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I would like to measure the phase difference of a 100 kHz tone. The tone is transmitted and then received.
The received tone is sampled using an 1 MHz 12 bit ADC(IQ) and the SNR is at least 35 dB.
Our aim is to measure the phase difference in at least 360/500= 0.72 degree steps.
The achievable rms accuracy is approximately the reciprocal of the SNR as an rms quantity, specifically $10^{-35/20}$ in your case assuming the small angle criteria, if your noise is all phase noise. It is likely your SNR is equally phase and amplitude noise, so the phase result as limited by your noise would be 3 dB better after hard limiting the signal to eliminate the AM component.
I linked other posts that include multiple variants for phase detector implementations, depending on if you have a complex or real representation of the signal. The simple approach is to hard limit the signals (as most phase detectors are sensitive to AM) and then use a multiplier. The output of a linear multiplier is proportional to the cosine of the phase angle between the two inputs.
Phase Detectors: Phase synchronization in BPSK
Phase Detection for complex signals: How to correct the phase offset for QPSK I-Q data
Phase Detection for Carrier Recovery: High modulation index PSK - carrier recovery
