# FFT based symbol synchronization for digital demodulation

Where can I read more about "slow search" methods for symbol synchronization based on FFT for extracting a clock signal from the modulated signal?

I have read here (8.7 Symbol synchronization)

One method of synchronization is to extract a harmonic of the symbol frequency from the received signal. Then a local symbol clock can be synchronized by methods that are very similar to the phase-locked loops used to recover the carrier phase. If necessary, a start-up procedure, such as one that uses a slow search, can be used for initialization. Synchronization is then maintained by locking a feedback loop to a clock signal that is extracted from the modulated waveform.

Then here I found a diagram which seems to be the kind of algorithm I am looking for:

The timing tone can be extracted by ... computing DFT at the symbol frequency (i.e., a single point of the DFT output is needed for each data block)

There must be more literature about this technique? I am not interested in high-performance methods for synchronization, but rather recovering the clock signal by any means without conserving memory or processing time.

I figure the basic technique is to

• Pass the signal through a matched filter
• "Condition" the signal (and make it purely real) by computing the magnitude (as in the diagram)
• Passing the signal through a DFT computation
• Searching the DFT bins for the highest power frequency
• Use the discovered frequency of the DFT bin to generate a local timing signal
• Use the discovered phase of the DFT bin (as in the diagram) to adjust the local timing signal offset

## 1 Answer

Symbol timing synchronization seems to be a complex topic although once you get some basic principles right, it all makes simple sense. The method you have referred to is known as Digital Filter and Square Timing Recovery$$\ ^{[1]}$$, also referred to as Oerder and Meyr algorithm.

EDIT:

And later steps in your summary are not correct. There is no search, timing phase is extracted from the first harmonic. Everything else except the DC term is zero due to the signal being bandlimited.

[1]: M. Oerder and H. Meyr, "Digital filter and square timing recovery," in IEEE Transactions on Communications, vol. 36, no. 5, pp. 605-612, May 1988.