White Gaussian Chaos

A discrete-time white Gaussian noise (WGN) is a random process with impulsive autocorrelation function. Also, the random variables obtained by sampling the process at any time instants are jointly Gaussian. WGN is widely used to model noise in engineering and physics. In this letter, we propose a way to generate chaotic signals that behave like WGN, due to the features of its autocorrelation function and its invariant density. From the tent map and by using as conjugacy map transformations commonly employed to random variables, we obtain a white Gaussian chaos (WGC) map. Numerical simulations are shown to illustrate the technique. WGC can be an interesting choice for chaos generator in chaos-based communication systems.

[1]  Georges Kaddoum,et al.  Wireless Chaos-Based Communication Systems: A Comprehensive Survey , 2016, IEEE Access.

[2]  Yan Zhang,et al.  One-to-Many Chaotic Synchronization with Application in Wireless Sensor Network , 2013, IEEE Communications Letters.

[3]  Celso Grebogi,et al.  Wireless communication with chaos. , 2013, Physical review letters.

[4]  Harald Haas,et al.  Harnessing Nonlinearity: Predicting Chaotic Systems and Saving Energy in Wireless Communication , 2004, Science.

[5]  Pascal Chargé,et al.  A generalized methodology for bit-error-rate prediction in correlation-based communication schemes using chaos , 2009, IEEE Communications Letters.

[6]  M S Baptista,et al.  Robustness of Chaos to Multipath Propagation Media , 2017 .

[7]  L. H. A. Monteiro,et al.  Chaotic Synchronization in Discrete-Time Systems Connected by Bandlimited Channels , 2011, IEEE Communications Letters.

[8]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[9]  Henry C. Tuckwell,et al.  Analysis of inverse stochastic resonance and the long-term firing of Hodgkin–Huxley neurons with Gaussian white noise , 2012, 1202.2491.

[10]  João Marcos Travassos Romano,et al.  Chaos-based communication systems in non-ideal channels , 2012 .

[11]  M. Mackey,et al.  Probabilistic properties of deterministic systems , 1985, Acta Applicandae Mathematicae.

[12]  Marcio Eisencraft,et al.  Correlation and spectral properties of chaotic signals generated by a piecewise-linear map with multiple segments , 2017, Signal Process..

[13]  Nikolai F. Rulkov,et al.  Chaotic pulse position modulation: a robust method of communicating with chaos , 2000, IEEE Communications Letters.

[14]  Celso Grebogi,et al.  Experimental validation of wireless communication with chaos. , 2016, Chaos.

[15]  Marconi Kolm Madrid,et al.  A method for Lyapunov spectrum estimation using cloned dynamics and its application to the discontinuously-excited FitzHugh–Nagumo model , 2012 .

[16]  Norbert Marwan,et al.  How to Avoid Potential Pitfalls in Recurrence Plot Based Data Analysis , 2010, Int. J. Bifurc. Chaos.

[17]  Guanrong Chen,et al.  Design and Performance Analysis of a New Multiresolution $M$-Ary Differential Chaos Shift Keying Communication System , 2015, IEEE Transactions on Wireless Communications.

[18]  Manas Ghosh,et al.  Exploring static and frequency—dependent third nonlinear polarizability of doped quantum dots driven by Gaussian white noise , 2015 .

[19]  Yi Fang,et al.  Design of an Adaptive Multiresolution $M$ -Ary DCSK System , 2017, IEEE Communications Letters.

[20]  Georges Kaddoum,et al.  Design of a Short Reference Noncoherent Chaos-Based Communication Systems , 2016, IEEE Transactions on Communications.

[21]  M. E. Muller,et al.  A Note on the Generation of Random Normal Deviates , 1958 .

[22]  P. Peebles.  Probability, Random Variables and Random Signal Principles , 1993 .

[23]  Ricardo Suyama,et al.  Chaotic Signals in Digital Communications , 2013 .

[24]  C. Williams.  Chaotic communications over radio channels , 2001 .

[25]  Alberto Tarable,et al.  Interleaver Design for Parallel Concatenated Chaos-Based Coded Modulations , 2013, IEEE Communications Letters.

[26]  Masoud Salehi,et al.  Contemporary Communication Systems Using MATLAB , 1999 .

[27]  L. H. A. Monteiro,et al.  Spectral properties of chaotic signals generated by the skew tent map , 2010, Signal Process..

[28]  Marcio Eisencraft,et al.  Spectral properties of chaotic signals with applications in communications , 2009 .

[29]  J. García-Ojalvo,et al.  Effects of noise in excitable systems , 2004 .