Typically, blind selection mapping techniques require high computational complexity when blind estimation is performed using the Euclidean distance between the original quadrature amplitude modulation (QAM) constellation and the received signal after demapping. In order to minimize the computational complexity of the system under the premise of ensuring the communication quality, a phase rotation sequence estimation method based on the minimum Euclidean distance of the quartile constellation is proposed. Due to the application of constellations to the power of the fourth power in this algorithm, the total number of signals used to calculate the minimum Euclidean distance can be reduced, thereby reducing the computational complexity of the system. In addition, a set of phase rotation sequences constructed by random selection are introduced to further reduce the complexity while maintaining high estimation accuracy. The simulation results show that when [Eb/N0>6 dB], for different modulation modes 16QAM and 64QAM, the computational complexity of phase rotation estimation is reduced to about 35% and 14% of the traditional blind SLM estimation based on the maximum likelihood estimation algorithm (ML), and reduced to about 50% and 21% of the two-step estimation, while the bit error rate (BER) is not significantly reduced. Therefore, the proposed method can effectively reduce the complexity of the algorithm without reducing the performance of the wireless communication system.