The impact of intersymbol interference (ISI) on single carrier frequency domain equalization with multiple input multiple output (MIMO-SCFDE) systems is severe. Most existing channel equalization methods fail to solve it completely. In this paper, given the disadvantages of the error propagation and the gap from matched filter bound (MFB), we creatively introduce a decision feedback equalizer with frequency-domain bidirectional noise prediction (DFE-FDBiNP) to tackle intersymbol interference (ISI) in MIMO-SCFDE systems. The equalizer has two-part equalizer, that is the normal mode and the time-reversal mode decision feedback equalization with noise prediction (DFE-NP). Equal-gain combining is used to realize a greatly simplified and low complexity diversity combining. Analysis and simulation results validate the improved performance of the proposed method in quasi-static frequency-selective fading MIMO channel for a typical urban environment.

Error-propagation is an important issue and should be carefully coped with in the decision-feedback equalizers (DFE). Ignoring the impact of error-propagation often leads to impractical laboratory results. In this paper, we investigate two novel layered space-frequency equalizers (LSFE) for single-carrier multiple-input multiple-output (MIMO) systems, where the recently proposed frequency-domain equalizer with time domain noise-predictor (FDE-NP) is adopted at each stage of the LSFE. We first derive the partially-connected LSFE with noise predictor (PC-LSFE-NP) which has exactly the same mean square error (MSE) as the conventional LSFE under the assumption of perfect feedback. However, if error-propagation is considered, the proposed PC-LSFE-NP can achieve better performance than the conventional LSFE due to the more reliable feedback output by the decoders. To reduce the interference from the not yet detected layers in the feedback section, we then introduce the fully-connected LSFE with noise predictor (FC-LSFE-NP), in which all layers are implicitly equalized within each stage and their decisions fed back internally. The powerful feedback filter of FC-LSFE-NP brings significant performance superiority over the conventional LSFE and PC-LSFE-NP with either perfect or imperfect feedback. Moreover, we propose a simple soft-demapper for the equalizers to avoid information loss during decoding, and thus, further improve the performance. Finally, we compare the performance of (PC/FC)-LSFE-NP with the existing schemes by computer simulations.

In this letter, we propose a novel frequency-domain equalizer (FDE) for single-carrier systems characterized by severe inter-symbol interference (ISI) channels; it consists of a linear FDE and an iterative block noise-predictor (IBNP). Unlike the FDE with time-domain noise predictor (FDE-NP), the proposed scheme allows the feedback equalizer being an uncausal filter, and performs the noise prediction in an iterative manner. For this reason, FDE-IBNP can remove both precursor and postcursor ISI, and alleviate the impact of error-propagation. Besides, our scheme has lower computational complexity than the present iterative block equalizers.

A single-carrier multiple-input multiple-output (MIMO) system with frequency-selective channels suffers from the inter-symbol interference (ISI) and the co-channel interference (CCI). To eliminate both type of interference, we propose in this letter a hybrid two-stage decision-feedback equalizer (HTS-DFE), which performs the frequency-domain equalization (FDE) in the first stage and the layered serial interference-cancellation (SIC) in the second stage. Since the decision-feedback (DF) or noise-prediction (NP) architecture can be employed in FDE or SIC, the proposed equalizer actually can have four variations that achieve the same mean square error (MSE) under the assumption of perfect feedback. Further, we combine HTS-DFE with the decoded decision-feedback (DDF) scheme to mitigate the error-propagation encountered in the practice. Simulation results confirm that the proposed HTS-DFE can outperform the existing equalizers significantly.

In this letter two noise-predictive equalization schemes, which are based on zero-forcing (ZF) and minimum mean square error (MMSE) criteria, are presented for unique-word (UW) based single-carrier systems. The correlation properties of the noises in the outputs of the frequency domain equalizer are exploited to predict and cancel the noise contained in the estimation of data. Theoretical analyses show that both of the proposed techniques perform better than the conventional frequency domain equalizers. Simulation results have confirmed the significant performance improvement they could achieve.