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

Abstract

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. In Part II, chaotic synchronization schemes are described in detail and proposed chaotic communications techniques are summarized. In Part III, examples of chaotic communications schemes with and without synchronization are given, and the performance of these schemes is evaluated in the context of noisy, bandlimited channels.

Applying Estimation Techniques to Chaos-Based Digital Communications

“…from any unauthorized receiver, it is difficult to even detect their presence in many cases; (iii) they are resistant to jamming; and (iv) they provide a measure of immunity to distortion due to multipath propagation. The unified low pass representation used here is based on (Kolumban et al, 1997;Kolumban, Kennedy & Chua, 1998) in the discrete time context which is more suitable to treating signals generated by chaotic maps. In the following, only the transmission of isolated symbols is considered, i.e.…”

“…We focus on Chaos Shift Keying (CSK) and its variants based on noncoherent or differential demodulation because of their promise in proposed practical applications (Kennedy, Kolumbán, Kis & Jákó, 2000;Kennedy, Setti & Rovatti, 2000;Kolumban et al, 1997;Kolumban, Kennedy & Chua, 1998;Lau & Tse, 2003;Stavroulakis, 2005). In fact, researchers from the Optical Communications Laboratory of the Athens University in Greece, implemented an 120km optical fiber link in metropolitan Athens and managed to transmit at gigabit rates using CSK (Argyris et al, 2005;Syvridis, 2009).…”

“…Chaos has also been shown in connection to devices used in signal processing such as nonlinear adaptive filters and phase-locked loop networks (Endo & Chua, 1988;Harb & Harb, 2004;Monteiro et al, 2009;Tavazoei & Haeri, 2009). In particular, many recent works have described digital modulations using chaotic carriers (Kennedy & Kolumban, 2000;Kennedy, Setti & Rovatti, 2000;Kolumban et al, 1997;Kolumban, Kennedy & Chua, 1998;Lau & Tse, 2003) even though their performance proved below that of equivalent conventional systems under additive white gaussian noise channel (Kaddoum et al, 2009;Williams, 2001). This chapter's first aim is to compare these chaos-based modulations to their conventional counterparts via their discrete-time low-pass equivalent models.…”

Digital Chaotic Synchronized Communication System

“…There are two main issues in studying the control of chaotic electronic circuits suitable for secure communications [9]. The first one is the way a non-linear circuit begins to operate in chaotic mode (route to chaos) [2, 10, 11] and the second one is the achievement of synchronization between transmitter-receiver [12,13].Since the discovery by Pecora and Carroll that chaotic systems can be synchronized [12], the topic of synchronization of coupled chaotic circuits and systems has been studied intensely [14] and some interesting applications such as broadband communication systems or cryptographic systems have come out of this research [15][16][17][18].In this paper the system synchronization properties of a chaotic communication system, suitable for secure communication, are examined. …”

“…Since the discovery by Pecora and Carroll that chaotic systems can be synchronized [12], the topic of synchronization of coupled chaotic circuits and systems has been studied intensely [14] and some interesting applications such as broadband communication systems or cryptographic systems have come out of this research [15][16][17][18].…”