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An adaptive filtering algorithm is proposed in this paper to remove mismatch, dc offsets, flicker noise, and intersymbol interference (ISI) simultaneously in a direct-conversion receiver. mismatch is cancelled by a real valued adaptive mismatch canceller, and dc offsets are removed with one complex tap. In addition, flicker noise is modeled as a complex autoregressive (AR) random process so the system to be identified transforms to an ARX model. After estimating the coefficients in the model during the training period, the desired signal can be estimated using the decision feedback method. To accelerate the convergence of the algorithm and to reduce the estimation variance, an internal iterative algorithm is introduced. The convergence analysis of the proposed algorithm is also given, and the closed form of the minimum mean square error of the proposed algorithm is derived. Simulation results are provided to verify the superior performance of the proposed algorithm.