Noise reduction methods for chaotic signals with application to secure communications

Noise reduction methods for contaminated chaotic signals and a potential application of chaotic signals and systems are investigated. First, an iterative noise reduction scheme for contaminated chaotic signals is developed. It has a simple structure, is computationally efficient and is not dependent on a specific form for system dynamics. One class of noise reduction methods uses an estimate of the deviation of the observed signal from the nearest noise-free signal to get the noise-reduced signal. To calculate this deviation, these techniques minimize a cost function composed of two parts: one containing information representing how close enhanced signals are to the observed signal and another composed of constraints that fit the dynamics of the system. A second class of these methods enhances the observed signal by directly estimating the signal that minimizes the cost function. Variations on these methods result from choosing different components for the cost function. The convergence conditions and error properties of the proposed methods are investigated, and guidelines for choosing the proper weighting constants and nonlinear functions are suggested. Augmented system approaches are considered for separating mixed chaotic signals under the assumption that all the system dynamics are known. As one aspect of noise reduction, the suppression of a chaotic interference signal is investigated.; Secondly, a preprocessing approach is proposed for initial SNR enhancement prior to further noise reduction via methods requiring relatively high SNR. This method can be used in conjunction with existing noise reduction methods and is applicable to noise corrupted data from any nonlinear dynamical system because no knowledge of the system dynamics is required. This method is based on a modification of the local tangent projection method.; As a potential application of chaotic signals and systems, secure communications using chaotic signals is discussed, and new secure communications schemes are considered. The receivers for these schemes exploit the proposed noise reduction techniques for their decisions. The proposed schemes make decisions on the incoming bits by comparing the power levels of the dynamical error of each symbol signal after processing by a noise reduction method with knowledge of the system dynamics. The strong point of this scheme is that it does not require knowledge of the chaotic system initial conditions or chaotic systems that have the self-synchronization property. A scramble matrix implementation of this scheme is considered to increase its robustness to interception and jamming. This kind of scheme can combat against smart jamming.