on a perfect match >>between transmit and receive clocks, so the change in delay from the >>start of a run to the end would require an equalizer with an unfeasible
>>amount of delay. Hence, I seek a reliable way to synchronize that does
>>not leave the equalizer holding the bag. >> >>-- >>My liberal friends think I'm a conservative kook. >>My conservative friends think I'm a liberal kook. >>Why am I not happy that they have found common ground? >> >>Tim Wescott, Communications, Control, Circuits & Software >>http://www.wescottdesign.com >> > >In the given scenario, in my opinion, the TED is not even supposed to
lock
>onto the timing phase; it will lock to the symbol rate (or transmit
clock).
>So any NDA TED like Gardner followed by a fractionally spaced equalizer >should do the job for you. A very interesting and practical reference
paper
>is the one by John Treichler, "Practical blind demodulators for
high-order
>QAM signals" published in 1998. The most important part I think is the >fractional tap-spacing because a symbol rate equalizer can easily lose
the
>battle due to aliasing.
Hello, I have read the whole discussion, it is very interesting. I have got two simple questions: - If the synchronization is placed before a T/2-FSE, the output of the interpolation unit is only to be fed to the TED? I mean, the signal is not resampled at this point, because I still want 2 samples per symbol at the input of the equalizer, isnt it? - If the synchronization is placed after equalization, and, thus, the input signal is at 1sample/symbol, must I use a synchronization algorithm which operates at this sample rate (1sample/symbol)? For example M&M? --------------------------------------- Posted through http://www.DSPRelated.com
Reply by Eric Jacobsen June 16, 20132013-06-16
On Sun, 16 Jun 2013 07:37:00 -0700, Eric Weaver <weav@sigma.net>
wrote:

> >EJ; > >Just out of curiosity, can it work to always start with a known training >symbol (or two or three), come up with a "deconvolution kernel" that >would transform the found one closer to the expected one, and use that >for the whole message block?
Yes. Many systems do exactly that. The training sequence may be significantly longer than two or three symbols depending on the expected channels and how much noise reduction you need in the estimate, but the idea is the same. The other assumption is that the channel is static, or close to it, during the length of the transmission. This is often a reasonable assumption if the burst isn't huge since the channel coherence time is usually very long compared to a usefully long burst.
>I suppose it depends on the mod scheme in question.
It's used in many different systems, including OFDM. 802.11 works this way. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by Eric Weaver June 16, 20132013-06-16
EJ;

Just out of curiosity, can it work to always start with a known training 
symbol (or two or three), come up with a "deconvolution kernel" that 
would transform the found one closer to the expected one, and use that 
for the whole message block?

I suppose it depends on the mod scheme in question.

Reply by June 13, 20132013-06-13
On Thursday, May 30, 2013 11:16:46 AM UTC-7, Vladimir Vassilevsky wrote:
> Optimal: > Make Kalman-like filter observing current decision. Derive equalizer > update, symbol sync and carrier sync updates altogether. > Dumb: > Put equalizer outside of timing/carrier loop. I.e. perform > synchronization before EQ.
Why don't you do the decoding jointly while you are at it? Do you have any estimate of the computational requirements of the optimal vs other solutions, say for a channel length L and a linear equalizer of length N ?
Reply by June 13, 20132013-06-13
On Thursday, May 30, 2013 9:58:18 AM UTC-7, Tim Wescott wrote:
> How does one maintain synchronization when one is using adaptive > equalization?
The easiest way to avoid interaction of timing recovery vs equalization is to keep the two loops completely separate ie non-decision directed timing error detection and feed-forward timing correction. If you can afford to oversample by 4x, use O&M TED, interpolate for correction and feed the output to fractional equalizer for fine phase adjustment.
