标题： 线性自适应滤波器在遍历混沌逻辑斯蒂映射驱动下的性能 显示英文标题

标题： On the Performance of Linear Adaptive Filters driven by the Ergodic Chaotic Logistic Map

摘要： 混沌动力系统越来越多地被考虑用于编码和传输系统。 这是由于它们对参数的敏感性和频谱特性。 后者与信道估计方法有关。 特别是逻辑斯蒂映射$f_\lambda =\lambda x\left( 1-x\right) $已经被用于混沌编码和扩频传输系统。 对于$\lambda =4$，由$f_4$生成的序列的统计特性被视为信道估计方案的理想驱动信号。 这一假设在本文中得到了证明。 为此，推导了由$f_4$生成的时间序列的高阶统计矩和自相关性。 结果显示，对于$\lambda =4$，零均值时间序列是不相关的。 分析了用于信道估计的有限脉冲响应（FIR）数字自适应滤波器（DAF）的适应性能。 结果显示，使用$f_4$的零均值序列可以达到最大的FIR DAF性能。 推导了LMS方案中阻尼参数的一个最优值，该值可以达到最大的性能并确保稳定性。 分析结果通过仿真结果得到了验证。 显示英文摘要

摘要： Chaotic dynamical systems are increasingly considered for use in coding and transmission systems. This stems from their parameter sensitivity and spectral characteristics. The latter are relevant for channel estimation methods. In particular the logistic map $f_\lambda =\lambda x\left( 1-x\right) $ has been employed in chaotic coding and spread spectrum transmission systems. For $\lambda =4$ the statistical properties of sequences generated by $f_4$ are considered as ideal drive signals for channel estimation schemes. This assumption is proven in the present paper. To this end the higher order statistical moments and the autocorrelation of time series generated by $f_4$ are derived. It is shown that for $\lambda =4$ the zero mean time series is uncorrelated. The adaptation performance of finite impulse response (FIR) digital adaptive filters (DAF) used for channel estimation is analyzed. It is shown that using zero mean sequences of $f_4$ leads to the maximal possible FIR DAF performance. An optimal value for the damping parameter in the LMS scheme is derived that leads to the maximal performance and ensures stability. The analytic considerations are confirmed by simulation results.