Chaotic frequency hopping sequences

This letter describes a novel family of frequency hopping sequences generated by chaotic systems. The sequences give a uniform spread over the entire frequency bandwidth. In addition to having good Hamming correlation properties, they possess ideal linear span. The sequences produce almost as good performance as random hopping patterns when used in frequency hopping code-division multiple-access (FH/CDMA) systems. Many numerical examples based on a digital chaos generator are presented.

[1]  P. Grassberger.  On Symbolic Dynamics of One-Humped Maps of the Interval , 1988 .

[2]  T. Kohda,et al.  Statistics of chaotic binary sequences , 1997, IEEE Trans. Inf. Theory.

[3]  Clare D. McGillem,et al.  A chaotic direct-sequence spread-spectrum communication system , 1994, IEEE Trans. Commun..

[4]  Mark A. Wickert,et al.  Probability of Error Analysis for FHSS/CDMA Communications in the Presence of Fading , 1992, IEEE J. Sel. Areas Commun..

[5]  James L. Massey,et al.  Shift-register synthesis and BCH decoding , 1969, IEEE Trans. Inf. Theory.

[6]  S. Grossmann,et al.  Invariant Distributions and Stationary Correlation Functions of One-Dimensional Discrete Processes , 1977 .

[7]  Bart Kosko,et al.  Adaptive fuzzy frequency hopper , 1995, IEEE Trans. Commun..

[8]  Laurence B. Milstein,et al.  Spread Spectrum Communications , 1983, Encyclopedia of Wireless and Mobile Communications.

[9]  Simon Haykin,et al.  A new pseudo-noise generator for spread spectrum communications , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[10]  V. Alekseev,et al.  Symbolic dynamics and hyperbolic dynamic systems , 1981 .

[11]  P. Vijay Kumar,et al.  Frequency-hopping code sequence designs having large linear span , 1988, IEEE Trans. Inf. Theory.

[12]  R. A. Rueppel.  Analysis and Design of Stream Ciphers , 2012 .

[13]  J. Cernák.  Digital generators of chaos , 1996 .

[14]  M. B. Pursley,et al.  Error Probabilities for Slow-Frequency-Hopped Spread-Spectrum Multiple-Access Communications Over Fading Channels , 1982, IEEE Trans. Commun..

[15]  Schack,et al.  Chaos for Liouville probability densities. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[16]  E. Ott.  Chaos in Dynamical Systems: Contents , 1993 .