Chaotic Waveforms Research Articles

Designing Sequence With Minimum PSL Using Chebyshev Distance and its Application for Chaotic MIMO Radar Waveform Design

Controlling peak side-lobe level (PSL) is of great importance in high-resolution applications of multiple-input multiple-output (MIMO) radars. In this paper, designing sequences with good autocorrelation properties are studied. The PSL of the autocorrelation is regarded as the main merit and is optimized through newly introduced cyclic algorithms, namely; PSL Minimization Quadratic Approach (PMQA), PSL Minimization Algorithm, the smallest Rectangular (PMAR), and PSL Optimization Cyclic Algorithm (POCA). It is revealed that minimizing PSL results in better sequences in terms of autocorrelation side-lobes when compared with traditional integrated side-lobe level (ISL) minimization. In order to improve the performance of these algorithms, fast-randomized Singular Value Decomposition (SVD) is utilized. To achieve waveform design for MIMO radars, this algorithm is applied to the waveform generated from a modified Bernoulli chaotic system. The numerical experiments confirm the superiority of the newly developed algorithms compared to high-performance algorithms in mono-static and MIMO radars.

Phase space interrogation of the empirical response modes for seismically excited structures

Conventional Phase Space Interrogation (PSI) for structural damage assessment relies on exciting the structure with low dimensional chaotic waveform, thereby, significantly limiting their applicability to large structures. The PSI technique is presently extended for structure subjected to seismic excitations. The high dimensionality of the phase space for seismic response(s) are overcome by the Empirical Mode Decomposition (EMD), decomposing the responses to a number of intrinsic low dimensional oscillatory modes, referred as Intrinsic Mode Functions (IMFs). Along with their low dimensionality, a few IMFs, retain sufficient information of the system dynamics to reflect the damage induced changes. The mutually conflicting nature of low-dimensionality and the sufficiency of dynamic information are taken care by the optimal choice of the IMF(s), which is shown to be the third/fourth IMFs. The optimal IMF(s) are employed for the reconstruction of the Phase space attractor following Taken’s embedding theorem. The widely referred Changes in Phase Space Topology (CPST) feature is then employed on these Phase portrait(s) to derive the damage sensitive feature, referred as the CPST of the IMFs (CPST-IMF). The legitimacy of the CPST-IMF is established as a damage sensitive feature by assessing its variation with a number of damage scenarios benchmarked in the IASC-ASCE building. The damage localization capability, remarkable tolerance to noise contamination and the robustness under different seismic excitations of the feature are demonstrated.

Anti-jamming property of Colpitts-based direct chaotic through-wall imaging radar

A direct chaotic through-wall imaging (TWI) radar using chaotic signal generated by improved Colpitts oscillator is proposed, and its good anti-jamming performance is investigated theoretically and experimentally. Compared with conventional TWI radar, the proposed radar has the advantages of very high range resolution, low probability of intercept, and immunity from jamming and interference. The characteristics of the chaotic signal are presented. According to the delta function-like autocorrelation of the chaotic signal, the range resolution of the radar is 6 cm. The cross-ambiguity functions with no discernible peaks are used to theoretically certify its interference immunity performance, and then the anti-jamming properties in the Colpitts jamming, linear frequency modulated chirp jamming, and noise jamming environments are demonstrated by numerical electromagnetic simulations using finite difference time domain, and the corresponding experiments. The simulation and experimental results show that the chaotic waveform possesses excellent jamming immunity to the noise and radio frequency interference. This feature makes the chaotic signal perform superbly in multi-radar environments.

Cognitive Chaotic UWB-MIMO Detect-Avoid Radar for Autonomous UAV Navigation

A cognitive detect and avoid radar system based on chaotic UWB-MIMO waveform design to enable autonomous UAV navigation is presented. A Dirichlet-process-mixture-model (DPMM)-based Bayesian clustering approach to discriminate extended targets and a change-point (CP) detection algorithm are applied for the autonomous tracking and identification of potential collision threats. A DPMM-based clustering mechanism does not rely upon any a priori target scene assumptions and facilitates online multivariate data clustering/classification for an arbitrary number of targets. Furthermore, this radar system utilizes a cognitive mechanism to select efficient chaotic waveforms to facilitate enhanced target detection and discrimination. We formulate the CP mechanism for the online tracking of target trajectories, which present a collision threat to the UAV navigation; thus, we supplement the conventional Kalman-filter-based tracking. Simulation results demonstrate a significant performance improvement for the DPMM-CP-assisted detection as compared with direct generalized likelihood-ratio-based detection. Specifically, we observe a 4-dB performance gain in target detection over conventional fixed UWB waveforms and superior collision avoidance capability offered by the joint DPMM-CP mechanism.

Fully photonics-based physical random bit generator.

We propose a fully photonics-based approach for ultrafast physical random bit generation. This approach exploits a compact nonlinear loop mirror (called a terahertz optical asymmetric demultiplexer, TOAD) to sample the chaotic optical waveform in an all-optical domain and then generate random bit streams through further comparison with a threshold level. This method can efficiently overcome the electronic jitter bottleneck confronted by existing RBGs in practice. A proof-of-concept experiment demonstrates that this method can continuously extract 5Gb/s random bit streams from the chaotic output of a distributed feedback laser diode (DFB-LD) with optical feedback. This limited generation rate is caused by the bandwidth of the used optical chaos.

