Maximum likelihood clockless feedback phase recovery for MPSK signals

For the symbol timing recovery techniques which are susceptible to carrier phase offset, clockless phase recovery is necessary in advance. In this paper, we propose a clockless nondata-aided (NDA) feedback phase error detector (PED) for M-ary phase-shift keying (MPSK) signal. Its derivation is given based on maximum likelihood (ML) criterion. The clockless NDA (Mth-power) PED can also be generalized with a design parameter 0≤ m ≤M to improve performance at low SNR. The open-loop S-curves and closed-loop phase error variances of these PEDs are given with extensive simulations. Results show that the S-curve of clockless Mth-power PED is robust to signal-to-noise ratio (SNR). Its phase error variance is investigated with excellent performance under different shaping roll-off factors and parameter m. We also analyze the clockless decision-directed (DD) PED which may not be a good choice for over-sampled signals due to its unstable equilibrium point of S-curve.