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In this paper, we propose a new feedback decision-directed (FB-DD) phase error detector for quadratic phase-shift keying (QPSK) signal and a self-normalizing FB-DD detector for M-PSK signal. The self-normalizing detector can be used in the hybrid carrier recovery loop as discussed by Linn, while its open loop characteristic is independent of the imperfection of automatic gain control (AGC). Moreover, the detector has an efficient fixed-point hardware implementation structure suitable for Field-Programmable Gate Array (FPGA). Simulation results of QPSK and 8PSK signals show that there is some negligible performance degradation at low SNR. The proposed first detector has good open-loop characteristic, while its phase error variance and complexity stay close to that of classical FB-DD and smaller than that of classical feedback non-data-aided (FB-NDA) detectors at medium to high signal-to-noise ratio (SNR).