I've been studying the basics of digital communications using the free book at desktopsdr.com.

One of the examples is a 4-QAM demodulator which where symbol timing recovery is done with some Early-Late Gates after match-filtering with RCC.

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I thought that Early-Late Gates were only useful when all pulses had triangular shape. However, binary data filtered with Raised Cosine does not:


For non-triangular signals, the Early-late algorithm seems to output an error even when the sampling point is exactly right:

  1. When there is a single symbol, I understand that the error L - E == 0
  2. If there is a transition to a sequence of repeated symbols, however, I see that the estimated error is non-zero, which is wrong.

What am I missing?

Early-Late Gate

  • $\begingroup$ re: RRC != triangle: the symbols after the Matched Filter aren't root raised cosined, they're raised cosine formed; that doesn't really change your question, though :) $\endgroup$ – Marcus Müller Feb 26 '20 at 7:26
  • $\begingroup$ It might help when you think about your early and late delays to be spaced in a way that – if the signal was already synced – they would sample exactly in the middle between two symbols. Apply the second Nyquist criterion to that point! $\endgroup$ – Marcus Müller Feb 26 '20 at 7:28
  • $\begingroup$ Thanks for responding! I'm still a little bit confused; for example, given the following signal; considering the early/late samples at exactly between symbols, I still don't see them at the same amplitude... the early one is at zero, and the late one is greater than zero. Re: RRC/RC, I will edit the question :) $\endgroup$ – Manuel Menzella Feb 26 '20 at 12:53
  • $\begingroup$ Wouldn't that "false" error be undone when the repeated sequence is over and you get the downward transition? $\endgroup$ – Engineer Feb 26 '20 at 13:24
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    $\begingroup$ @ManuelMenzella You're right that this kind of synchronizer works best with pulses that don't overlap in the time domain. However, it turns out that you can still use this idea with pulses that overlap, as long as the overlap is not too large. This is called "self noise" in many papers; see for example the original paper by Gardner where he suggests a large excess bandwidth, 70% or so IIRC. I've used Gardner with 35% excess bandwidth and it works well enough at moderate to large SNR. $\endgroup$ – MBaz Feb 26 '20 at 21:13

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