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The focus of this paper is the extension of maximum asymptotic efficiency (MAE) equalization for application to time-varying communication channels. While the asymptotically optimal MAE equalizer is very attractive in its low runtime complexity, it suffers from high (exponential in channel and equalizer length) design complexity. Frequent redesign renders the effective operational complexity of the MAE equalizer impractical for implementation in time-varying channels. In this work, we address this issue by mapping the time-varying channel to a fixed channel for which the MAE equalizer is pre-designed. The channel mapping is performed via a linear pre-filter. Simulation results reveal that a pre-filter followed by a fixed MAE equalizer achieves gains of up to 4 dB over a conventional minimum mean square error (MMSE) linear equalizer in the high SNR regime. The proposed adaptive equalizer provides a balance between the optimal bit error rate performance and design complexity.