In this Paper, the training principles and the control method of adaptive array antennas using the LMS and CMA algorithms for the $pi$/4 QPSK signal is showed and the convergence characteristics, the adaptivity of directional pattern SINR and the replication of desired signal of adaptive arrays are compared and discussed each other. Computer simulation results showed that the SINR of LMS adaptive array was 13.8［dB］, and that of CMA was 12.8［dB］, and also the convergence characteristics of LMS was fast a little than that of CMA. The LMS adaptive array was also performed null point well for the interference signal direction than that of the CMA adaptive array.