Practical Gardner timing error implementation

Question

I'm trying to demodulate a QPSK communication. For the moment I do:

1. Signal detection by computing the ratio between the power of the carrier wave compared to the signal power.
2. Initial clock synchronization with a preamble.
3. Initial phase recovery with the same preamble.

This works great with my signal but now I want to go further and take into consideration a clock frequency offset betweem the TX Clock and the RX Clock.

I made some research and a good way to do it seem to be Gardner Timing Error Detector which should be able to compensate for my clock offset.

To implement it I do: $$\epsilon_k = Real[(signal(t_k)-signal(t_{k-1}))*conj(signal(t_{k-1/2})]$$ $$t_k = t_{k-1}+T+\gamma*\epsilon_k$$

My problem is that I don't know how to chose the proportional parameter. $$\gamma$$

I've sometime seen it with something called the normalized narrowband noise BlT but I have no idea what it is. If you could point me in the right direction any help would be very appreciated!

Answer 1

If you have access to Mengali's book 'Synchronization Techniques for Digital Receivers', you will find the details how to choose it for a tracking loop, be it for frequency, phase or timing. Otherwise, just read about a standard discrete-time phase locked loop and see how the choice of paramters affect the loop bandwidth, which is what you are after.