Minimum mean squared error equalization using a priori information

TLDR

Joint equalization and decoding over ISI channels has progressed with turbo equalization, an iterative MAP‑based approach that exchanges soft information between equalizer and decoder, and with reduced‑complexity variants that replace MAP equalization with suboptimal low‑complexity methods. The study investigates low‑complexity soft‑input/soft‑output equalization algorithms based on the minimum mean square error (MMSE) criterion. The authors extend existing MMSE approaches to general signal constellations, derive a novel lower‑complexity method, and qualitatively analyze all approaches by averaging the mean‑square error over equalized data sequences. Results show that MMSE‑based SISO equalizers achieve performance comparable to MAP equalizers in turbo equalization while delivering a substantial reduction in complexity.

Abstract

A number of important advances have been made in the area of joint equalization and decoding of data transmitted over intersymbol interference (ISI) channels. Turbo equalization is an iterative approach to this problem, in which a maximum a posteriori probability (MAP) equalizer and a MAP decoder exchange soft information in the form of prior probabilities over the transmitted symbols. A number of reduced-complexity methods for turbo equalization have been introduced in which MAP equalization is replaced with suboptimal, low-complexity approaches. We explore a number of low-complexity soft-input/soft-output (SISO) equalization algorithms based on the minimum mean square error (MMSE) criterion. This includes the extension of existing approaches to general signal constellations and the derivation of a novel approach requiring less complexity than the MMSE-optimal solution. All approaches are qualitatively analyzed by observing the mean-square error averaged over a sequence of equalized data. We show that for the turbo equalization application, the MMSE-based SISO equalizers perform well compared with a MAP equalizer while providing a tremendous complexity reduction.