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Reasonable bit error rate performance requires perfect channel state information (CSI) in traditional turbo equalization (TE), which is hard to obtain in practice. Soft and hard iterative algorithms have been developed to address the channel estimation problem with the performance of the soft iterative channel estimate based on the recursive least square algorithm. This paper presents an analysis of the performance of hard iterative channel estimation (HICE) based on the least mean square algorithm. The analysis uses a cost function with the hard decision on the TE output. An iterative channel correction (ICC) algorithm based on the gradient descent algorithm is used to iteratively minimize the cost function. The simulation results agree with the theoretical lower bound for the mean square error (MSE) of the estimated channels. Simulations show that, given an imperfect CSI with an MSE below the upper bound, the linear minimum mean squared error TE (LMMSE-TE) using the ICC has only small performance degradation compared to that with a perfect CSI, while the traditional LMMSE-TE suffers from severe error floor effect even with more iterations.