Optimal Spreading Sequences for Chaos-Based Communication Systems

As a continuation from [2], some higherorder statistical dependency aspects of chaotic spreading sequences used in communication systems are presented. The autocorrelation function (ACF) of the mean-adjusted squares, termed the quadratic autocorrelation function, forms the building block of nonlinear dependence assessment of the family of spreading sequences under investigation. Explicit results are provided for the theoretical lower bound, the so-called Fr´echet lower bound, of the quadratic ACF of that family. A method for producing a spreading sequence which attains the Fr´echet bound is introduced

Higher order Dependency of Chaotic Maps

Some higher-order statistical dependency aspects of chaotic maps are presented. The autocorrelation function (ACF) of the mean-adjusted squares, termed the quadratic autocorrelation function, is used to access nonlinear dependence of the maps under consideration. A simple analytical expression for the quadratic ACF has been found in the case of fully stretching piece-wise linear maps. A minimum bit energy criterion from chaos communications is used to motivate choosing maps with strong negative quadratic autocorrelation. A particular map in this class, a so-called deformed circular map, is derived which performs better than other well-known chaotic maps when used for spreading sequences in chaotic shift-key communication systems

Simulation of Some Autoregressive Markovian Sequences of Positive Random Variables

Winter Simulation ConferenceMethods of simulation depending sequences of continuous positive-valued random variables with exponential and uniform marginal distributions are given. In most cases the sequences are first-order, linear autoregressive, Markovian processes. A two-parameter family of this type with exponential marginals is defined and its transformation to a similar multiplicative process with uniform marginals is given. It is shown that for a subclass of this two-parameter family extension to mixed exponential marginals is possible, giving a model of broad applicability for analyzing data and modeling stochastic systems. Efficient simulation of some of these schemes is discussed

The Exponential Autoregressive-Moving Average EARMA (p,q) Process

A new model for pth‐order autoregressive processes with exponential marginal distributions, ear(p), is developed and an earlier model for first‐order moving average exponential processes is extended to qth‐order, giving an ema(q) process. The correlation structures of both processes are obtained separately. A mixed process, earma(p,q), incorporating aspects of both ear(p) and ema(q) correlation structures is then developed. The earma(p, q) process is an analog of the standard arma(p, q) time series models for Gaussian processes and is generated from a single sequence of independent and identically distributed exponential varables.Office of Naval Research NR-42-284National Science Foundation AF 47