a synchronization establishing method of a mobile station in a mobile communication system is proposed which can reduce the effect of noise or interference , and achieve higher accuracy than conventional method . to enable the mobile station to detect a signal transmitted from a base station , and to establish synchronization to the signal in a mobile communication system in which a synchronization channel is multiplexed periodically into the downlink signal , the mobile station averages , in phase and in complex numbers , correlation values of the synchronization channel over a plurality of periods , followed by detecting the power of them to carrying out peak detection .