In this paper, we develop a practical approach for deploying Physical Layer Network Coding (PNC) in multi-user M-Ary Quadrature Amplitude Modulation (M-QAM) Massive Multiple-Input Multiple-Output (MIMO) systems. We formulate a PNC mapping scheme as a function of clusters of estimated summation and difference (SD) of the transmitted symbols from user pairs. Utilizing existing linear detection schemes, such as Zero Forcing (ZF) and Minimum Mean Square Error (MMSE), a cluster of SD symbols are detected using an SD linearly transformed channel matrix. Furthermore, utilizing Maximum a Posteriori (MAP) soft decoding, the SD symbols are mapped to the PNC symbols, leveraging on the PNC symbol that maximizes the likelihood function. For each variant of M-QAM, we derive and simplify a specialization of the generalized PNC mapping function. The error performance results, through simulation, reveal that the proposed PNC scheme achieves twice the spectral efficiency in Massive MIMO, without changing the latter's underlying framework and without any degradation in the bit-error-rate (BER). In fact, our investigation has proved that the BER of the proposed Massive MIMO and PNC is slightly better than that of the conventional Massive MIMO. The feasibility of deploying our proposed PNC scheme in Massive MIMO systems paves way for NC applications to be realized in cellular systems.

中文翻译：

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采用 M-QAM 调制的大规模 MIMO 系统中物理层网络编码的性能分析


在本文中，我们开发了一种在多用户 M 进制正交幅度调制 (M-QAM) 大规模多输入多输出 (MIMO) 系统中部署物理层网络编码 (PNC) 的实用方法。我们将 PNC 映射方案制定为来自用户对的传输符号的估计和与差 (SD) 簇的函数。利用现有的线性检测方案，例如迫零（ZF）和最小均方误差（MMSE），使用SD线性变换的信道矩阵来检测SD符号簇。此外，利用最大后验（MAP）软解码，SD符号被映射到PNC符号，利用最大化似然函数的PNC符号。对于 M-QAM 的每个变体，我们推导并简化了广义 PNC 映射函数的特化。通过仿真，错误性能结果表明，所提出的 PNC 方案在 Massive MIMO 中实现了两倍的频谱效率，而无需改变后者的底层框架，也不会降低误码率 (BER)。事实上，我们的调查证明，所提出的 Massive MIMO 和 PNC 的 BER 略好于传统的 Massive MIMO。在大规模 MIMO 系统中部署我们提出的 PNC 方案的可行性为在蜂窝系统中实现 NC 应用铺平了道路。