基于有限维随机矩阵理论的协作频谱感知理论及技术研究

The proposed research utilizes the Finite Random Matrix Theory (FRMT) to analyze and address cooperative spectrum sensing issues in cognitive radio. Specifically, there are two key themes within the proposed research. The first theme is to explore the exact and analytical probability distribution theory of extreme eigenvalues and standard condition number in FRMT. The second one is to explore how to deduce key algorithms of cooperative spectrum sensing using the above distribution theories. On the other hand, we also research how to analyze and construct the high precision and robust cooperative spectrum sensing system using FRMT. It is different from previous relative research which tried to solve the cooperative spectrum sensing issues mainly using infinite random matrix theory (IRMT). In IRMT, it is required that the sizes of matrix should go to infinite and the probability distributions of eigenvalues are inexact and approximate. Such shortcomings of IRMT impose a limitation on its further application in the research field of cooperative spectrum sensing. Therefore, the proposed research innovatively utilizes FRMT to explore novel methods of cooperative spectrum sensing in order to enhance the spectrum sensing performance of the proposed system. The proposed project will firstly explore the eigenvalue probability distributions of random matrix under the condition that the sizes of matrix are finite. We will try to explore the probability distribution theory of extreme eigenvalues and standard condition number. During the exploration, we will focus the research on the exactness and complexity of the probability distribution functions. Secondly, we will research how to deal with the cooperative spectrum sensing issues using the novel theory results. The proposed research will provide a promotion in the research of FRMT and have a broad impact in the actual spectrum sensing applications. More importantly, such research will enrich the theory and method system of cooperative spectrum sensing.

本项目利用有限维随机矩阵理论，分析和解决认知无线电中协作频谱感知问题。拟研究两个关键问题：1.有限维随机矩阵理论中极限特征值和标准条件数精确概率分布理论；2.利用该理论，研究协作频谱感知关键算法，分析和构建高性能协作频谱感知系统。 以往的相关研究，主要利用大维随机矩阵理论分析协作频谱感知问题。该理论要求矩阵维数趋向于无穷大，同时特征值概率分布为近似分布，这些不足限制了该理论在协作频谱感知领域的应用。因此本项目创新性地首次引入有限维随机矩阵理论，旨在探索协作频谱感知新方法，提升系统频谱感知性能。 本项目将首先研究随机矩阵在有限维数条件下的特征值分布规律，探索极限特征值和标准条件数精确概率分布理论，重点关注概率分布函数的精确度和复杂度。其次，研究如何利用该理论分析协作频谱感知问题。本项目将推动有限维随机矩阵理论研究，并在实际频谱感知的应用领域产生影响，可望充实协作频谱感知理论体系和方法体系。

5G和未来无线通信技术在世界范围内引起广泛关注，各国都力争在该技术竞争中占得先机。频谱智能管理和高效利用技术在无线通信系统中占有重要地位，该技术能够解决频谱固定分配机制和有限频谱资源之间的矛盾，大大提高频谱效率。.本项目利用有限维随机矩阵理论分析和解决认知无线网络中协作频谱感知问题， 主要研究两个方面内容：1.有限维随机矩阵理论中极限特征值和标准条件数精确概率分布理论；2.利用该理论，研究协作频谱感知关键算法，分析和构建高性能协作频谱感知系统。.项目组经过四年的研究，重要成果总结如下：.1. 给出了有限维随机矩阵的标准条件数精确概率分布理论，推导出了任意维Wishart矩阵标准条件数精确概率分布(PDF和CDF) （结果发表于IEEE Transactions on Vehicular Technology，2017）；.2. 根据大维随机矩阵理论和有限维随机矩阵理论，提出了维数界(Dimension boundary)概念，从理论上界定了大维随机矩阵和有限维随机矩阵的边界关系，给出了两种理论体系的应用领域（结果发表于IEEE Communications Letters，2017）； .3. 针对有限维随机矩阵理论，推导出了极限特征值分布、特征值联合分布、特征值比例分布等，分别发表在了Sensors 2016, IET Communications 2015 和Wireless personal communications 2017。另外还分析了基于Demmel 条件数的协作频谱感知系统，发表于Wireless personal communications 2015；.4. 频谱效率和能量效率是认知无线网络中的两个核心技术指标。项目研究了认知无线网络中的能效和频效折中问题，解决了针对三种认知无线网络的参数设计与优化问题（结果发表于IEEE Transactions on Vehicular Technology，2015）；.5. 项目组成员还研究了无线通信中的其他关键技术，发表了一些重要学术成果。.本项目深入研究了有限维随机矩阵理论中的标准条件数和极限特征值的精确概率分布问题，推动了随机矩阵理论的发展。利用以上理论成果，项目研究分析了基于随机矩阵理论的协作频谱感知系统。同时也为随机矩阵理论在无线通信领域的深入应用打下了基础、开拓了新思路。

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