IQ signal processing is widely utilized in today's communication receivers. However, it usually faces a common problem of mismatch of the amplitudes and phases on I and Q branches because of the gain and phase imbalance between quadrature mixers. In this paper, we propose a novel method to estimate and compensate for the IQ imbalances for communication channels with frequency offset by using a preamble of repeated training sequence. The proposed method, as it jointly adapts schemes in the system of estimation, is more robust and gives better performance than the earlier results. The performance of such a scheme has been validated by computer simulation on IEEE 802.11a signals.