Reply by Eric Jacobsen June 8, 20132013-06-08
On Sat, 08 Jun 2013 07:31:08 -0500, "commsignal" <58672@dsprelated>
wrote:

>>On Fri, 07 Jun 2013 18:35:38 -0500, Tim Wescott <tim@seemywebsite.com> >>wrote: >> >>>On Fri, 07 Jun 2013 17:44:19 +0000, Eric Jacobsen wrote: >>> >>>> On Fri, 07 Jun 2013 02:14:58 -0500, "commsignal" <58672@dsprelated> >>>> wrote: >>>> >>>>>>On Fri, 07 Jun 2013 00:23:29 -0500, "commsignal" <58672@dsprelated> >>>>>>wrote: >>>>>> >>>>>>>>On Mon, 03 Jun 2013 06:48:26 -0500, DougB wrote: >>>>>>>> >>>>>>>>>>>Only a fractionally spaced equalizer will resolve timing phase. >>>>>>>>>>>If >>>>>>>you >>>>>>>>> use >>>>>>>>>>>a T spaced equalizer you had better have good symbol timing >>>>>>>>>>>recovery >>>>>>>>> prior >>>>>>>>>>>to the equalizer. Carrier reference can be resolved after >>>>>>>equalization >>>>>>>>>>>unless the frequency offset is large in which case you can split >>>>>>>>>>>the >>>>>>>>> loop >>>>>>>>>>>and recover frequency prior to the equalizer and phase/remaining >>>>>>>>> frequency >>>>>>>>>>>after the equalizer. >>>>>>>>>>>-Doug >>>>>>>>>> >>>>>>>>>> >>>>>>>>>>One of the disadvantages of using the EQ to correct timing is >that >>>>>>>>>>it consumes degrees of freedom usually intended for combating the >>>>>channel >>>>>>>>>>distortion. Those degrees of freedom cost complexity, and >usually >>>>>the >>>>>>>>>>complexity of the EQ is much greater than the complexity of a >>>>>>>>>>decent timing recovery system. So, in my experience, the >systems >>>>>>>>>>that try >>>>>to >>>>>>>>>>use the EQ for synchronization or to aid in synchronization wind >up >>>>>>>with >>>>>>>>>>a heavier complexity load than alternative methods. Separating >the >>>>>two >>>>>>>>>>tasks can be advantageous for the performance of both the EQ and >>>>>>>>>>the timing recovery as well as complexity. >>>>>>>>>> >>>>>>>>>> >>>>>>>>>> >>>>>>>>>>Eric Jacobsen >>>>>>>>>>Anchor Hill Communications >>>>>>>>>>http://www.anchorhill.com >>>>>>>>>> >>>>>>>>>> >>>>>>>>> That's true, but if the channel highly distorted, there is no TED >>>>>that >>>>>>>>> is going to give you the optimum timing phase - that can only be >>>>>gotten >>>>>>>>> from a fractionally spaced equalizer. Still use timing recovery >as >>>>>>>>> normal, but let the FSE optimize the timing phase - it can >>>>>>>>> synthesize the proper fractional delay. >>>>>>>> >>>>>>>>I considered just letting the equalizer take care of delay. It >would >>>>>>>>certainly make my life easier in many respects. >>>>>>>> >>>>>>>>My problem with this system is that I can't count on a perfect >match >>>>>>>>between transmit and receive clocks, so the change in delay from >the >>>>>>>>start of a run to the end would require an equalizer with an >>>>>>>>unfeasible >>>>> >>>>>>>>amount of delay. Hence, I seek a reliable way to synchronize that >>>>>>>>does >>>>> >>>>>>>>not leave the equalizer holding the bag. >>>>>>>> >>>>>>>>-- >>>>>>>>My liberal friends think I'm a conservative kook. My conservative >>>>>>>>friends think I'm a liberal kook. Why am I not happy that they have >>>>>>>>found common ground? >>>>>>>> >>>>>>>>Tim Wescott, Communications, Control, Circuits & Software >>>>>>>>http://www.wescottdesign.com >>>>>>>> >>>>>>>> >>>>>>>In the given scenario, in my opinion, the TED is not even supposed >to >>>>>lock >>>>>>>onto the timing phase; it will lock to the symbol rate (or transmit >>>>>clock). >>>>>>>So any NDA TED like Gardner followed by a fractionally spaced >>>>>>>equalizer should do the job for you. >>>>>> >>>>>>Exactly. >>>>>> >>>>>>> A very interesting and practical reference paper >>>>>>>is the one by John Treichler, "Practical blind demodulators for >>>>>high-order >>>>>>>QAM signals" published in 1998. The most important part I think is >the >>>>>>>fractional tap-spacing because a symbol rate equalizer can easily >lose >>>>>the >>>>>>>battle due to aliasing. >>>>>> >>>>>>Depending on the system constraints and how the system is >>>>>>engineered/architected, a T-spaced EQ can still work well in many >>>>>>applications. In my experience I've never had to resort to a >>>>>>fractional-spaced EQ for the systems that I've worked on (which >aren't >>>>>>universal), which saves a lot of complexity. Perhaps I've been >lucky. >>>>>> >>>>>> >>>>>>Eric Jacobsen >>>>>>Anchor Hill Communications >>>>>>http://www.anchorhill.com >>>>>> >>>>>> >>>>>My understanding which can be wrong is the following. Symbol-rate >>>>>tap-spacing is optimal if the equalizer is preceded by a filter >matched >>>>>to the *channel distorted* transmit pulse, which is only possible if >the >>>>>channel response is known beforehand. In that case, the >autocorrelation >>>>>values at integer lags of the composite channel (Tx, channel, Rx) are >>>>>known and the correlated noise can be whitened through a noise >whitening >>>>>filter after symbol-rate