To combat intersymbol interference (ISI) in single-carrier block transmission systems, the hybrid decision feedback equalizer (HDFE) is a low-complexity, symbol-by-symbol detector that combines a frequency-domain feedforward filter and a time-domain feedback filter. To mitigate the error propagation effect of HDFE while preserving the implementation advantages of frequency-domain equalization, we propose the parallel HDFE (P-HDFE) algorithm that operates, based on the reliability of the decision variable, as an ordinary HDFE or a sequence detector that consists of multiple HDFEs running in parallel. Our study shows that, at moderate to high signal-to-noise ratios (SNRs), P-HDFE outperforms HDFE with little increase in complexity. We analyze the symbol error rate of P-HDFE at high SNRs for the case of quaternary phase-shift keying and static ISI channels, accounting for error propagation and residual ISI. Simulations demonstrate the accuracy of the analysis.
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