I am trying to figure out how timing recovery is used after equalization (or, being more correct, when the equalizer is in the timing recovery loop), having a T/2 fractional spaced equalizer and using the Gardner algorithm as timing error detector. The usual situation is to have the equalizer output at 1sample/symbol, by having downsampled, or combining the outputs of the even and odd filters. The latter is my case (case (a) in figure). But Gardner algorithm works at 2samples/symbol, so I wonder what I must do with the samples coming out from the even and odd filters. Must I multiplex the outputs of the two filters so I have a 2samples/symbol, as depicted in (b)?

(a)conventional situation, (b) equalization+time multiplex. + TED at 2 samples/symbol



The answer is to NOT down-select to one sample per symbol until after using the Gardner Timing recovery since the TED requires 2 samples per symbol. If the equalizer is running at 2 samples per symbol, that is perfect for use with the Gardner; why would you down-select to one sample per symbol after the equalizer? You can downselect after timing recovery since at that point you have determined the precise sample location.

Also note that the fine timing adjustment can also operate on just 2 samples per symbol using polyphase filters! Below I show an example for a CDMA waveform before and after timing recovery using a Gardner TED at 2 samples per symbol with then with a loop filter adjusted timing using a polyphase resampler. There was no analog change in the sampling clock position nor an actual interpolation to a higher sampling rate (the polyphase filter design is based on interpolation but no actual higher sampling rate is used!).




Maybe that's a very late answer for that question, but anyway, let's answer about it for others who will read this post.

The idea of fractionally spaced equalizers is to upsampler the symbol by M time the sampling rate, and combining the output in order to choose the best sample. It means it will compare them one by one. I don't have more details because I'm still searching about that kind of equalizers



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