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Brief background

There is a known problem that high order modulation schemes suffers from phase noise of reference generator. It's very important issue for e.g. line-of-sight (LOS) modems exploiting QAM-256 or even higher. Some compensation schemes are possible to solve this task. The main challenge in these schemes is to estimate phase noise in a time span of data reception. Knowing actual samples of phase noise we can eliminate it from data symbols significantly improving BER for high order modulation. Such estimation is possible due to phase noise is in general low band random process which can be adaptively predicted/estimated. One can trade off communication speed inserting known pilots in data flow to estimate phase noise at some moments of time. Phase noise from pilots' time span could be used to evaluate phase noise for the interval of data samples. So the question is about pilot mapping scheme and estimation techniques.

Point

Gathering some information about this topic, I can pick out two major approaches:

1) Sending a group of pilots (QPSK) $\to$ eliminating pilot modulation to get phase noise (PN) samples $\to$ learning of adaptive prediction filter (e.g. by LMS) $\to$ finding predictive PN samples $\to$ eliminating PN from data samples $\to$ wait for the next pilot group and repeat. It's extrapolation method.

2) Inserting pilot sample (QPSK) periodically in the data stream, e.g. 1 pilot/32 data $\to$ evaluating PN at pilots (like discussed above) $\to$ finding PN between pilots by interpolation, number of pilots from left and right are used $\to$ eliminating PN from data samples. It's interpolation method.

Has someone any experience with similar technologies? Or maybe someone face to phase noise compensation problem in practice?

I wonder to know which of these approaches (I mean pilot-based, interpolation or extrapolation) is more preferable/robust in real life modem design?

Remark

Work environment is to be considered as a channel with AWGN. SNR is pretty high, e.g. 40-50 dB. Phase noise is in the order of -70...-90 dB/Hz. Phase noise bandwidth is significantly less then signal's one.

Here is an interesting article in IEEE:

Simon V., et el. - Phase noise estimation via adapted interpolation

It's about the second approach. Adaptive interpolation via LMS is discussed. Does someone know any interesting references, I'm curious to learn about. enter image description here

In the picture above the first case is illustrated.

Thanks in advance

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