Physical-layer network coding (PNC) can increase end-to-end throughput in bi-directional multi-hop underwater acoustic (UWA) networks. However, multipath delay spread and Doppler-induced inter-carrier interference (ICI) in UWA channels can degrade the reliability of PNC transmission in a three-node relay configuration. More critically, error accumulation across multiple relay nodes leads to a pronounced increase in the end-to-end bit error rate (BER) in multi-hop networks. To address this issue, we develop an iterative detection and decoding processing strategy for relay nodes within a PNC-enabled multi-hop UWA network based on orthogonal frequency division multiplexing (OFDM) modulation. The proposed design integrates three key algorithms: (i) an adaptive channel-aware factor graph detection algorithm that is suited for time-varying UWA channels; (ii) a parity-check-constrained soft-information refinement algorithm that improves the accuracy of the information feedback from the decoder to the detector; and (iii) a linear minimum mean square error (LMMSE) detection algorithm based on a superimposed model, which offers low computational complexity as an alternative scheme. Extensive simulation results demonstrate that the adaptive detection algorithm achieves BERs on the order of $10^{-5}$ at a relative velocity of 1.5 m/s UWA channel and a signal-to-noise (SNR) of 8~dB. Both lake experiments and sea trials in the Taiwan Strait confirm that the proposed iterative receiver algorithms outperform baseline schemes in terms of BER performance under practical UWA channel conditions, showing their robustness and applicability in real multi-hop deployments.

翻译：物理层网络编码（PNC）可提升双向多跳水声网络中的端到端吞吐量。然而，水声信道中的多径时延扩展与多普勒效应引起的载波间干扰会降低三节点中继配置下PNC传输的可靠性。更关键的是，多跳网络中跨中继节点的误差累积将导致端到端误比特率显著增加。为解决这一问题，本文针对基于正交频分复用调制的PNC多跳水声网络中继节点，提出了一种迭代检测与解码处理策略。该设计方案集成了三种核心算法：（i）适用于时变水声信道的自适应信道感知因子图检测算法；（ii）基于校验约束的软信息精炼算法，用于提升解码器反馈至检测器的信息精度；（iii）基于叠加模型的线性最小均方误差检测算法，作为低计算复杂度的替代方案。大量仿真结果表明，在相对速度为1.5 m/s的水声信道及8 dB信噪比条件下，自适应检测算法可实现约$10^{-5}$量级的误比特率。台湾海峡湖试与海试结果均证实，在实际水声信道条件下，所提迭代接收算法的误比特率性能优于基准方案，展现了其在真实多跳部署环境中的鲁棒性与适用性。