Can we get away with Sampling clock offset tracking and Symbol timing in a single carrier system if we use fractionally spaced equalizer for bursty transmission since fractionally spaced equalizeris insensitive to symbol timing offset?
If I'm reading correctly, you're looking for an answer to the old equalizer issues when matching to musical instruments?? If that's so, maybe look into the "constant Q Transform".
Fred, I'd like your input as well. I've been looking at it, but haven't gotten around to actually implementing one as yet. Have you experience or thoughts on this??
I think the original question addressed timing acquisition of a QAM receiver. Phase alignment of the receiver's clock sample times with the phase of the underlying received signal's modulation clock is required for proper demodulation of the received QAM signal.
Equalizers are capable of removing all small unknown errors in received signal. this means AGC, small residual carrier phase offsets, small residual carrier frequency offsets, small residual timing phase error, small residual timing frequency error, as well as channel distortion. We keep the equalizer from doing all these things by putting it at the end of the signal processing chain and by slowing down its rate of convergence with small mu, same as low bandwidth loop filters.
I tell my student's that the equalizer likes to show off. It can fix all the problems; let me show you how! Stopping it from showing off will give you a better receiver.
This gives the earlier loops time for them to do their assigned tasks. Years ago (30 of them) when we were building our first DSP based modems we ran into the problem of adaptive equalizers tracking out timing offset errors. When the timing error increased due to clock frequency error instead of clock phase error.. we could watch the equalizer track the time shifting peak of the matched filter output until that peak position ran out of ground.. addresses in the equalizer's data registers. We could modify equalizer algorithm to keep the filter's peak in the center of the filter register. That would happen if you let the interpolator in the timing loop do its job which it can accomplish better than the modified equalizer. This let's the equalizer commit its degrees of freedom to its primary task... that of suppressing the distortion caused by the channel.
thanks for the enlightening answer. I feel like a beginner again. I took BASIC DSP back in about '82. I've not had the opportunity to use it only a few times since, and each time I referred back to either my original textbook or, more recently, Mr. Lyons book. (I purchased that one twice, as someone borrowed my first copy)
At any rate, I guess I didn't catch on to that in the original question. Got caught up by the "fractional equalixer" comment and my mind went off in a totally different direction. My first usage of QAM was a few years ago, in fact. So, I don't know that I can actually claim much experience with that.
So, quickly, if you can, have you any experience with "Constant Q transforms" ?? My son put together a project making a graphic equalizer for his home stereo (well, his iPhone connected to some speakers etc...), but the project used a standard FFT casting each bucket to an amplitude and lighting the "tower" of LEDs in that column according to that amplitude. And, when it was done, he was unhappy with the spread of his buckets. As you may know, musical notes are no where near evenly spaced.
I did a little research, trying to force an FT into "not so evenly spaced" buckets (I'm betting you know how that went) and found the Constant Q transfom. As I mentioned earlier, I've not had time to get to coding one up for him, but from the math I found on it, I'm hopeful it will do the trick better.
See if you can pick up a copy of my book, Multirate signal processing for communication systems.. second edition. I have a description of a graphical equalizer design using IIR filters and multirate, proportional BW and center frequencies equally spaced on a log scale. There is also a section that discusses proportionally spaced filter bank for hearing aids.
Thanks Fred, and thanks for the pptx file. I'll read through it and see if I can push it down to my son for his project...
What you say about equalizers in your question is true. But the results won't be to your liking. A fractional spaced equalized can correct timing offsets as well as small phase offsets as well as channel distortion. The problem is you don't want it to do all those things. We run the equalizer at the end of the signal processing chain so the earlier loops, timing and frequency can conduct their function. If the timing error is due to small clock phase error the equalizer will be able to change its weights to absorb the phase offset...However if the timing error is due to a small clock frequency error, the equalizer will keep changing its weights to follow the shifting peak of the matched filter. the shift will eventually walk off the filter register and the equalizer will no longer be able to correct for its position. You need a timing loop which can respond to overflow or underflow of the interpolator control pointer to absorb the shifting timing peak. The rule that if it can go wrong it will! is true... if you think the equalizer can take care of timing offset when it is actually a clock frequency error... you are due to be surprised! Don't do it!
I was refering bursty transmission and not continuous transmission.Since Fractionally spaced equalizer can correct for unknown symbol timing offset even for commercial crystals with short bursts the accumulated clock with in a burst will be less than one symbol.So the timing will not slip for a fixed equalizer length.We can do it by adopting the taps for short bursts.This will be true when the clock frequency error is small and it will not burden equalizer much and it can take care of the timing phase.
As others have alluded, any adaptive equalizer design has limited degrees of freedom in which to work, and a certain amount of complexity required to provide that capability. Generally the capability of the equalizer is needed to correct for unknown channel impairments, and using the capability of the equalizer to correct timing means that less capability is available to correct the channel impairments. If the equalizer is powerful enough to do both, it is generally way more complex than it needs to be and therefore the demodulator is inefficient.
It can go deeper than that, but, basically, there's a reason that this is seldom done in practice.
Thank you for the kind reply
If you have a burst transmission to a peer, you would use a preamble to teach the receiver what is the channel's impulse response or frequency response to initialize the weights of the equalizer. If the equalizer is operating with decision directed updates, the convergence time will be 100s to 1000s of symbol intervals. That is ok for a broadcast system but not for a burst peer to peer link. A burst may still contain hundreds of symbols and clock migration may still be a problem.
Thank you for the reply.