Complexity and bandwidth enhancement in unidirectionally coupled semiconductor lasers with time-delayed optical feedback.

We numerically investigate the frequency bandwidth and the autocorrelation characteristics of chaotic temporal wave forms in unidirectionally coupled semiconductor lasers with time-delayed optical feedback. We evaluate the complexity of the chaotic temporal wave forms by using Lyapunov exponents. We found that larger maximum Lyapunov exponents can be obtained for smaller peak values of the autocorrelation function at the delay time of the optical feedback. On the contrary, the maximum Lyapunov exponent is independent from the frequency bandwidth of the chaotic temporal wave forms.

Optical ultrafast random number generation at 1 Tb/s using a turbulent semiconductor ring cavity laser.

A simple method of high-speed random bit generation is presented that utilizes the turbulent output of a fiber ring cavity semiconductor laser. Random bits are generated by multi-bit sampling of the chaotic optical waveform passed through a simple post-processing procedure, leading to generation rates up to and potentially exceeding 1Tb/s. The resulting random bit streams are tested statistically using a software package designed to test random number generators, the NIST statistical test suite. The bit streams pass each of these test sets, indicating their suitability for use in random number generation applications. This novel technique allows the generation of random bits from less complex experimental conditions than previously reported, while improving upon recent previous studies in terms of bit rate and quality of bits.

A Matched Filter Developed for Chaotic Waveforms

A matched filter developed for use in chaos-based communications systems is presented. A matched filter is the optimum filter for maximizing the signal-to-noise ratio of a received signal in the presence of additive Gaussian white noise (AGWN). Chaos-based communications systems encode information into a chaotic waveform using arbitrary small perturbations to control the trajectory of the chaotic oscillator. Chaotic waveforms are deterministic, are sensitive to initial conditions, have aperiodic long-term behavior, have a spread frequency spectrum, and are theoretically immune to interference. There has been great interest in using chaotic waveforms in communication applications. One reason for this interest is that the spread spectrum of a chaotic waveform gives the appearance of noise when observed over a prolonged period of time. This masks the waveform from anyone without prior knowledge of its presence. Another reason is that to retrieve the information encoded in the chaotic waveform, complete knowledge of the waveform must be known. This makes it difficult for anyone other than the intended recipient to decrypt the information. Normally, implementing a matched filter for a chaotic waveform is difficult because such waveforms do not have a fixed basis function and have irregular timing. However, a unique chaotic oscillator has been developed that can be represented as an exact analytic solution. The waveform's solution can be written as a convolution of a symbol sequence and a fixed basis function. This fixed basis function makes it possible to derive a delay differential equation describing the matched filter. In order to test the matched filter, an amplitude modulated communications system was developed. In the system, the oscillator's output is first amplitude modulated with 2.3GHz carrier before being transmitted. The receiver then demodulates the signal and applies it to the matched filter. Any encoded information can then be extracted from the output of the matched filter. The oscillator and matched filter were designed to operate at 1.8MHz. In both simulation and testing, the matched filter was able to detect the chaotic waveform in the presence of AWGN.

Wireless Chaos-Based Communication Systems: A Comprehensive Survey

Since the early 1990s, a large number of chaos-based communication systems have been proposed exploiting the properties of chaotic waveforms. The motivation lies in the significant advantages provided by this class of non-linear signals. For this aim, many communication schemes and applications have been specially designed for chaos-based communication systems where energy, data rate, and synchronization awareness are considered in most designs. Recently, the major focus, however, has been given to the non-coherent chaos-based systems to benefit from the advantages of chaotic signals and non-coherent detection and to avoid the use of chaotic synchronization, which suffers from weak performance in the presence of additive noise. This paper presents a comprehensive survey of the entire wireless radio frequency chaos-based communication systems. First, it outlines the challenges of chaos implementations and synchronization methods, followed by comprehensive literature review and analysis of chaos-based coherent techniques and their applications. In the second part of the survey, we offer a taxonomy of the current literature by focusing on non-coherent detection methods. For each modulation class, this paper categorizes different transmission techniques by elaborating on its modulation, receiver type, data rate, complexity, energy efficiency, multiple access scheme, and performance. In addition, this survey reports on the analysis of tradeoff between different chaos-based communication systems. Finally, several concluding remarks are discussed.

Nonlinear low-to-high-frequency energy cascades in diatomic granular crystals.

We study wave propagation in strongly nonlinear one-dimensional diatomic granular crystals under an impact load. Depending on the mass ratio of the "light" to "heavy" beads, this system exhibits rich wave dynamics from highly localized traveling waves to highly dispersive waves featuring strong attenuation. We demonstrate experimentally the nonlinear resonant and antiresonant interactions of particles, and we verify that the nonlinear resonance results in strong wave attenuation, leading to highly efficient nonlinear energy cascading without relying on material damping. In this process, mechanical energy is transferred from low to high frequencies, while propagating waves emerge in both ordered and chaotic waveforms via a distinctive spatial cascading. This energy transfer mechanism from lower to higher frequencies and wave numbers is of particular significance toward the design of novel nonlinear acoustic metamaterials with inherently passive energy redistribution properties.