sampling. >>>>> >>>>>However, when channel is not known, 1/2T becomes the folding frequency >>>>>and since the filtered samples depend on the delay (sampling done at >>>>>times kT+tau), the overlappend spectra can easily cancel each other >>>>>depending on the value of tau (timing offset). >>>> >>>> That all seems like a reasonable argument. >>>> >>>> Remember also that if all the functions are linear the order of >>>> operation doesn't matter. So as long as linearity is preserved, the >>>> order of the pulse-shaping filter and EQ are inconsequential. Aliasing >>>> certainly has to be considered within that context. >>> >>>Linearity and shift invariance (or time invariance) must be preserved for > >>>order to not matter. Sampling (or simple decimation) are linear, but >>>they are not time- or shift-invariant and order matters in that case. >> >>I did a really crappy job of conveying what I meant. >> >>I wish we were all in a room with a white board or something, as I >>don't think I can do it justice in a few paragraphs. The gist is >>that I think this stuff gets made more complicated than it needs to be >>in many cases, and sometimes effects that people worry about can be >>neglected completely without issue. >> >>Basically, many systems get by with a T-spaced EQ after the pulse >>filter and timing recovery because the expected "issues" aren't really >>issues in most cases. >> >>>-- >>>My liberal friends think I'm a conservative kook. >>>My conservative friends think I'm a liberal kook. >>>Why am I not happy that they have found common ground? >>> >>>Tim Wescott, Communications, Control, Circuits & Software >>>http://www.wescottdesign.com >> >>Eric Jacobsen >>Anchor Hill Communications >>http://www.anchorhill.com >> > >You are right. Two things come into my mind. One, the same equalizer can >have very different performance with two very dissimilar channels. So >T-spaced equalizer can definitely make things reasonable if the channel is >not extreme. Second, the powerful error correcting codes don't know the >difference between thermal noise and residual interference. So they must be >extracting a good deal of burried information correctly.
That is a very good point: integrating well with the FEC makes a big difference, and a soft-decision FEC will, as you suggest, see the effective noise amplification of the EQ as a reduction in SNR. So the EQ can be thought of as turning some of the distortion into noise, which is more easily handled by a good FEC. If things are going well the residual distortion won't be large compared to the "noise" impairments. When the channel gets extreme enough that the required complexity exceeds that required for an OFDM (or other multicarrier) system in the same channel, then there's motivation to switch modulation schemes. So there's sort of an upper limit to how bad things can get before one changes horses. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by commsignal June 8, 20132013-06-08
>On Fri, 07 Jun 2013 18:35:38 -0500, Tim Wescott <tim@seemywebsite.com> >wrote: > >>On Fri, 07 Jun 2013 17:44:19 +0000, Eric Jacobsen wrote: >> >>> On Fri, 07 Jun 2013 02:14:58 -0500, "commsignal" <58672@dsprelated> >>> wrote: >>> >>>>>On Fri, 07 Jun 2013 00:23:29 -0500, "commsignal" <58672@dsprelated> >>>>>wrote: >>>>> >>>>>>>On Mon, 03 Jun 2013 06:48:26 -0500, DougB wrote: >>>>>>> >>>>>>>>>>Only a fractionally spaced equalizer will resolve timing phase. >>>>>>>>>>If >>>>>>you >>>>>>>> use >>>>>>>>>>a T spaced equalizer you had better have good symbol timing >>>>>>>>>>recovery >>>>>>>> prior >>>>>>>>>>to the equalizer. Carrier reference can be resolved after >>>>>>equalization >>>>>>>>>>unless the frequency offset is large in which case you can split >>>>>>>>>>the >>>>>>>> loop >>>>>>>>>>and recover frequency prior to the equalizer and phase/remaining >>>>>>>> frequency >>>>>>>>>>after the equalizer. >>>>>>>>>>-Doug >>>>>>>>> >>>>>>>>> >>>>>>>>>One of the disadvantages of using the EQ to correct timing is
that
>>>>>>>>>it consumes degrees of freedom usually intended for combating the >>>>channel >>>>>>>>>distortion. Those degrees of freedom cost complexity, and
usually
>>>>the >>>>>>>>>complexity of the EQ is much greater than the complexity of a >>>>>>>>>decent timing recovery system. So, in my experience, the
systems
>>>>>>>>>that try >>>>to >>>>>>>>>use the EQ for synchronization or to aid in synchronization wind
up
>>>>>>with >>>>>>>>>a heavier complexity load than alternative methods. Separating
the
>>>>two >>>>>>>>>tasks can be advantageous for the performance of both the EQ and >>>>>>>>>the timing recovery as well as complexity. >>>>>>>>> >>>>>>>>> >>>>>>>>> >>>>>>>>>Eric Jacobsen >>>>>>>>>Anchor Hill Communications >>>>>>>>>http://www.anchorhill.com >>>>>>>>> >>>>>>>>> >>>>>>>> That's true, but if the channel highly distorted, there is no TED >>>>that >>>>>>>> is going to give you the optimum timing phase - that can only be >>>>gotten >>>>>>>> from a fractionally spaced equalizer. Still use timing recovery
