相关跳频转移函数的双随机矩阵模型及其应用

Doubly Stochastic Matrices Model of DFH G-Function and Its Application

该文分别从状态空间的分解和平稳分布等角度对双随机矩阵以及双随机马氏(Markov)链的性质进行了研究,并将这些性质应用到相关跳频转移函数的分析和建模。文中证明了转移函数的双随机矩阵数学模型就状态转移过程的均匀性来说是完备的。基于对该模型的分析,提出了一种转移函数构造方法——周期分组法,通过将频率转移过程构造成一个周期性双随机马氏链,可以获得纠错性能和频率间隔性能俱佳的转移函数。

In this paper, the properties of doubly stochastic matrices and doubly stochastic Markov chains are researched from the viewpoints of the classification of states and equilibrium distributions. These properties are applicable to the analysis and modeling of differential frequency hopping G-functions. It is proved that the doubly stochastic matrix model of G-functions is complete in terms of the state transition＇s uniformity. Based on this mathematic model, a periodic grouping method is proposed to design G-functions by regarding the state transition as a periodic doubly stochastic Markov chain, and it can achieve good performance both in error-correcting and in frequency interval.