Chaos-Based Digital Communication Systems

Communication systems, in their most primitive form, are systems that enable or improve the transmission and dissemination of useful information among people in different locations. Technically speaking, the purpose of a communication system is to transmit messages from an information source to one or more destinations. In general, we can identify four basic components in a communication system, as represented by the functional block diagram shown in Fig. 1.1, namely, information source, transmitter, channel, and receiver [Proakis and Salehi (1994); Wozencraft and Jacobs (1965)].

In this chapter we introduce chaos-based digital communications. Our discussion begins with the conventional digital communication systems. We first review the basic operation of digital modulation, which is to represent digital symbols by periodic basis signals.¹ In our main discussion, this same basic operation is extended to chaos-based digital communication systems, in which chaotic basis signals are used in lieu of periodic basis signals in the modulation process. In this chapter we present a summary of the recent development in this field and review a few most widely studied chaos-based digital modulation schemes.

In this chapter we begin our formal study of chaos-based digital communication systems. The areas of investigation to be described here include the operation, analysis and performance evaluation of communication systems that employ chaotic signals for carrying digital information. As surveyed in the previous chapter, the most widely studied chaos-based digital communication systems are the so-called chaos-shift-keying (CSK) system [Dedieu et al. (1993)] and the differential chaos-shift-keying (DCSK) system [Kolumbán et al. (1996)]. In this chapter we focus our attention on the CSK system, in which digital symbols are encoded with different chaotic signals. In the binary case, the CSK transmitter essentially transmits two chaotic signals which are derived from two chaos generating sources, one at a time, according to the binary signal being sent. Clearly, the receiver is able to demodulate the transmitted signal if it can distinguish between the chaotic signal segments generated from the two chaos generators. Alternatively, the transmitted signal may be generated from one chaos generator in which a parameter is modulated according to the binary signal being sent. In this case, the receiver’s job is to work out the parametric change by observing the transmitted signal.

Coherent systems such as the chaos-shift-keying (CSK) system studied in the previous chapter are theoretically better than their non-coherent counterparts in terms of performance in additive white Gaussian noise (AWGN) channels. However, as practical techniques for robust chaos synchronization are not yet available for the required signal-to-noise conditions, the requirement of the receivers to reproduce replicas of chaotic carriers remains a major technical barrier to the practical implementation of coherent systems. Without the need for chaos synchronization, non-coherent systems therefore represent more practical forms of systems, despite their less favorable performance. In this chapter we focus on non-coherent chaos-based communication systems. In general, non-coherent detection can take a variety of forms, but its basic principle is to make use of some distinguishable properties of the transmitted signals, which can be some generic deterministic properties (e.g., return-map based detection [Tse et al. (2001)] and maximum-likelihood method [Kisel et al. (2001)]), or fabricated by a suitable bit arrangement (e.g., differential CSK (DCSK) [Kolumbán et al. (1996)]). In particular, we investigate in depth in this chapter, using the discrete-time baseband model described in Sect. 2.6, the DCSK system under single-user and multi-user environments. Broadly we may classify the implementation of multiple access into two types, namely, time-delay-based [Kolumbán et al. (1997c); Kennedy et al. (1998)] and permutation-based [Lau et al. (2002a)] implementations. In this chapter we present the analysis and performance evaluation of these two types of multiple access as applied to DCSK systems.

In the previous chapters, we have described in detail the major digital modulation schemes that exploit chaotic signals as information carriers, and discussed the analytical approaches for evaluating performance. In this and the next chapters, we focus our attention on an important performance aspect for spread-spectrum communication systems, namely, anti-jamming capability [Peterson et al. (1995)]. Intuitively, any coherent system, where the receiver knows or is able to reproduce the chaotic carriers, is expected to be considerably better in anti-jamming than its non-coherent counterpart. In chaos-based communications, coherent systems suffer serious drawbacks due to the fragility of chaos synchronization which is the main technique for reproducing the chaotic carriers [Chen and Yao (2000)]. Non-coherent systems are practically more favourable although their noise performance is inherently worse than coherent systems. It is therefore of interest to study thoroughly the anti-jamming properties of chaos-based communication systems in order to gain a better understanding of how well or poorly, in exact quantitative terms, a practical non-coherent chaotic communication system performs in comparison with the theoretically better coherent systems.

In this chapter we continue our study of the anti-jamming capability of chaos-based digital communication systems. In particular, we attempt to analyze the performance of chaos-based digital communication systems under the influence of a pulsed-noise jammer, which turns on and off periodically producing a wideband jamming source [Peterson et al. (1995)]. The philosophy of the pulsed-noise jammer is to concentrate the jamming power during the “on” time to severely disrupt the spread-spectrum communication system. The duty factor, p, is the fraction of time during which the jammer turns on. Two types of pulsed-noise jammers are considered, namely, slowly switching and fast switching jammers. For the slowly switching jammer, the frequency at which the jamming signal switches between “on” and “off” is much lower than the bit frequency of the information signal. For the fast switching jammer, the switching frequency is assumed to be very close to the bit frequency. Within each bit period, therefore, the jammer is assumed to be turned on for a fraction p of the symbol period and is off for the remaining symbol period. The objective of our study is to determine the factors and the extent to which these factors would affect the performance of chaos-based systems. Analytical bit error rates (BERs) are derived, allowing the evaluation of performance for a range of noise level, jamming power, spreading factor and duty factor. For the case of slowly switching jammers, the value of p that maximizes the BER is also found analytically.

In this chapter we continue our investigation of the coexistence of chaos-based communication systems and conventional systems. As mentioned in the previous chapter, our motivation in performing this analysis is the possible co-operation of chaos-based and conventional systems under mutual interference. Specifically, being spread-spectrum, chaos-based communication systems are expected to perform reasonably well even in the presence of other wideband signals sharing the same bandwidth. Such a scenario may occur in normal practice, for example, when chaos-based systems are introduced while the conventional systems are still in operation. This aspect of performance is important, though it has rarely been addressed in the literature. It is therefore of interest to probe into the error performance of chaos-based systems in channels where other wideband communication systems coexist. Furthermore, it is useful to compare the relative performances of coherent and non-coherent chaos-based systems and the extent to which coherent systems excel in the presence of other coexisting wideband systems. Our objective in this chapter is to investigate the performance of selected chaos-based digital systems when their bandwidths are co-occupied by a conventional spread-spectrum signal. The chaos-based systems under study are the coherent CSK and the non-coherent DCSK systems, and the coexisting system is a standard direct-sequence spread-spectrum (DS-SS) system [Proakis and Salehi (1994); Ziemer and Tranter (1995)]. Analytical expressions for the bit error rates are derived in terms of system parameters such as spreading factor, chaotic signal power, conventional spread-spectrum signal power and noise power spectral density. Finally, computer simulations are performed to verify the analytical findings.