as
>>>>>>>> normal, but let the FSE optimize the timing phase - it can >>>>>>>> synthesize the proper fractional delay. >>>>>>> >>>>>>>I considered just letting the equalizer take care of delay. It
would
>>>>>>>certainly make my life easier in many respects. >>>>>>> >>>>>>>My problem with this system is that I can't count on a perfect
match
>>>>>>>between transmit and receive clocks, so the change in delay from
the
>>>>>>>start of a run to the end would require an equalizer with an >>>>>>>unfeasible >>>> >>>>>>>amount of delay. Hence, I seek a reliable way to synchronize that >>>>>>>does >>>> >>>>>>>not leave the equalizer holding the bag. >>>>>>> >>>>>>>-- >>>>>>>My liberal friends think I'm a conservative kook. My conservative >>>>>>>friends think I'm a liberal kook. Why am I not happy that they have >>>>>>>found common ground? >>>>>>> >>>>>>>Tim Wescott, Communications, Control, Circuits & Software >>>>>>>http://www.wescottdesign.com >>>>>>> >>>>>>> >>>>>>In the given scenario, in my opinion, the TED is not even supposed
to
>>>>lock >>>>>>onto the timing phase; it will lock to the symbol rate (or transmit >>>>clock). >>>>>>So any NDA TED like Gardner followed by a fractionally spaced >>>>>>equalizer should do the job for you. >>>>> >>>>>Exactly. >>>>> >>>>>> A very interesting and practical reference paper >>>>>>is the one by John Treichler, "Practical blind demodulators for >>>>high-order >>>>>>QAM signals" published in 1998. The most important part I think is
the
>>>>>>fractional tap-spacing because a symbol rate equalizer can easily
lose
>>>>the >>>>>>battle due to aliasing. >>>>> >>>>>Depending on the system constraints and how the system is >>>>>engineered/architected, a T-spaced EQ can still work well in many >>>>>applications. In my experience I've never had to resort to a >>>>>fractional-spaced EQ for the systems that I've worked on (which
aren't
>>>>>universal), which saves a lot of complexity. Perhaps I've been
lucky.
>>>>> >>>>> >>>>>Eric Jacobsen >>>>>Anchor Hill Communications >>>>>http://www.anchorhill.com >>>>> >>>>> >>>>My understanding which can be wrong is the following. Symbol-rate >>>>tap-spacing is optimal if the equalizer is preceded by a filter
matched
>>>>to the *channel distorted* transmit pulse, which is only possible if
the
>>>>channel response is known beforehand. In that case, the
autocorrelation
>>>>values at integer lags of the composite channel (Tx, channel, Rx) are >>>>known and the correlated noise can be whitened through a noise
whitening
>>>>filter after symbol-rate sampling. >>>> >>>>However, when channel is not known, 1/2T becomes the folding frequency >>>>and since the filtered samples depend on the delay (sampling done at >>>>times kT+tau), the overlappend spectra can easily cancel each other >>>>depending on the value of tau (timing offset). >>> >>> That all seems like a reasonable argument. >>> >>> Remember also that if all the functions are linear the order of >>> operation doesn't matter. So as long as linearity is preserved, the >>> order of the pulse-shaping filter and EQ are inconsequential. Aliasing >>> certainly has to be considered within that context. >> >>Linearity and shift invariance (or time invariance) must be preserved for
>>order to not matter. Sampling (or simple decimation) are linear, but >>they are not time- or shift-invariant and order matters in that case. > >I did a really crappy job of conveying what I meant. > >I wish we were all in a room with a white board or something, as I >don't think I can do it justice in a few paragraphs. The gist is >that I think this stuff gets made more complicated than it needs to be >in many cases, and sometimes effects that people worry about can be >neglected completely without issue. > >Basically, many systems get by with a T-spaced EQ after the pulse >filter and timing recovery because the expected "issues" aren't really >issues in most cases. > >>-- >>My liberal friends think I'm a conservative kook. >>My conservative friends think I'm a liberal kook. >>Why am I not happy that they have found common ground? >> >>Tim Wescott, Communications, Control, Circuits & Software >>http://www.wescottdesign.com > >Eric Jacobsen >Anchor Hill Communications >http://www.anchorhill.com >
You are right. Two things come into my mind. One, the same equalizer can have very different performance with two very dissimilar channels. So T-spaced equalizer can definitely make things reasonable if the channel is not extreme. Second, the powerful error correcting codes don't know the difference between thermal noise and residual interference. So they must be extracting a good deal of burried information correctly.
