Unbiased maximum SINR prefiltering for reduced-state equalization

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.