We develop fast recursive equalizers to be used in the one-dimensional (1D) or two-dimensional (2D) linear minimum mean-squared error equalization of a known linear finite-length channel. In particular, these equalization algorithms address the communications scenario in which the channel or the prior information on the transmitted symbols may be time varying. The latter case of time-varying priors is especially pertinent for turbo equalization, on which we focus here. We first consider a 1D sliding-window equalizer based on a Cholesky-factorization update and then generalize this approach to the 2D case. Finally, we develop a 2D equalizer that is based on a recursive matrix-inverse update. We summarize each of these algorithms and describe their computational complexities.
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