We consider prefiltering for a single–carrier transmission over frequency–selective channels, where reduced–state trellis–based equalization is employed at the receiver. While previously proposed prefiltering schemes are based on the optimum filters of decision–feedback equalization (DFE), the prefiltering scheme introduced in this paper is designed according to a signal–to–interference–plus–noise ratio (SINR), whose definition takes into account explicitly the subsequent trellis–based equalizer and its complexity. In addition to the prefilter, a finite–length target impulse response for trellis–based equalization and a feedback filter for state–dependent decision feedback in equalization, respectively, is determined. However, it is shown that a direct maximization of the SINR with respect to all filters results in a biased solution, and the relation of this solution to an optimum unbiased solution with improved error rate performance, which is also derived, is investigated.
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