We propose an optical domain pilot-aided carrier phase recovery (PA-CPR) scheme used in a single-carrier Nyquist system. A comprehensive mathematical description of the proposed PA-CPR scheme is presented. Optimal parameters for the system are obtained through optimizations. Furthermore, we propose the two-stage PA-CPR algorithm combinations which use the maximum likelihood or constellation transformation phase estimation as the second stage just after the pilot phase compensation. We also make the evaluation and comparison of the linewidth tolerance performances among the proposed two-stage PA-CPR algorithm combinations and other typical CPR algorithms in a 28-Gbaud Nyquist polarization-division multiplexed (PDM)-16QAM optical communication system. The calculation results show that the proposed two-stage PA-CPR algorithm combinations, which have lower complexities, show better performances than others.