Géza Kolumbán

The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization

For pt. I see ibid., vol. 44, p. 927-36 (1997). In a digital communications system, data are transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a conventional system the analog sample functions sent through the channel are weighted sums of one or more sinusoids; in a chaotic communications system the sample functions are segments of chaotic waveforms. At the receiver, the symbol may be recovered by means of coherent detection, where all possible sample functions are known, or by noncoherent detection, where one or more characteristics of the sample functions are estimated. In a coherent receiver, synchronization is the most commonly used technique for recovering the sample functions from the received waveform. These sample functions are then used as reference signals for a correlator. Synchronization-based coherent receivers have advantages over noncoherent receivers in terms of noise performance, bandwidth efficiency (in narrow-band systems) and/or data rate (in chaotic systems). These advantages are lost if synchronization cannot be maintained, for example, under poor propagation conditions. In these circumstances, communication without synchronization may be preferable. The theory of conventional telecommunications is extended to chaotic communications, chaotic modulation techniques and receiver configurations are surveyed, and chaotic synchronization schemes are described.

The role of synchronization in digital communications using chaos. I . Fundamentals of digital communications

In a digital communications system, data is transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a conventional system the analog sample functions sent through the channel are weighted sums of one or more sinusoids; in a chaotic communications system, the sample functions are segments of chaotic waveforms. At the receiver, the symbol may be recovered by means of coherent detection, where all possible sample functions are known, or by noncoherent detection, where one or more characteristics of the sample functions are estimated. In a coherent receiver, synchronization is the most commonly used technique for recovering the sample functions from the received waveform. These sample functions are then used as reference signals for a correlator. Synchronization-based receivers have advantages over noncoherent ones in terms of noise performance and bandwidth efficiency. These advantages are lost if synchronization cannot be maintained, for example, under poor propagation conditions. In these circumstances, communication without synchronization may be preferable. The main aim of this paper is to provide a unified approach for the analysis and comparison of conventional and chaotic communications systems. In Part I, the operation of sinusoidal communications techniques is surveyed in order to clarify the role of synchronization and to classify possible demodulation methods for chaotic communications.A composite material which has a substantially reduced incidence of defects after drawing, and a method of producing it. The composite material is comprised of at least one layer of plain carbon steel containing up to 1.5% of carbide former present in a carbide former-to-carbon ratio of from about 1.5 to about 25 and at least one layer of stainless steel. It is formed by pressure bonding carbon steel containing carbide former to stainless steel.

Chaotic communications with correlator receivers: theory and performance limits

This paper provides a review of the principles of chaotic digital communications using correlator receivers. Modulation schemes using one and two chaotic basis functions, as well as coherent and noncoherent correlation receivers, are discussed. The performance of differential chaos shift keying (DCSK) in multipath channels is characterized. Results are presented for DCSK with multiuser capability and multiple bits per symbol.

Digital communications using chaos

Abstract During the past five years, there has been tremendous interest worldwide in the possibility of exploiting chaos in wideband communications systems. This survey paper discusses the implications of using chaotic basis functions in digital communications. Preliminary performance results are given, potential benefits are discussed, and possible application domains are identified.

Communications using chaos/spl Gt/MINUS. III. Performance bounds for correlation receivers

For pt. II, see ibid., vol. 45, p. 1129-40 (1998). In a digital communications system, data is transmitted from one location to another by mapping bit sequences to symbols, and symbols to sample functions of analog waveforms. The analog waveform passes through a bandlimited (possibly time-varying) analog channel, where the signal is distorted and noise is added. In a typical conventional system, the analog sample functions sent through the channel are weighted sums of one or more sinusoids, called basis functions; in a chaotic communications system, the sample functions are segments of chaotic waveforms. This three-part paper shows in a tutorial manner how the theory of conventional telecommunications systems can be applied to chaotic modulation schemes. In addition, it discusses the latest results in the field of chaotic communications. In Part III, examples are given of chaotic communications schemes with and without synchronization, and the performance of correlator-based systems is evaluated in the context of noisy, bandlimited channels.

Theoretical noise performance of correlator-based chaotic communications schemes

In wireless local area networks and indoor communications, multipath propagation limits the performance of data communications systems. To overcome the multipath propagation problem, a spread spectrum system has to be used. The chaotic communications technique, where inherently wideband chaotic basis functions are used, offers a cheap alternative to conventional spread spectrum communications. Unfortunately, analytic expressions for the noise performance of chaotic modulation schemes are not available in the literature. This has so far prevented a full exploitation of the features of chaotic modulation schemes. By generalizing the waveform communications concept, this paper develops exact expressions for the noise performance of the coherent antipodal chaos shift keying (CSK), coherent differential chaos shift keying (DCSK), and differentially coherent DCSK modulation schemes. We show that the properties of the basis functions have no effect on the noise performance of a modulation scheme, provided that the energy per bit is constant. In this sense, the concept of waveform communications is generalized. Finally, our theoretical results are verified by computer simulations.

Performance evaluation of FM-DCSK modulation in multipath environments

G. Kolumban [2000] has shown that, under specified conditions, the noise performance of frequency-modulated differential chaos shift keying (FM-DCSK) in a single-ray additive white Gaussian noise channel is independent of the shape of the underlying waveform. This paper discusses the qualitative features of the FM-DCSK system and characterizes the performance of this system in standard reference multipath channels.

A NOVEL DIFFERENTIAL CHAOS SHIFT KEYING MODULATION SCHEME

In binary Differential Chaos Shift Keying (DCSK), the reference and information bearing chaotic wavelets are transmitted in two consecutive time slots. This TDMA approach provides two independent c...

FM-DCSK: a novel method for chaotic communications

In binary Differential Chaos Shift Keying (DCSK), each information bit is mapped to the correlation between two pieces of a chaotic waveform. The receiver determines the correlation (which is proportional to the energy per bit) in order to demodulate the received signal. Since a chaotic signal is not periodic, the energy per bit is not constant and can only be estimated, even in the noise-free case. This estimation has a non-zero variance that limits the attainable data rate. This problem can be avoided if the energy per bit is kept constant. In this paper, the DCSK technique is combined with frequency modulation in order to achieve two properties: the excellent noise performance of DCSK is maintained; in addition, the energy per bit is kept constant in order not to limit the data rate. A low-pass equivalent model that significantly speeds up the simulation of an FM-DCSK system is also developed. Finally the noise performance of the proposed FM-DCSK system is given.

Recent advances in communicating with chaos

The past few years have witnessed rapid growth in the field of mobile and indoor radio applications. Chaotic communications schemes are potentially suitable for these applications, offering simpler and cheaper solutions that currently available Spread Spectrum (SS) techniques. This paper presents an overview of the most promising chaotic communications schemes which have been developed recently and proposes some multilevel extensions of these methods to increase the data rate.