Reply by Eric Jacobsen June 8, 20132013-06-08
On Fri, 07 Jun 2013 18:35:38 -0500, Tim Wescott <tim@seemywebsite.com>
wrote:

>On Fri, 07 Jun 2013 17:44:19 +0000, Eric Jacobsen wrote: > >> On Fri, 07 Jun 2013 02:14:58 -0500, "commsignal" <58672@dsprelated> >> wrote: >> >>>>On Fri, 07 Jun 2013 00:23:29 -0500, "commsignal" <58672@dsprelated> >>>>wrote: >>>> >>>>>>On Mon, 03 Jun 2013 06:48:26 -0500, DougB wrote: >>>>>> >>>>>>>>>Only a fractionally spaced equalizer will resolve timing phase. >>>>>>>>>If >>>>>you >>>>>>> use >>>>>>>>>a T spaced equalizer you had better have good symbol timing >>>>>>>>>recovery >>>>>>> prior >>>>>>>>>to the equalizer. Carrier reference can be resolved after >>>>>equalization >>>>>>>>>unless the frequency offset is large in which case you can split >>>>>>>>>the >>>>>>> loop >>>>>>>>>and recover frequency prior to the equalizer and phase/remaining >>>>>>> frequency >>>>>>>>>after the equalizer. >>>>>>>>>-Doug >>>>>>>> >>>>>>>> >>>>>>>>One of the disadvantages of using the EQ to correct timing is that >>>>>>>>it consumes degrees of freedom usually intended for combating the >>>channel >>>>>>>>distortion. Those degrees of freedom cost complexity, and usually >>>the >>>>>>>>complexity of the EQ is much greater than the complexity of a >>>>>>>>decent timing recovery system. So, in my experience, the systems >>>>>>>>that try >>>to >>>>>>>>use the EQ for synchronization or to aid in synchronization wind up >>>>>with >>>>>>>>a heavier complexity load than alternative methods. Separating the >>>two >>>>>>>>tasks can be advantageous for the performance of both the EQ and >>>>>>>>the timing recovery as well as complexity. >>>>>>>> >>>>>>>> >>>>>>>> >>>>>>>>Eric Jacobsen >>>>>>>>Anchor Hill Communications >>>>>>>>http://www.anchorhill.com >>>>>>>> >>>>>>>> >>>>>>> That's true, but if the channel highly distorted, there is no TED >>>that >>>>>>> is going to give you the optimum timing phase - that can only be >>>gotten >>>>>>> from a fractionally spaced equalizer. Still use timing recovery as >>>>>>> normal, but let the FSE optimize the timing phase - it can >>>>>>> synthesize the proper fractional delay. >>>>>> >>>>>>I considered just letting the equalizer take care of delay. It would >>>>>>certainly make my life easier in many respects. >>>>>> >>>>>>My problem with this system is that I can't count on a perfect match >>>>>>between transmit and receive clocks, so the change in delay from the >>>>>>start of a run to the end would require an equalizer with an >>>>>>unfeasible >>> >>>>>>amount of delay. Hence, I seek a reliable way to synchronize that >>>>>>does >>> >>>>>>not leave the equalizer holding the bag. >>>>>> >>>>>>-- >>>>>>My liberal friends think I'm a conservative kook. My conservative >>>>>>friends think I'm a liberal kook. Why am I not happy that they have >>>>>>found common ground? >>>>>> >>>>>>Tim Wescott, Communications, Control, Circuits & Software >>>>>>http://www.wescottdesign.com >>>>>> >>>>>> >>>>>In the given scenario, in my opinion, the TED is not even supposed to >>>lock >>>>>onto the timing phase; it will lock to the symbol rate (or transmit >>>clock). >>>>>So any NDA TED like Gardner followed by a fractionally spaced >>>>>equalizer should do the job for you. >>>> >>>>Exactly. >>>> >>>>> A very interesting and practical reference paper >>>>>is the one by John Treichler, "Practical blind demodulators for >>>high-order >>>>>QAM signals" published in 1998. The most important part I think is the >>>>>fractional tap-spacing because a symbol rate equalizer can easily lose >>>the >>>>>battle due to aliasing. >>>> >>>>Depending on the system constraints and how the system is >>>>engineered/architected, a