This dissertation proposes two new decision feedback equalization schemes suitable for multilevel modulation systems employing turbo equalization. One is soft-decision feedback equalization (SDFE) that takes into account the reliability of both soft a priori information and soft decisions of the data symbols. The proposed SDFE exhibits lower signal to noise ratio (SNR) threshold that is required for "water fall" bit error rate (BER) and much faster convergence than the near-optimal exact minimum mean square error linear equalizer (Exact-MMSE-LE) for high-order constellation modulations. The proposed SDFE also offers a low computational complexity compared to the Exact-MMSE-LE.;The drawback of the SDFE is that its coefficients cannot reach the matched filter bound (MFB) and therefore after a large number of iterations (e.g. 10), its performance becomes inferior to that of the Exact-MMSE-LE. Therefore, soft feedback intersymbol interference (ISI) canceller-based (SIC) structure is investigated. The SIC structure not only exhibits the same low complexity, low SNR threshold and fast convergence as the SDFE but also reaches the MFB after a large number of iterations. Both theoretical analysis and numerical simulations demonstrate why the SIC achieves MFB while the SDFE cannot.;These two turbo equalization structures are also extended from single-input single-output (SISO) systems to multiple-input multiple-output (MIMO) systems and applied in high data-rate underwater acoustic (UWA) communications.
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