This paper investigates coherent detection for physical-layer network coding (PNC) with short packet transmissions in a two-way relay channel (TWRC). PNC turns superimposed EM waves into network-coded messages to improve throughput in a relay system. To achieve this, accurate channel information at the relay is a necessity. Much prior work applies preambles to estimate the channel. For long packets, the preamble overhead is low because of the large data payload. For short packets, that is not the case. To avoid excessive overhead, we consider a set-up in which short packets do not have preambles. A key challenge is how the relay can estimate the channel and detect the network-coded messages jointly based on the received signals from the two end users. We design a coherent detector that makes use of a belief propagation (BP) algorithm to do so. For concreteness, we focus on binary frequency-shift-keying (FSK) modulation. We show how the BP algorithm can be simplified and made practical with Gaussian-mixture passing. In addition, we demonstrate that prior knowledge on the channel distribution is not needed with our framework. Benchmarked against the detector with prior knowledge of the channel distribution, numerical results show that our detector can have nearly the same performance without such prior knowledge.

中文翻译：

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二进制 FSK 调制的短包物理层网络编码的相干检测

本文研究了在双向中继信道 (TWRC) 中具有短数据包传输的物理层网络编码 (PNC) 的相干检测。PNC 将叠加的 EM 波转换为网络编码消息，以提高中继系统的吞吐量。为了实现这一点，必须在中继站提供准确的信道信息。许多先前的工作应用前导码来估计信道。对于长数据包，由于数据负载较大，前导开销较低。对于短数据包，情况并非如此。为了避免过多的开销，我们考虑一种短数据包没有前导码的设置。一个关键的挑战是中继如何根据从两个最终用户接收到的信号来估计信道并联合检测网络编码消息。我们设计了一个相干检测器，它利用置信传播 (BP) 算法来做到这一点。具体而言，我们专注于二进制频移键控 (FSK) 调制。我们展示了如何通过高斯混合传递简化 BP 算法并使其实用。此外，我们证明了我们的框架不需要有关渠道分布的先验知识。以具有通道分布先验知识的检测器为基准，数值结果表明，我们的检测器可以在没有这种先验知识的情况下具有几乎相同的性能。