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A new Spatial Diversity Equalizer (SDE) is proposed to overcome signal fading and Inter-Symbol Interference (ISI) simultaneously in wireless communication. The proposed SDE consists of equal gain combining technique, a Modified Constant Modulus Algorithm (MCMA) and a new dual-mode algorithm. Compared with conventional SDE, the proposed SDE has not only faster convergence rate and lower residual error but also the ability to recover carrier phase rotation. The efficiency of the method is proved by computer simulation in time-varying channels.