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The constant modulus algorithm (CMA) is one widely used algorithm for blind equalization of quadrature amplitude modulation (QAM) signals. The algorithm exhibits slow convergence rate and large steady state mean square error and the phase blind nature in comparison with the algorithms used in conventional data-aided equalization schemes. In this paper, a variable step size modified constant modulus algorithm is proposed. The proposed algorithm can achieve fast convergence rate and decrease steady state mean square error and correct phase shift and carrier frequency offset at the same time. The simulation results demonstrate the effectiveness of the proposed algorithm in improving convergence behavior and bit error rate performance.