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.

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