This thesis deals with the joint maximum likelihood (ML) estimation approach of distortion matrix and I/Q mismatch in the array system using direct-conversion receivers (DCR). First, it investigates the influence of I/Q mismatch on the performance of the MVDR (Minimum Variance Distortionless Response) optimum beam-former that is one of the representative array processing systems. Then, the joint ML estimator is proposed that jointly estimate the distortion matrix and I/Q mismatch for calibration of the DCR array. This joint estimator is a data-aided technique which requires a training sequence. In particular, it is shown that its accuracy almost achieves the Cramer-Rao lower bound (CRLB). The advantages of the proposed estimator are demonstrated through computer simulations.