I'm currently studying a decision directed carrier recovery scheme. Basically a PLL try to estimate the phase error in the current received symbol, the phase detector compensate the incoming symbol's phase with the estimated one and then the result is multiplied my the complex conjugate of the decision taken. My notes say:
Another phenomenon that should be taken into account is the phase ambiguity of $n \pi/2$ that affects the decisions with conventional QAM constellations.
What is he talking about? I don't understand why he tells that there is phase ambiguity in the decision of a QAM symbol. Also citing Wikipedia:
Most QAM constellations also have $\pi/2$ phase symmetry
To me there is no phase ambiguity, in fact if I have a 4-QAM with 1 symbol in each quadrant I can just sample the I and Q branch after a matched filter and than perform a simple unambiguous atan like this: