A receiver to be employed in a digital mobile communication system, more particularly to a receiver for performing complex correlation against a received signal so as to establish and supervise the synchronization with the received signal. The receiver estimates a transmission channel between sending and receiving stations using the received signal and a predetermined reference signal (S11). The phase of the received signal is compensated for using the estimated phase error resulting from the estimation (S12). Complex correlation of the received signal which is compensated for in phase is performed against the reference signal (S13) to obtain a correlation value. The correlation value is compared with a predetermined threshold value (S14). The presence or absence of the synchronization between the sending and receiving stations can be detected, based on the result of the comparison. In case of detecting synchronization again after the synchronization is once detected, the phase of the received signal is compensated for (S22) using a previously obtained phase variation amount whereby the complex correlation value can be obtained (S23).