T-spaced EQ can still work well in many >>>>applications. In my experience I've never had to resort to a >>>>fractional-spaced EQ for the systems that I've worked on (which aren't >>>>universal), which saves a lot of complexity. Perhaps I've been lucky. >>>> >>>> >>>>Eric Jacobsen >>>>Anchor Hill Communications >>>>http://www.anchorhill.com >>>> >>>> >>>My understanding which can be wrong is the following. Symbol-rate >>>tap-spacing is optimal if the equalizer is preceded by a filter matched >>>to the *channel distorted* transmit pulse, which is only possible if the >>>channel response is known beforehand. In that case, the autocorrelation >>>values at integer lags of the composite channel (Tx, channel, Rx) are >>>known and the correlated noise can be whitened through a noise whitening >>>filter after symbol-rate sampling. >>> >>>However, when channel is not known, 1/2T becomes the folding frequency >>>and since the filtered samples depend on the delay (sampling done at >>>times kT+tau), the overlappend spectra can easily cancel each other >>>depending on the value of tau (timing offset). >> >> That all seems like a reasonable argument. >> >> Remember also that if all the functions are linear the order of >> operation doesn't matter. So as long as linearity is preserved, the >> order of the pulse-shaping filter and EQ are inconsequential. Aliasing >> certainly has to be considered within that context. > >Linearity and shift invariance (or time invariance) must be preserved for >order to not matter. Sampling (or simple decimation) are linear, but >they are not time- or shift-invariant and order matters in that case.
I did a really crappy job of conveying what I meant. I wish we were all in a room with a white board or something, as I don't think I can do it justice in a few paragraphs. The gist is that I think this stuff gets made more complicated than it needs to be in many cases, and sometimes effects that people worry about can be neglected completely without issue. Basically, many systems get by with a T-spaced EQ after the pulse filter and timing recovery because the expected "issues" aren't really issues in most cases.
>-- >My liberal friends think I'm a conservative kook. >My conservative friends think I'm a liberal kook. >Why am I not happy that they have found common ground? > >Tim Wescott, Communications, Control, Circuits & Software >http://www.wescottdesign.com
Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by Tim Wescott June 7, 20132013-06-07
On Fri, 07 Jun 2013 17:44:19 +0000, Eric Jacobsen wrote:

> On Fri, 07 Jun 2013 02:14:58 -0500, "commsignal" <58672@dsprelated> > wrote: > >>>On Fri, 07 Jun 2013 00:23:29 -0500, "commsignal" <58672@dsprelated> >>>wrote: >>> >>>>>On Mon, 03 Jun 2013 06:48:26 -0500, DougB wrote: >>>>> >>>>>>>>Only a fractionally spaced equalizer will resolve timing phase. >>>>>>>>If >>>>you >>>>>> use >>>>>>>>a T spaced equalizer you had better have good symbol timing >>>>>>>>recovery >>>>>> prior >>>>>>>>to the equalizer. Carrier reference can be resolved after >>>>equalization >>>>>>>>unless the frequency offset is large in which case you can split >>>>>>>>the >>>>>> loop >>>>>>>>and recover frequency prior to the equalizer and phase/remaining >>>>>> frequency >>>>>>>>after the equalizer. >>>>>>>>-Doug >>>>>>> >>>>>>> >>>>>>>One of the disadvantages of using the EQ to correct timing is that >>>>>>>it consumes degrees of freedom usually intended for combating the >>channel >>>>>>>distortion. Those degrees of freedom cost complexity, and usually >>the >>>>>>>complexity of the EQ is much greater than the complexity of a >>>>>>>decent timing recovery system. So, in my experience, the