A Unified Approach to Reduced-Redundancy Transceivers: Superfast Linear and Block-Iterative Generalized Decision Feedback Equalizers

This paper shows, under general input data models, how block memoryless equalizers should be formulated considering reduced-redundancy transmissions for superfast detection. We propose linear and DFE-based, both multicarrier (MC) and single-carrier-frequency-domain (SC-FD) transceivers, along with efficient methods for the equalizer calculation, in a unified manner. We argue that, under a one-tap block decision feedback, transmitted redundancy can be reduced below the minimum
$\lceil(L-1)/2\rceil$
samples allowed in the linear case, where
$L$
is the channel length, even down to zero-redundancy, with improved BER performance. This is quantified in light of the optimal reconstruction delay set for a minimum-norm zero-forcing feedforward matrix in terms of the channel zeros location. The proposed MC and SC-FD block DFEs do not cancel inter-block-interference (IBI) via zeros-jamming; Instead, it removes IBI completely, in part by decision-feedback, and in part by zero-padding, which allows for much lower redundancy transmissions. The remaining ISI is further eliminated through a one-step block-iterative-generalized-DFE (BI-GDFE) obtained in the minimum-mean-square-error (MMSE) sense. Unlike computationally demanding block DFEs that eliminate ISI via successive cancelation, the proposed DFE schemes are as efficient as a superfast block-linear equalizer, requiring at most 3 receive branches to realize the order-
$M$
feedforward matrices in
${\cal O}(M \log M)$
operations.