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Expectation-Maximization (EM) algorithms have been widely adopted in a variety of areas such as clustering, hidden Markov modeling, channel estimation and equalization, etc. The EM-based approaches to resolve the likelihood maximization involving latent variables are usually very complicated for signal processing and communication applications. To combat this problem, we construct an alternative metric for likelihood or log-likelihood, namely auxiliary function, which results in a novel EM hill-climbing (EM-HC) optimization procedure. We extend our previous efforts along this line of the auxiliary function research to generalize the EM-HC scheme and solve the blind equalization for the complex-valued signals. In this paper, our new EM-HC method, namely efficient Iterative Weighted LeastMean Squared (IWLMS) algorithm is extended for QPSK and QAM signals. The new version of the IWLMS algorithm greatly outperforms the prevalent blind equalization algorithms based on the constant-modulus and kurtosis criteria according to Monte Carlo simulations.