基于Markov过程的宽间隔跳频地址码序列的概率分布及谱特性的研究

A Study of the Stochastic and Spectral Distribution for the Wide-Interval Frequency-Hopped Pattern Based on the Markov′s Process

本文给出了和宽间隔跳频地址码序列相对应的Markov过程模型 ,并基于此模型研究了具有实对称特性的q元宽间隔跳频地址码序列的一步转移概率矩阵P和n步转移概率矩阵P(n) 及n步转移概率p(n)ij ,给出了最小间隔d =1时p(n)ij 的解析表达式和d >1时以用正交矩阵和特征矩阵来表示的p(n)ij 一般表达式 .然后 ,根据一般形式的P(n) 定义了q元宽间隔跳频地址码序列的自相关函数和N步谱 .

In this paper,a model based on the Markov′s chain is given for the wide-interval frequency-hopped sequence of q-states (q-WDFHS).Based on the model,the probability distribution of the q-WDFHS can be written out through its 1-step and n-step transition probability matrices P and P (n).By deriving the analytical expression of p (n) ij and P (n),this paper provides the spectral characteristics of a q-WDFHS.Through the calculation of the spectrum distribution,this paper shows that the spectrum of a q-WDFHS with smaller interval is flatter and more concentrated on the domain of low frequencies,while those with larger intervals have more components of high frequency and sharper spectrum distribution.