Design and realization of an FPGA-based generator for chaotic frequency hopping sequences

Chaos-based pseudonoise (PN) sequences for spread spectrum (SS) communications ranks amongst the most promising applications of chaos to communications. This paper deals with the design and realization of a chaotic frequency hopping (FH) sequence generator that is compatible with current FH/SS technologies. A simplistic generator architecture adopting nonlinear auto-regressive (AR) filter structures is proposed, which is based on the random sequence model and the metric entropy criterion for generation of random sequences. Conventional PN sequences are employed to perturb the generator such that the resulted sequences fulfil the FH requirements on period and family size. In addition, a chaos-based FH sequence generator prototype is realized in field programmable gate arrays (FPGAs) and various tests are performed. The generator produces long period FH sequences with uniform distribution over the available bandwidth, large linear complexity as well as suboptimal Hamming correlation properties. Bit error rate (BER) performance of the chaos-based asynchronous FH/CDMA system is evaluated by means of computer simulation. These results suggest that the cost-effective and well-performing generator has the potential to be incorporated into existing FH systems.

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

[2]  Sang Tao,et al.  Perturbance-based algorithm to expand cycle length of chaotic key stream , 1998 .

[3]  M. J. Werter An improved chaotic digital encoder , 1998 .

[4]  Gianluca Mazzini,et al.  Interference minimisation by auto-correlation shaping in asynchronous DS-CDMA systems: chaos-based spreading is nearly optimal , 1999 .

[5]  K. Kelber,et al.  N-dimensional uniform probability distribution in nonlinear autoregressive filter structures , 2000 .

[6]  Riccardo Rovatti,et al.  Chaotic complex spreading sequences for asynchronous DS-CDMA. I. System modeling and results , 1997 .

[7]  Grebogi,et al.  Roundoff-induced periodicity and the correlation dimension of chaotic attractors. , 1988, Physical review. A, General physics.

[8]  Leon O. Chua,et al.  A new class of pseudo-random number generator based on chaos in digital filters , 1993, Int. J. Circuit Theory Appl..

[9]  Géza Kolumbán,et al.  Quality evaluation of random numbers generated by chaotic sampling phase-locked loops , 1998 .

[10]  Gianluca Mazzini,et al.  Interference in DS-CDMA systems with exponentially vanishing autocorrelations: chaos-based spreading is optimal , 1998 .

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

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

[13]  Michael A. Lieberman,et al.  Secure random number generation using chaotic circuits , 1989, IEEE Military Communications Conference, 'Bridging the Gap. Interoperability, Survivability, Security'.

[14]  Ling Cong,et al.  Chaotic frequency hopping sequences , 1998 .

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

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

[17]  Li Shaoqian,et al.  Chaotic spreading sequences with multiple access performance better than random sequences , 2000 .

[18]  Ian Oppermann,et al.  Complex spreading sequences with a wide range of correlation properties , 1997, IEEE Trans. Commun..

[19]  C. Beck,et al.  Effects of phase space discretization on the long-time behavior of dynamical systems , 1987 .

[20]  Tohru Kohda,et al.  Pseudonoise Sequences by Chaotic Nonlinear Maps and Their Correlation Properties , 1993 .

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

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

[23]  John G. Proakis,et al.  Introduction to Digital Signal Processing , 1988 .

[24]  Laurence B. Milstein,et al.  Spread-Spectrum Communications , 1983 .

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

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

[27]  D. R. Frey,et al.  Chaotic digital encoding: an approach to secure communication , 1993 .

[28]  Abraham Lempel,et al.  Families of sequences with optimal Hamming-correlation properties , 1974, IEEE Trans. Inf. Theory.

[29]  M. Gotz,et al.  Discrete-time chaotic encryption systems. I. Statistical design approach , 1997 .

[30]  Mohammad Umar Siddiqi,et al.  Optimal Large Linear Complexity Frequency Hopping Patterns Derived from Polynomial Residue Class Rings , 1998, IEEE Trans. Inf. Theory.