In this paper, a new class of soft-input soft-output block decision feedback equalizer (BDFE) for turbo equalization over inter-symbol interference (ISI) channels under minimum mean-square error (MMSE) criterion is proposed. First, the BDFE which employs both the a posteriori moments of estimated symbols and the a priori moments of unestimated symbols is investigated, and two recursive schemes are derived to reduce the complexity. Then, to mitigate error propagation, the bidirectional BDFE (Bi-BDFE) consisting of a forward BDFE and a backward BDFE is proposed. Furthermore, a threshold is employed to reduce the number of inverse matrix update process for the BDFE (T-BDFE), which can attain a flexible trade-off between complexity and performance. Finally, the bidirectional equalization is introduced into a low-complexity approximate solution of the BDFE (Bi-LC-BDFE) to further reduce the complexity and obtain time diversity gain, which utilizes a time-invariant covariance matrix. Simulation results show that the proposed equalizers significantly outperform the block linear equalizer (BLE), the exact MMSE-based linear equalizer (Exact-MMSE-LE) and the soft-decision feedback equalizers (SDFE), while keeping a similar complexity as the BLE. In addition, the Bi-BDFE can achieve better performance than the Max-Log-MAP equalizer while its complexity is on the same order as the BDFE.

中文翻译：

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ISI 通道的软输入软输出模块判决反馈均衡


本文提出了一类新型软输入软输出块判决反馈均衡器（BDFE），用于在最小均方误差（MMSE）准则下对符号间干扰（ISI）信道进行涡轮均衡。首先，研究了同时采用估计符号的后验矩和未估计符号的先验矩的BDFE，并导出了两种递归方案以降低复杂度。然后，为了减轻错误传播，提出了由前向 BDFE 和后向 BDFE 组成的双向 BDFE (Bi-BDFE)。此外，采用阈值来减少BDFE（T-BDFE）的逆矩阵更新过程的数量，这可以实现复杂性和性能之间的灵活权衡。最后，将双向均衡引入BDFE的低复杂度近似解（Bi-LC-BDFE）中，利用时不变协方差矩阵，进一步降低复杂度并获得时间分集增益。仿真结果表明，所提出的均衡器显着优于块线性均衡器 (BLE)、基于精确 MMSE 的线性均衡器 (Exact-MMSE-LE) 和软判决反馈均衡器 (SDFE)，同时保持与 BLE 相似的复杂度。此外，Bi-BDFE 可以实现比 Max-Log-MAP 均衡器更好的性能，而其复杂度与 BDFE 处于同一量级。