systems >>>>>>>that try >>to >>>>>>>use the EQ for synchronization or to aid in synchronization wind up >>>>with >>>>>>>a heavier complexity load than alternative methods. Separating the >>two >>>>>>>tasks can be advantageous for the performance of both the EQ and >>>>>>>the timing recovery as well as complexity. >>>>>>> >>>>>>> >>>>>>> >>>>>>>Eric Jacobsen >>>>>>>Anchor Hill Communications >>>>>>>http://www.anchorhill.com >>>>>>> >>>>>>> >>>>>> That's true, but if the channel highly distorted, there is no TED >>that >>>>>> is going to give you the optimum timing phase - that can only be >>gotten >>>>>> from a fractionally spaced equalizer. Still use timing recovery as >>>>>> normal, but let the FSE optimize the timing phase - it can >>>>>> synthesize the proper fractional delay. >>>>> >>>>>I considered just letting the equalizer take care of delay. It would >>>>>certainly make my life easier in many respects. >>>>> >>>>>My problem with this system is that I can't count on a perfect match >>>>>between transmit and receive clocks, so the change in delay from the >>>>>start of a run to the end would require an equalizer with an >>>>>unfeasible >> >>>>>amount of delay. Hence, I seek a reliable way to synchronize that >>>>>does >> >>>>>not leave the equalizer holding the bag. >>>>> >>>>>-- >>>>>My liberal friends think I'm a conservative kook. My conservative >>>>>friends think I'm a liberal kook. Why am I not happy that they have >>>>>found common ground? >>>>> >>>>>Tim Wescott, Communications, Control, Circuits & Software >>>>>http://www.wescottdesign.com >>>>> >>>>> >>>>In the given scenario, in my opinion, the TED is not even supposed to >>lock >>>>onto the timing phase; it will lock to the symbol rate (or transmit >>clock). >>>>So any NDA TED like Gardner followed by a fractionally spaced >>>>equalizer should do the job for you. >>> >>>Exactly. >>> >>>> A very interesting and practical reference paper >>>>is the one by John Treichler, "Practical blind demodulators for >>high-order >>>>QAM signals" published in 1998. The most important part I think is the >>>>fractional tap-spacing because a symbol rate equalizer can easily lose >>the >>>>battle due to aliasing. >>> >>>Depending on the system constraints and how the system is >>>engineered/architected, a T-spaced EQ can still work well in many >>>applications. In my experience I've never had to resort to a >>>fractional-spaced EQ for the systems that I've worked on (which aren't >>>universal), which saves a lot of complexity. Perhaps I've been lucky. >>> >>> >>>Eric Jacobsen >>>Anchor Hill Communications >>>http://www.anchorhill.com >>> >>> >>My understanding which can be wrong is the following. Symbol-rate >>tap-spacing is optimal if the equalizer is preceded by a filter matched >>to the *channel distorted* transmit pulse, which is only possible if the >>channel response is known beforehand. In that case, the autocorrelation >>values at integer lags of the composite channel (Tx, channel, Rx) are >>known and the correlated noise can be whitened through a noise whitening >>filter after symbol-rate sampling. >> >>However, when channel is not known, 1/2T becomes the folding frequency >>and since the filtered samples depend on the delay (sampling done at >>times kT+tau), the overlappend spectra can easily cancel each other >>depending on the value of tau (timing offset). > > That all seems like a reasonable argument. > > Remember also that if all the functions are linear the order of > operation doesn't matter. So as long as linearity is preserved, the > order of the pulse-shaping filter and EQ are inconsequential. Aliasing > certainly has to be considered within that context.
