The Gardner timing error detector is independent of carrier phase and frequency error, and is also quite immune to self noise (to my understanding, I may wrong about that). Can one assume that it is a recommended timing error detector for these reasons? Please if the answer is going to be "it depends on your system" with no further brief input/explanation , then abstain please.
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2$\begingroup$ If you haven't seen this already, please see this post dsp.stackexchange.com/questions/31517/… where I detailed my studies on the Gardner Timing Error Detector (TED) vs Mueller & Mueller (M&M) Detector and showed the considerations for each including frequency error. $\endgroup$– Dan BoschenAug 21, 2018 at 0:53
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2 Answers
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It depends on your system :)
Seriously, it depends. Gardner is a pretty solid algorithm with a simple implementation, especially if you're using BPSK or QPSK. It can even be used in some MIMO systems. Its main disadvantage is that it requires two samples per symbol. M&M requires only one, but it has its own disadvantages.
I think that these days the preferred solution is some variation of the polyphase detectors first proposed by fred harris. However, if you're experimenting and building your own system and you want to keep it simple, Gardner is a safe bet.
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$\begingroup$ thank you for the brief explanation after the scary comment :"It depends on your system"! :) ... is the Polyphase filter bank detector proposed by Fred Harris also independent of phase and frequency error? $\endgroup$ Aug 21, 2018 at 0:00
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$\begingroup$ Yes, it also is independent of phase and carrier error. $\endgroup$– MBazAug 21, 2018 at 0:15
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2$\begingroup$ The polyphase implementation is not a TED, but an interpolator combined with a matched filter. What fred harris proposed in his polyphase proposal used a small signal ML approximation TED. The Gardner TED is an approximation of that TED, FWIW. $\endgroup$ Aug 21, 2018 at 0:20
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$\begingroup$ For RRC pulse shaped PSK, fred harris recently recommended a band edge filter TED. researchgate.net/publication/… $\endgroup$ Aug 21, 2018 at 0:23
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1$\begingroup$ @AndyWalls Gardner TED is not an approximation of an ML TED, that approximation is an early-late TED. Gardner TED is just the non-data-aided version of a zero crossing TED. $\endgroup$– QMCAug 21, 2018 at 0:38
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Here is a short comparison for your purpose.
- The Gardner TED output depends on the excess bandwidth of the pulse shaping filter. Its performance is better if you have moderate to large excess bandwidth.
- It is a non-data-aided version of a zero crossing TED. A ZC TED has zero self noise for binary modulation and 100% excess bandwidth, not for all cases.
- As you said, the TED output works despite a phase offset or a (small) frequency offset, so it is well suited for timing recovery applications before the carrier recovery (although that can also be divided into stages).
- Polyphase clock synchronization is not a TED, it is just a method to do combine matched filtering and interpolation into one operation. Fred used the ML TED for this purpose, you can use zero crossing or Gardner.
- M&M is a sort of standard TED when it comes to timing acquisition at 1 sample/symbol. It has zero self noise for any excess bandwidth. However, its performance is very poor for higher excess bandwidths and that makes sense. At 1 sample/symbol and large rolloffs, the pulse sidelobes in time domain are very small and not much useful information can be extracted from them.
- Remember that self noise is not everything in a TED. The performance with respect to SNR needs to be taken into account as well.
