Statistical Analysis and Optimization of Chaos Based Broadband Communications

This thesis treats the topic of chaos based broadband communication schemes, with particular emphasis on the statistical analysis and optimization of such schemes. The work is motivated by the recent advances in nonlinear system theory suggesting advantages of using chaos in digital communication applications. In particular, the inherent broadband nature of chaotic signals and their synchronization and decorrelation properties have inspired a number of chaos based communications applications. On the transmitter side, chaos based broadband communication typically involves one or more chaotic generators which are modulated in one of their system parameters or their initial state according to the information to be transmitted. Due to a number of fundamental properties of chaos, it is not difficult to conceive transmitters which benefit from the ease of generating signals with desirable statistical characteristics. However, by the same token it is in general challenging to design robust receivers that result in a scheme exhibiting good performance. A central purpose of this thesis is to optimize the choice of the transmitter part and the receiver part (before chosen in a relatively ad-hoc manner) with respect to overall efficiency criteria of the complete communication system. Considered criteria are: overall bit error rate, computational cost; with given statistical channel properties. The chaotic systems considered mainly belong to the class of discrete time systems defined by the iteration of piecewise linear maps. It is shown that, in particular on the receiver side, optimality implies exponential computational cost. Since, due to this fact, sub-optimal receivers (with linear cost) are of great interest, a significant result of this work has been the systematic establishment of efficient receivers in conjunction with an understanding about the implications of their sub-optimality. Furthermore, supported by an information theoretic argument, a number of rather general implications of the use of chaotic signals in communication applications are derived. In more detail, this thesis deals with the following aspects: Chaos in communication systems (Chapter 1) An overview of properties and applications of chaotic systems is given, with particular emphasis on engineering applications to communication systems. The historical motivation of the use of chaos in this context is introduced and recent advances in this field are surveyed. Fundamentals of narrowband and broadband communications (Chapters 2 and 3) Frameworks for the communication of digital information in general and for the communication over an imperfect channel in particular are given in these two chapters. Standard approaches from classical digital communications theory are introduced and the use of chaos is put into the appropriate context. Frequently used assumptions and their implications are established and a systematic framework for the use of chaos at the modulation level, leading to easily obtained broadband features, is introduced. Noise filtering (Chapter 4) The optimal reconstruction of chaotic signals from noisy observations is the subject matter of this chapter. Optimal and sub-optimal approaches are introduced both at the conceptual and at the applied level. Furthermore, the use of such techniques in the context of communication applications is investigated. Optimal and sub-optimal receivers (Chapters 5 and 6) The design of receivers for chaos based communication schemes is one of the central themes of this thesis. In these two chapters, several design choices are evaluated, leading to optimal and sub-optimal receivers in a systematic way on one hand, and implying a number of properties with respect to traditional receiver structures for digital communication schemes on the other hand. The optimization considers several transmitters using