Linearity and shift invariance (or time invariance) must be preserved for order to not matter. Sampling (or simple decimation) are linear, but they are not time- or shift-invariant and order matters in that case. -- My liberal friends think I'm a conservative kook. My conservative friends think I'm a liberal kook. Why am I not happy that they have found common ground? Tim Wescott, Communications, Control, Circuits & Software http://www.wescottdesign.com
Reply by Eric Jacobsen June 7, 20132013-06-07
On Fri, 07 Jun 2013 02:14:58 -0500, "commsignal" <58672@dsprelated>
wrote:

>>On Fri, 07 Jun 2013 00:23:29 -0500, "commsignal" <58672@dsprelated> >>wrote: >> >>>>On Mon, 03 Jun 2013 06:48:26 -0500, DougB wrote: >>>> >>>>>>>Only a fractionally spaced equalizer will resolve timing phase. If >>>you >>>>> use >>>>>>>a T spaced equalizer you had better have good symbol timing recovery >>>>> prior >>>>>>>to the equalizer. Carrier reference can be resolved after >>>equalization >>>>>>>unless the frequency offset is large in which case you can split the >>>>> loop >>>>>>>and recover frequency prior to the equalizer and phase/remaining >>>>> frequency >>>>>>>after the equalizer. >>>>>>>-Doug >>>>>> >>>>>> >>>>>>One of the disadvantages of using the EQ to correct timing is that it >>>>>>consumes degrees of freedom usually intended for combating the >channel >>>>>>distortion. Those degrees of freedom cost complexity, and usually >the >>>>>>complexity of the EQ is much greater than the complexity of a decent >>>>>>timing recovery system. So, in my experience, the systems that try >to >>>>>>use the EQ for synchronization or to aid in synchronization wind up >>>with >>>>>>a heavier complexity load than alternative methods. Separating the >two >>>>>>tasks can be advantageous for the performance of both the EQ and the >>>>>>timing recovery as well as complexity. >>>>>> >>>>>> >>>>>> >>>>>>Eric Jacobsen >>>>>>Anchor Hill Communications >>>>>>http://www.anchorhill.com >>>>>> >>>>>> >>>>> That's true, but if the channel highly distorted, there is no TED >that >>>>> is going to give you the optimum timing phase - that can only be >gotten >>>>> from a fractionally spaced equalizer. Still use timing recovery as >>>>> normal, but let the FSE optimize the timing phase - it can synthesize >>>>> the proper fractional delay. >>>> >>>>I considered just letting the equalizer take care of delay. It would >>>>certainly make my life easier in many respects. >>>> >>>>My problem with this system is that I can't count on a perfect match >>>>between transmit and receive clocks, so the change in delay from the >>>>start of a run to the end would require an equalizer with an unfeasible > >>>>amount of delay. Hence, I seek a reliable way to synchronize that does > >>>>not leave the equalizer holding the bag. >>>> >>>>-- >>>>My liberal friends think I'm a conservative kook. >>>>My conservative friends think I'm a liberal kook. >>>>Why am I not happy that they have found common ground? >>>> >>>>Tim Wescott, Communications, Control, Circuits & Software >>>>http://www.wescottdesign.com >>>> >>> >>>In the given scenario, in my opinion, the TED is not even supposed to >lock >>>onto the timing phase; it will lock to the symbol rate (or transmit >clock). >>>So any NDA TED like Gardner followed by a fractionally spaced equalizer >>>should do the job for you. >> >>Exactly. >> >>> A very interesting and practical reference paper >>>is the one by John Treichler, "Practical blind demodulators for >high-order >>>QAM signals" published in 1998. The most important part I think is the >>>fractional tap-spacing because a symbol rate equalizer can easily lose >the >>>battle due to aliasing. >> >>Depending on the system constraints and how the system is >>engineered/architected, a T-spaced EQ can still work well in many >>applications. In my experience I've never had to resort to a >>fractional-spaced EQ for the systems that I've worked on (which aren't >>universal), which saves a lot of complexity. Perhaps I've been >>lucky. >> >> >>Eric Jacobsen >>Anchor Hill Communications >>http://www.anchorhill.com >> > >My understanding which can be wrong is the following. Symbol-rate >tap-spacing is optimal if the equalizer is preceded by a filter matched to >the *channel distorted* transmit pulse, which is only possible if the >channel response is known beforehand. In that case, the autocorrelation >values at integer lags of the composite channel (Tx, channel, Rx) are known >and the correlated noise can be whitened through a noise whitening filter >after symbol-rate sampling. > >However, when channel is not known, 1/2T becomes the folding frequency and >since the filtered samples depend on the delay (sampling done at times >kT+tau), the overlappend spectra can easily cancel each other depending on >the value of tau (timing offset).
That all seems like a reasonable argument. Remember also that if all the functions are linear the order of operation doesn't matter. So as long as linearity is preserved, the order of the pulse-shaping filter and EQ are inconsequential. Aliasing certainly has to be considered within that context.
>Is it possible that the systems you worked on had very small excess >bandwidth, due to which the effects of this aliasing were minimized?
In my experience systems from 20% to 100% EBW have worked fine with T-spaced EQs, but there are some caveats that I won't go into for various reasons. That's not to say there's not degradation, because there always is, but the performance achieved was such that there was not an expectation of much (if any) improvement with a T/2 or whatever-spaced EQ. I don't doubt that there are applications or combinations of applications and architectures that benefit from a T/2 (or whatever)-spaced EQ. I've managed to get by with T-spaced in a lot of apps, including mobile multipath. That doesn't mean that what we did had optimal performance, but it met our requirements and has had successful deployments. If complexity doesn't matter (which is a case I've yet to run into personally), then using fractional spacing is definitely something to consider using. So, as usual, one must manage the tradeoff space within the constraints they're given. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com