基于特殊网络结构和分数阶微积分的正交信号构造理论、方法及其在MIMO雷达中的应用研究

正交信号在雷达信号处理、通信理论、信息安全、等诸多领域有着非常重要和广泛的应用背景。相比智能算法只能得到近似正交或较低自（互）相关信号，用构造法能得到完全正交信号和具有最低自（互）相关信号，因而受到研究者们的极大关注。现有的构造方法只能得到特定码长的正交信号和由窗函数得到的非线性调频信号。本项目拟针对离散和连续型正交信号各自建立统一的构造方法和工具，搭建正交信号的构造理论和方法。首先，将现有Hadamard矩阵和低自相关序列的构造思想相结合，提出了通过有限正交递推方法构造具有特殊网络结构的正则偶图来得到H矩阵，并将此方法推广用于构造拟H矩阵，其次，利用正交信号的自相似性和分数维特征，结合分抗电路可用于实现分数阶信号，提出运用分数阶微积分理论构造非线性调频信号；再次，对正交信号进行灵敏性和稳定性分析，为正交信号的实际应用提供理论支撑；最后，将构造理论和方法应用于MIMO雷达的正交信号设计。

Orthogonal signal has an extremely wide application in many domains such as radar signal processing, communication theory, information security and so on. Compared with intelligent algorithms that may only get approximately orthogonal or lower (cross-correlation) autocorrelation signals, the construction method can obtain the completely orthogonal signal as well as the lowest (cross-correlation) autocorrelation signals, which has caught much attention recently. However, the current construction methods can only achieve the orthogonal signals with a specific code length and the NLFM signals by the window function. To address this problem, this project tries to develop a unified construction method and tools to both discrete and continuous orthogonal signals, which may set up new construction theory and method for orthogonal signals. First, through combining the existing Hadamard matrix and the low autocorrelation sequences, the H matrix is obtained by finite orthogonal recursive method to construct the regular bipartite graph with special network structure, and then this method is applied to construct the quasi H matrix; Secondly, based on the self-similarity and fractal dimension of discrete orthogonal signals, fractional signals can be achieved with the fractance circuit and further the NLFM signals can be constructed by fractional calculus theory; Thirdly, the sensitivity and stability of orthogonal signals are examined to provides theoretical support for the practical application of orthogonal signals. Finally, the proposed theory and method will be used in the orthogonal signal design of MIMO radar.