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In a receiver employing turbo equalization for an unknown, time-varying, frequency-selective channel, the channel estimate can be improved for each iteration by using soft information fed back from the decoder. The reference signal to the channel estimator is then the expected value of each transmitted symbol and not the symbol itself. Therefore, classical channel estimation theory must be applied carefully. Four different channel estimation algorithms for soft iterative channel estimation are compared through simulations, showing that the LMS algorithm is the best choice among the considered algorithms, because it is simplest without performing significantly worse than any other algorithm.