Relatively new to DSP, I've came across the approach for phase-estimation of PSK-Signals x(k): 
My question is:
- What do we get by exponentiating the Baseband-Signal?
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$\begingroup$ Usually, the books that introduce the M-law synchronizers also have an explanation right next to it! The answer is simple: write your M-PSK symbols in amplitude/phase form (i.e. $x = |x| \cdot e^{j\angle x}$) and exponentiate by M, and don't forget about the $2\pi$-periodicity of $e^{jt}$. Question answered! $\endgroup$ – Marcus Müller Jun 7 '18 at 14:47
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$\begingroup$ Ah, OK so the symbols |x| are becoming "1" by exponating with M? $\endgroup$ – John75 Jun 7 '18 at 14:59
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$\begingroup$ :) you've got it! And: what will you do if you get something that is not exactly +1 or -1? $\endgroup$ – Marcus Müller Jun 7 '18 at 15:08
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$\begingroup$ (by the way, I'm counting on you writing your own answer to your own question if you solve this :) I could write an answer, but I'll be honest: It'd be the same perspective that everyone has who's read the same textbook as me, and thus a bit redundant to similar answers. Your perspective and wording would be valueable!) $\endgroup$ – Marcus Müller Jun 7 '18 at 15:10
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$\begingroup$ when the symbols are not exactly +1 and -1, then we have to accumulate over a long stream? dividing by M is normalizing the phase... $\endgroup$ – John75 Jun 7 '18 at 17:26
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