模拟波束成型网络综合的矩阵分解方法研究

In view of the theoretical limitations of the current synthesis technique of complex analog beam-forming networks, this project proposes and studies a matrix decomposition method for synthesizing analog beam-forming networks. Firstly, simplified transmission matrix models with cascade characteristics are proposed to characterize the electrical parameters and port cascade characteristics of multi-port devices and analog beam-forming networks. Secondly, a matrix decomposition method is proposed, which decomposes the simplified transmission matrix of the analog beam-forming network into a cascade of simplified transmission matrices of multi-port devices. The physical meaning and application scope of different matrix decomposition methods are mainly studied, with the engineering problems of network synthesis problem transformed into mathematical problems of matrix decomposition. Finally, taking into account the network impedances, losses, number of devices and other performance, the matrix decomposition method is combined with the optimization algorithm to optimize the performance of the analog beam-forming network. The matrix decomposition method proposed in this project breaks through the theoretical limitations of traditional analog beam-forming network synthesis, and has the ability to synthesize analog beam-forming network with any number of ports. It not only guarantees the electrical performance index but also improves the network performance of the analog beam-forming network. As a brand-new basic research topic, the research results of this project can be widely used in the design of analog beam-forming networks with different frequency bands and different uses, which not only has important theoretical significance, but also has wide application value.

针对当前复杂模拟波束成型网络综合技术的理论局限，本项目提出并研究综合模拟波束成型网络的矩阵分解方法。首先，提出具有级联特性的简化传输矩阵模型，实现表征多端口器件和模拟波束成型网络的电参数和端口级联特性。其次，提出矩阵分解方法，将模拟波束成型网络的简化传输矩阵分解为多端口器件的简化传输矩阵的级联，重点研究不同矩阵分解方法的物理含义和适用范围，实现将网络综合的工程问题转化为矩阵分解的数学问题。最后，将矩阵分解方法与优化算法相结合，兼顾网络阻抗、损耗、器件数目等指标，综合优化模拟波束成型网络的性能。本项目提出的矩阵分解方法突破了传统模拟波束成型网络综合的理论局限，具有综合任意端口数目的模拟波束成型网络的能力，保证其参数指标的同时优化了网络性能。作为一项崭新的基础研究课题，该项目的研究成果可广泛用于设计不同频段、不同用途的模拟波束成型网络，不仅具有重要的理论意义，同时亦具有广泛的应用价值。

针对当前复杂模拟波束成型网络综合技术的理论局限，本项目提出并研究综合模拟波束成 型网络的矩阵分解方法。首先，研究具有级联特性的简化传输矩阵模型，实现表征多端口器件和模拟波束成型网络的电参数和端口级联特性。其次，提出矩阵分解方法，将模拟波束成型网络的简化传输矩阵分解为多端口器件的简化传输矩阵的级联，重点研究不同矩阵分解方法的物理含义和适用范围，实现将网络综合的工程问题转化为矩阵分解的数学问题。最后，将矩阵分解方法与优化算法相结合，兼顾网络阻抗、损耗、器件数目等指标，综合优化模拟波束成型网络的性能。本项目提出的矩阵分解方法突破了传统模拟波束成型网络综合的理论局限，具有综合任意端口数目的模拟波束成型网络的能力，保证其参数指标的同时优化了网络性能。作为典型实例验证，本项目设计两款2×6正交波束成形网络，当与阵列天线级联时，可实现具有平顶方向图赋形，并兼顾方向图辐射指向。本项目作为一项崭新的基础研究课题，相关研究成果可广泛用于设计不同频段、不同用途的模拟波束成型网络。于此同时，具有任意端口数目的正交波束成形网络可应用于混合波束成形网络系统中，能够在满足波束覆盖性能指标的同时减小射频链路数目，有效降低系统能耗。综上所述，本项目的相关研究成果不仅具有重要的理论意义，同时亦具有广泛的应用价值。