A self-iterating soft equalizer (SISE) consisting of a few relatively weak constituent equalizers is shown to provide robust performance even in severe intersymbol interference (ISI) channels that exhibit deep nulls and valleys within the signal band. Constituent equalizers are allowed to exchange soft information in the absence of interleavers based on the method that are designed to handle significant correlation among their soft outputs. The resulting SISE works well as a stand-alone equalizer or as the equalizer component of a turbo equalization system. The performance advantages over existing methods are validated with bit-error-rate (BER) simulations and extrinsic information transfer (EXIT) chart analysis. It is shown that in turbo equalizer setting the SISE achieves performance closer to the maximum a posteriori probability equalizer than any other known schemes in very severe ISI channels.

Provable lower bounds are presented for the information rate I(X; X+S+N) where X is the symbol drawn independently and uniformly from a finite-size alphabet, S is a discrete-valued random variable (RV) and N is a Gaussian RV. It is well known that with S representing the precursor intersymbol interference (ISI) at the decision feedback equalizer (DFE) output, I(X; X+S+N) serves as a tight lower bound for the symmetric information rate (SIR) as well as capacity of the ISI channel corrupted by Gaussian noise. When evaluated on a number of well-known finite-ISI channels, these new bounds provide a very similar level of tightness against the SIR to the conjectured lower bound by Shamai and Laroia at all signal-to-noise ratio (SNR) ranges, while being actually tighter when viewed closed up at high SNRs. The new lower bounds are obtained in two steps: First, a “mismatched” mutual information function is introduced which can be proved as a lower bound to I(X; X+S+N). Secondly, this function is further bounded from below by an expression that can be computed easily via a few single-dimensional integrations with a small computational load.

We design a self-iterating soft equalizer (SISE) consisting of several suboptimal equalizers that are weak individually but, when working together, show good performance. In order to process correlated soft information through serially concatenated modules, a sophisticated method to generate the extrinsic information is proposed that suppresses the correlation effect between the soft information of suboptimal equalizers. This algorithm performs well in turbo equalization system as well as the classic uncoded equalization system. The performance advantages are validated with bit-error-rate (BER) simulations and extrinsic information transfer (EXIT) chart analysis.

We design a soft-in soft-out (SISO) decision feedback equalizer (DFE) that performs better than its linear counterpart in turbo equalizer (TE) setting. Unlike previously developed SISO-DFEs, the present DFE scheme relies on extrinsic information formulation that directly takes into account the error propagation effect. With this new approach, both error rate simulation and the extrinsic information transfer (EXIT) chart analysis indicate that the proposed SISO-DFE is superior to the well-known SISO linear equalizer (LE). This result is in contrast with the general understanding today that the error propagation effect of the DFE degrades the overall TE performance below that of the TE based on a LE. We also describe a new extrinsic information combining strategy involving the outputs of two DFEs running in opposite directions, that explores error correlation between the two sets of DFE outputs. When this method is combined with the new DFE extrinsic information formulation, the resulting "bidirectional" turbo-DFE achieves excellent performance-complexity tradeoffs compared to the TE based on the BCJR algorithm or on the LE. Unlike turbo LE or turbo DFE, the turbo BiDFE's performance does not degrade significantly as the feedforward and feedback filter taps are constrained to be time-invariant.

We utilize a pair of decision feedback equalizers (DFEs) operating in opposite directions in turbo equalization setting to remove the effect of intersymbol interference (ISI) at the receiver. With a specific residual interference processing strategy proposed, the bi-directional DFE (BiDFE) are free from any significant error propagation. A diversity combining scheme is also proposed that effectively combines the extrinsic outputs of two opposite direction DFEs to minimize any correlation that may exist between them. A resulting scheme is a low-complexity equalizer that closely approaches the performance of the much more complex BCJR algorithm at the expense of an increased number of decoder-equalizer iterations. The BiDFE turbo equalizer also provides considerably better performance than the well-known soft linear minimum mean square error (MMSE) equalizer in severe ISI channels. The performance advantages are validated with bit-error-rate (BER) simulations and extrinsic information transfer (EXIT) charts analysis.