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

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.最后给出了谱分析的理论推导和计算的结果.

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

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.