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Optimally regularized channel tracking techniques for sequence estimation based on cross-validated subspace signal processing

New methods for maximum-likelihood sequence estimation based on the Viterbi algorithm (VA) are presented. In the proposed scheme, the channel estimator and the Viterbi processor operate concurrently. At any given time-step, the sequence provided to the channel estimator comes from the survivor with the best metric value. These already known modifications of the traditional decision-directed VA cause large variance in the estimated channel coefficients. In fact, sequences with a high error rate may be used to perform estimation, and also the adjustment term of the channel tracking algorithm may exhibit abrupt changes caused by a "survivor swap", (that is by the event in which a different survivor has the best metric at step n, with respect to the step n-1). The proposed regularization procedure forces the channel vector to lie in the appropriate a priori known subspace: while the variance decreases, a certain amount of bias is introduced. The variance-bias tradeoff is then automatically adjusted by means of a cross-validation "shrinkage" estimator, which is at the same time optimal in a "small sample" predictive sum of squares sense and asymptotically model mean squared-error optimal. The method is shown by means of hardware experiments on a wide-band base station to be extremely more effective than per survivor processing, minimum survivor processing, and traditional decision directed approaches.