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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 42 ›› Issue (6): 1089-1097.doi: 10.3969/j.issn.1005-3085.2025.06.008cstr: 32411.14.cjem.CN61-1269/O1.2025.06.008

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基于线性方程组的信号重建理论及频分信道技术研究

单广均1,2   

  1. 1. 湖北经济学院信息工程学院，武汉 430205

    2. 数字金融创新湖北省重点实验，武汉 430205

  • 收稿日期:2024-12-09 接受日期:2025-07-23 出版日期:2025-12-15 发布日期:2026-02-15
  • 基金资助:
    国家留学基金(202108420134).

Research on Signal Reconstruction Theory and Frequency Division Channel Technology Based on Linear Equations

SHAN Guangjun1,2   

  1. 1. School of Information Engineering, Hubei University of Economics, Wuhan 430205
    2. Key Laboratory of Digital Finance Innovation of Hubei Province, Wuhan 430205
  • Received:2024-12-09 Accepted:2025-07-23 Online:2025-12-15 Published:2026-02-15
  • Supported by:
    The China Scholarship Council Grant (202108420134).

摘要：

基于线性方程组的信号重建理论(Linear Equation Groups, LER)，提出了一种新型的多载波技术–频分信道(Frequency Division Channel Utilization, FDCU)技术，可有效提升信道容量。不同于OFDM等其他多载波信号，FDCU信号的各次谐波在数学上并不完全正交，因而传统的傅里叶信号处理方法并不适用FDCU信号的解调。该研究利用BP(Back-Propagation)神经网络成功解调了包含三个频率分量的FDCU信号，验证了其在非正交信号处理中的有效性。研究结果将为电子通信、图像处理、遥感等领域提供一种新的信号应用方式和信号处理手段。

关键词: 信号重建, 多载波技术, 频分信道, 傅里叶信号处理, BP神经网络

Abstract:

Based on the signal reconstruction theory of linear equation groups, a novel multi-carrier technology called frequency division channel utilization (FDCU) is proposed, aimed at effectively enhancing channel capacity. Unlike other multi-carrier signals such as OFDM, the harmonics of FDCU signals are not fully orthogonal mathematically, which renders traditional Fourier signal processing methods unsuitable for their demodulation. An FDCU signal comprising three frequency components was successfully demodulated using a back-propagation (BP) neural network, demonstrating the effectiveness of BP neural networks in processing non-orthogonal signals. This approach provides a new perspective on signal application and processing methods in fields such as electronic communications, image processing, and remote sensing.

Key words: signal reconstruction, multi-carrier technology, frequency division channel, Fourier signal processing, BP neural network

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