Pilot-Assisted Decision-Aided Maximum-Likelihood Phase Estimation in Coherent Optical Phase-Modulated Systems With Nonlinear Phase Noise

We proposed pilot-assisted (PA) decision-aided maximum-likelihood (DA ML) phase estimation for coherent optical $M$-ary phase-shift-keying systems. In a nonlinear-phase-noise channel with laser phase noise, the required launched power at bit-error-rate (BER) $=10 ^{-4}$ using the proposed PA DA ML algorithm without differential encoding (DE) can be reduced by about 0.7 dB in quadrature phase-shift keying and eight-phase-shift keying systems, and about 0.4 dB in 16-quadrature amplitude modulation format, compared to their DE counterparts using DA ML.