物理层网络编码（PNC）在无线物理层将干扰转变为有用信息，可逼近双向中继信道容量。目前PNC研究主要集中在理论领域，通常假设终端和中继间信道理想匹配来简化分析。然而，申请人前期研究揭示，信道失配（即信道增益非完美已知，载波相位偏差和频率偏移存在）在实际系统中不可回避，且对PNC性能影响巨大。在PNC中，与信道失配相关的参数难以从相互叠加的信号中估计；并且传统分离式的失配校正和信号解码方法不能去除这些失配的影响。因此，本项目提出利用期望最大化、置信度传播等迭代算法来联合解决PNC的信道失配校正与目标信号解码问题。具体的，我们将利用因子图构建信号概率模型；提出迭代交换失配参数和目标信号软信息的处理算法；使用迭代算法优化系统总体性能；将所提迭代算法由单载波扩展到多载波PNC；提出低复杂度的迭代算法；最后，利用软件无线电来实现和验证所提迭代算法。本项目的研究将为PNC实用化提供理论依据和技术支撑。

By transforming interferences into useful information at the wireless physical-layer, physical-layer network coding (PNC) can achieve the capacity of two-way relay channels. Currently, researches on PNC mainly focus on theoretical problems. It is usually assumed that the channels between the relay and the terminals are perfectly matched to simplify the analysis. However, our previous research results reveal that the channel mismatch (i.e., the channel gains are not perfectly known, the carrier phase shifts and carrier frequency offsets exist) cannot avoided in systems, and it has important impacts on PNC performances. In PNC systems, the parameters related to the channel mismatch are hard to estimate from the overlapping of signals; moreover, traditional separate channel mismatch calibration and signal decoding methods cannot remove the impact of these mismatch parameters. Therefore, this project proposes to use iterative expectation maximization (EM), belief propagation (BP) algorithms to solve the problems of channel mismatch calibration and target signal decoding jointly for PNC. Specifically, we employ factor graphs to represent the probabilistic model of signals; we propose signal processing algorithms for iteratively exchanging soft information of channel mismatch parameters and target signals; we use iterative algorithms to optimize the system overall performance; we extend the proposed iterative algorithms from single-carrier PNC to multi-carrier OFDM-PNC; we propose iterative algorithm with lower complexities; finally, we employ soft-ware defined radios to implement and validate our proposed iterative algorithms. The researches of this project can provide theoretical proofs and technique supports for the progress on the application of PNC in practice real systems.