In this thesis, the blind phase estimator algorithms are studied, including Histogram Algorithm (HA), Modified Histogram Algorithm (MHA), Maximum Likelihood (ML), 4th power-law and modified 4th power-law to compare their performance under quadrature amplitude modulation and additive white gaussian noise(AWGN) channel. Owing to the development of wireless communication, I used the fading channel of wireless communication and studied the performance of all algorithms again. After differential encoding and quadrature amplitude modulation, signals enter additive white gaussian noise(AWGN), constant phase offset and fading channel. At receiver, I use the above estimator to find the phase offset. If there is not line of sight under fading channel, all estimators performance are not good from simulation results, if there is a strong line of sight, all estimators performance are good and approximate to the AWGN channel.