phase difference detection For application of syncing sampling clock phase to carrier phase of received signal where the received signal is sampled with 10 times the carrier phase and modulated with the PSK shown in the figure (Baud rate up to 0.5*fc)

 

I had many ideas to apply on my system (where interpolation is not possible) and I need your help figuring out which is the best:


Timing Error Delay: most proposed algorithms require interpolation
Hilbert filter:where generating I/Q requires shifting 2.5 samples or Fractional Delay Filter (where I need help with determining the best FIR implementation of such a filter)
thanks in advance
For fractional delay filters see this article: https://www.dsprelated.com/showarticle/22.php. 

Timing error delay is not used for carrier recovery. Carrier offset and symbol timing offset are not the same thing.

Carrier recovery can be done at 1 sample per symbol assuming you do timing recovery first. For this a simple phase detector is the cross product phase detector where you derive phase from the imaginary term of the complex conjugate product. 

The Gardner Timing Error Detector is a good choice as it can determine timing offset over a relatively large carrier offset. If resolving timing offsets to within 1/10th of a symbol then this would be a very simple approach without further interpolation. However, I question why the OP precludes interpolation; combining a timing error detector with a polyphase interpolator is an excellent approach to resolve timing with fractional delay filters without having to increase the sampling rate- however interpolation techniques are still applied. 

I have more information in other posts for both of these approaches listed below:

Gardner TED:

Isn&#39;t Gardner&#39;s algorithm and Early-Late gate the same thing?

Fractional spaced equalizer + timing (clock) recovery

Phase Detectors and Carrier Recovery Loops

Phase synchronization in BPSK

More Carrier Recovery and Timing Recovery

How to demodulation BPSK in real case(through a channel)?