Continuous Chaotic Signals Research Articles

Detection of a chaotic signal with noise by quantization over several amplitude levels in the model of a radio engineering chaos generator

A method for detecting a continuous chaotic signal with a Gaussian noise by quantizing over four amplitudes and comparing the parameters of the obtained discrete sequence with the parameters of a similar sequence for a non-noisy chaotic signal is proposed. A quantization scheme is developed. It is determined by the structure of the phase space of a dynamic system that generates a chaotic signal. The source of the chaotic signal is a model of a radio engineering generator. The identified chaotic signal has a positive senior Lyapunov exponent and a continuous power spectrum. Keywords: chaotic signals, detection of chaotic signals, non-coherent reception of chaotic signals, quantization of chaotic oscillations.

Обнаружение хаотического сигнала на фоне шума путем квантования по нескольким уровням амплитуды в модели радиотехнического генератора хаоса

A method for detection a continuous chaotic signal with a Gaussian noise by quantizing over four amplitudes and comparing the parameters of the obtained discrete sequence with the parameters of a similar sequence for a non-noisy chaotic signal is proposed. A quantization scheme is developed. It is determined by the structure of the phase space of a dynamic system that generates a chaotic signal. The source of the chaotic signal is a model of a radio engineering generator. The identified chaotic signal has a positive senior Lyapunov exponent and a continuous power spectrum.

Digital underwater communication with chaos

Recent work has shown that chaotic signals used for communication are capable of maximizing the signal to noise ratio with a simple matched filter algorithm. The present work extends that result by showing that a specially designed continuous chaotic signal and matched filter can be used to communicate digitally in wireless channels with severe physical constrains such as the underwater acoustic channel. To demonstrate this state-of-the-art applicability of chaos, we consider a broadly used Wi-Fi communication system protocol, adapted to create the differential chaos shift keying (DCSK) method, and benchmarking its performance with several current DCSK variants. Our performance analysis shows that the proposed method has reasonably better anti-interference ability, lower Bit Error Rate (BER) and similar or better bit transmission rate as compared with other existing DCSK variants.

A novel noise reduction method based on geometrical properties of continuous chaotic signals

In this paper, based on Local Projection (LP) algorithm, a new method for noise reduction in continuous chaotic signals is proposed. We use flexible curves for local approximation of the trajectory. To do so, a new adaptive algorithm is proposed to select the appropriate curve based on stretching and folding property of chaotic trajectories. Since there is a lack of appropriate index to determine the efficiency of noise reduction methods for signals, noise-free version of which we do not have, we propose a new indicator to measure the enhancement. The signals generated by Lorenz system and observed monthly series of sunspots are applied for simulation analysis and results exhibit acceptable performance of these methods.

Partially blind extraction of continuous chaotic signals from a linear mixture

In this paper, we address the problem of blind extraction and separation of a continuous chaotic signal from a linear mixture consisting of some chaotic signal and/or random signals. The problem of blind extraction is firstly formulated as a problem of the synchronization-based parameter estimation. Then an efficient least square based parameter estimation method is introduced to determine the desired extracting vector. The proposed blind signal extraction scheme is applicable to blind separation of chaotic signals by formulating the separation problem as the extraction of each chaotic source. Numerical simulation shows that the proposed approach can blindly extract and separate the desired chaotic signals and it is also robust to measurement noise.

Partially blind source separation of continuous chaotic signals from linear mixture

The authors consider the problem of partially blind source separation of continuous chaotic signals from a linear mixture, in which the generating systems of chaotic signals are assumed to be available and the mixture matrix is unknown. Determination of the mixture matrix is firstly formulated as a problem of the synchronisation-based parameter estimation. Then an efficient parameter estimation method by exploiting the generating dynamics of chaotic signals is introduced. The estimated mixture matrix is used to design a signal separator to blindly separate the mixed chaotic signals. Three examples are given to illustrate the applicability of the proposed approach for the mixed chaotic signals generated by different and/or same dynamical systems and contaminated in measurement noise. In comparison with statistics-based methods, the new approach can solve the magnitude scaling indeterminacy and shows the separability of the mixed signals in strong noise background.

A General Response System Control Method Based on BacksteppingDesign for Synchronization of Continuous Scalar Chaotic Signal

A general response system control method for synchronization ofcontinuous scalar chaotic signal is presented. The proposed canonicalgeneral response system can cover most of the well-known chaoticsystems. Conversely, each of these chaotic systems can also be used toconstruct the general response system. Furthermore, a novel controllerof the proposed response system is designed based on backsteppingtechnique, with which the output of the general response system and thegiven continuous chaotic signal can synchronize perfectly. Twonumerical examples are given to illustrate the effectiveness of theproposed control method.

A DCT domain quadratic predictor for real-time prediction of continuous chaotic signals

A DCT domain quadratic predictor with normalized least mean square (NLMS) algorithm, efficient implementing structure of the reduced parameter second-order Vloterra filter (RPSOVF), is proposed to investigate nonlinear real-time multi-step prediction performance of three kinds of continuous chaotic signals. Experimental results show that the real-time ahead one-step prediction mean square errors of the DCT domain quadratic predictor proposed in this paper are at least 100 times smaller than that of RPSOVF, which indicates that this predictor has better predictive performance, its structure is simple and easy to implement. Multi-step prediction performance of this DCT domain quadratic predictor to three continuous chaotic time series is superior to the one of local prediction method obviously, and its mean square errors do not increase exponentially according as the prediction step.