The analysis of adaptive carrier phase estimation is investigated in long-haul high speed n-level phase shift keying (n-PSK) optical fiber communication systems based on the one tap normalized least-mean-square (LMS) algorithm. The close form expressions for the estimated carrier phase and the bit error-rate floor have been derived in the n-PSK coherent optical transmission systems. The results show that the one-tap normalized LMS algorithm performs pretty well in the carrier phase estimation, but will be less effective with the increment of modulation levels, in the compensation of both intrinsic laser phase noise and equalization enhanced phase noise.