Abstract

The design approach of pseudo-random discrete signals with fractional power-law angular modulation (FM/PM) is considered in the article. These signals as a discrete set of time values with the uniform sample spacing acquire the properties of pseudo-random sequences. The envelope and phase are defined for the constructed signals using the analytical signal concept. It is found that the time discretization of the oscillation representation by the product of two functions, using the WKB-approximation (Wentzel–Kramers–Brillouin) to solve the parametric oscillator equation, violates the condition of its frequency change slowness (physical feasibility of the solution). The appearance mechanism of pseudo-random behavior of discrete signals with the fractional power-law FM/PM is based on the properties of algebraic irrational numbers sequences. The ambiguity and autocorrelation functions of the Fourier spectra of the designed signals are investigated. The designed signals stealthiness is considered, from the point of view of their disguising as noise, based on the calculation of nonparametric BDS statistics (Brock–Dechert–Scheinkman). The BDS statistics values for different durations of the designed signals are estimated. The method to increase the designed signals stealthiness is proposed.

中文翻译：

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分数幂律角调制伪随机离散信号的设计

摘要

本文考虑了具有分数幂律角调制（FM/PM）的伪随机离散信号的设计方法。这些信号作为具有均匀采样间隔的离散时间值集获得伪随机序列的特性。使用分析信号概念为构建的信号定义包络和相位。发现通过两个函数的乘积对振荡表示的时间离散化，使用 WKB 近似 (Wentzel–Kramers–Brillouin) 求解参量振荡器方程，违反了其频率变化缓慢的条件（解决方案）。分数幂律FM/PM离散信号伪随机行为的出现机制是基于代数无理数序列的性质。研究了设计信号的傅里叶谱的模糊度和自相关函数。基于非参数 BDS 统计 (Brock-Dechert-Scheinkman) 的计算，从伪装为噪声的角度考虑了设计的信号隐身性。估计设计信号的不同持续时间的 BDS 统计值。提出了提高设计信号隐身性的方法。