S-curve Theoretical Analysis of a Classical and a Hierarchical Phase Detector for QAM Constellations

In this paper, an optimized carrier recovery phase-error detector, based on hierarchical constellation concept is proposed in order to improve acquisition performances of the phase recovery loop. Theoretical and simulation results for quadrature amplitude modulation (16-QAM) signals and for a 5 dB signal-to-noise ratio per bit, show that a phase-error sensitivity gain of about 5 deg is obtained. Furthermore, this paper provides the analytical evaluation of the S-curve of a classical phase-error detector, selected in this study for being the most attractive for QAM constellations.