A new scheme is proposed for spread spectrum communication which transmits both analog and binary data via chaotic carriers. The proposed systems have some standard properties of spread spectrum communication. Some computer simulations and performance analysis are given to examine the validity of this scheme.

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Spread spectrum communication via chaos

The paper explores the calculation of exact bit error rates (BERs) for some single-user chaotic-shift-keying (CSK) communications systems, in contrast to approximate Gaussian-based approximations in current use. The conventional signal-to-noise-ratio approach is shown to give only lower bounds on the BERs. An analytical Gaussian approach based on exact mean and variance of the decoder function gives inexact results. Exact BERs are given here for several CSK systems with spreading sequences from different types of chaotic map. They achieve exactness from fully exploiting the dynamical and statistical features of the systems and the results correspond theoretically to impractically large Monte Carlo simulations. A further aspect of the paper is the derivation of likelihood optimal bit decoders which can be superior to correlation decoders. The inapplicability of Gaussian assumptions is viewed through some exact distributional results for one system.

Exact calculation of bit error rates in communication systems with chaotic modulation

The recent advances in acoustic modem technology have enabled the development of Underwater Acoustic Networks (UAN). Application interests include oceanographic information gathering, environmental monitoring or coastal defense. Due to its ability of simultaneously sharing the same frequency band for various users and the poor propagation conditions usually encountered in shallow water environment, the Code Division Multiple Access (CDMA) is a promising scheme for UAN. Recent results show that a standard CDMA direct-sequence spread spectrum approach is not sufficient to ensure Low Probabilities of Detection (LPD) and/or Interception (LPI), that is an unauthorized observer may notice that a communication signal is present. For many applications, this drawback is not acceptable. In this paper, the application of chaos to transmission of information is under investigation to achieve an LPI/LPD objective in an UAN context. Performance results of two receivers are shown for a single user through a realistic simulation scenario. An experiment at sea will be conducted by GESMA soon to confirm these first results.

/pdf/a-chaotic-direct-sequence-spread-spectrum-system-for-ml69pdm83e.pdf

A chaotic Direct-Sequence Spread-Spectrum system for underwater communication

In this paper, sufficient conditions of global synchronization in finite-time, which can be a minimum, are presented for the generic class of piecewise linear maps. The conditions of synchronization are based upon general results of the robust control theory, the observability theory, and the specificity of the chaotic motion generated by the map. The robust control theory results enable global synchronization with disturbances cancellation. Observability and assignment of eigenvalues ensure finite-time synchronization. A systematic methodology for designing a global finite-time synchronization derived from those conditions is presented. From a practical point of view, this only requires classical numerical solvers. Finite-time global synchronization can be of interest for applications such as digital communications.

Finite-time global chaos synchronization for piecewise linear maps

In a multiuser chaotic communications scheme, each user's information is modulated with a chaotic system and then transmitted independently over a common communication channel The receiver sees the superposition of the distorted transmitted signals with additive noise In this paper, a novel channel equalization algorithm is proposed for multiuser chaotic communications systems where each user's information is encoded using symbolic dynamics The goal is to recover the chaotic signal being sent by each individual user so that its information can be estimated This paper begins with the symbolic dynamics representation of chaotic systems being exploited to enable the representation of the multiuser chaotic system with an equivalent trellis diagram Then, the trellis diagram is expanded to accommodate FIR channel distortions Finally, the Viterbi algorithm is used to obtain maximum-likelihood estimates of the transmitted sequences The performance of this algorithm in terms of bit-error rate (BER) is simulated for different channel distortions

Channel equalization for multiuser chaotic communications systems

A novel scheme is proposed for chaotic communications which is robust to noise and amplitude fluctuations in the channel. The scheme implements spread spectrum communication of binary data utilizing synchronized discrete-time chaotic systems. The chaotic signals of the transmitter are used as spreading codes, while the synchronized chaotic outputs of the receiver despread the signal, thereby recovering the message. The improved synchronization algorithm and the implementation of spread spectrum communications techniques result in reliable performance in the presence of considerable signal distortions in the channel. The method is implemented with a chaotic logistic map and also with a piecewise-linear map of a chaotic neuron. In both cases, average bit-error-rates were computed for varied signal-to-noise ratio, using additive white Gaussian noise. The proposed scheme also offers high privacy because of the non-periodicity of the chaotic spreading sequences.

Khalid M. Syed

Papers

Combating Noise and Other Channel Distortions in Chaotic Communications