Stochastic Chaotic Radar Waveform Design Based on Function-driven

Stochastic Chaotic Radar Waveform Design Based on Function-driven

Fault location for WDM‐PON using a multiple‐longitudinal‐mode laser modulated by chaotic wave

ABSTRACTWe experimentally demonstrate a cost‐effective method to locate faults in wavelength‐division‐multiplexing passive optical network (WDM‐PON) utilizing a multiple‐longitudinal‐mode Fabry–Perot semiconductor laser directly modulated by chaotic wave from a Colpitts oscillator. Due to chaos modulation, every longitudinal mode of the laser has chaotic intensity waveform. Using a tunable optical filter selects a mode to detect the wavelength‐matched branch of WDM‐PON using chaos correlation technique. Experimental results show that the unterminated fiber end, mismatch connector and fiber breakpoint can be preciously located. A detection range of approximately 75 km and a range‐independent spatial resolution of 14 cm are achieved. © 2015 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:2502–2506, 2015

Wiring fault detection with Boolean-chaos time-domain reflectometry

We experimentally demonstrate a time-domain reflectometry (TDR) method for detecting cable faults, which employs a Boolean circuit to generate a wideband chaotic waveform acting as probe signal and further locates faults by correlating a duplicate of the probe signal and the back-reflected signal. The Boolean circuit is a small delayed-feedback system mainly consisting of two exclusive-OR (XOR) gates and one exclusive-NOR gate. Benefiting from fast response and high operating voltage of logical gates, the Boolean circuit can achieve a high-bandwidth and large-amplitude output which cause a high resolution and a long measurable distance for the TDR. Our experimental results show that a 2 km detection distance of a breakpoint and a \(\sim \)0.1 m spatial resolution can be achieved by means of a chaotic signal from the Boolean circuit with 533 MHz bandwidth and 2.5 V amplitude. Furthermore, we experimentally demonstrate the detection of short circuits and impedance mismatches can be successfully implemented using our method.

A Simple RLCC-Diode-Opamp Chaotic Oscillator

This paper presents a simple autonomous chaotic oscillator. The design method is primarily based on a linear oscillator constructed by a closed loop connection of two building blocks, i.e. an inverting active integrator and a passive second-order LC integrator. A diode is inserted in parallel to the two building blocks for inducing chaos. The mathematical model reveals a set of three-dimensional ordinary differential equations, containing seven terms with four constants and an exponential nonlinearity. The dynamics properties are investigated in terms of an equilibrium point, Jacobian matrix, chaotic attractors, bifurcation, Lyapunov exponents, and chaotic waveforms in time domain. The proposed chaotic oscillator potentially exhibits complex dynamical behaviors through the utilization of only six minimal electronic components.

Fast physical random bit generation with photonic integrated circuits with different external cavity lengths for chaos generation.

We generate random bit sequences from chaotic temporal waveforms by using photonic integrated circuits (PICs) with different external cavity lengths. We investigate the condition for generating random bits at different sampling rates of single-bit generation method with the PICs. We succeed in generating certified random bit sequences by using the PIC with 3, 4, 5, or 10-mm-long external cavity, whereas random bits cannot pass all the statistical tests of randomness when the PIC with 1 or 2 mm-long external cavity is used.

Optimal Waveforms for Efficient Wireless Power Transmission

This work shows how using specifically selected or designed waveforms in wireless power transfer (WPT) systems can lead to improved RF to dc conversion efficiency in rectifier circuits in the receiving end of these systems. Signals with different time domain waveforms are considered such as OFDM, white noise and chaotic waveforms, and the performance of a rectifier circuit operating at 433 MHz is evaluated when using these signals in comparison to a single carrier constant envelope signal. The performed experiments show that selecting high peak to average power ratio (PAPR) signals lead to improved RF-DC conversion efficiency in rectifier circuits.

HOPF BIFURCATION OF CODIMENSION ONE AND DYNAMICAL SIMULATION FOR A 3D AUTONOMOUS CHAOTIC SYSTEM

In this paper, a 3D autonomous system, which has only sta- ble or non-hyperbolic equilibria but still generates chaos, is presented. This system is topologically non-equivalent to the original Lorenz sys- tem and all Lorenz-type systems. This motivates us to further study some of its dynamical behaviors, such as the local stability of equilibrium points, the Lyapunov exponent, the dissipativity, the chaotic waveform in time domain, the continuous frequency spectrum, the Poincar e map and the forming mechanism for compound structure of its special cases. Especially, with the help of the Project Method, its Hopf bifurcation of codimension one is in detailed formulated. Numerical simulation results not only examine the corresponding theoretical analytical results, but also show that this system possesses abundant and complex dynamical properties not solved theoretically, which need further attention.

Noise and Chaos Contributions in Fast Random Bit Sequence Generated From Broadband Optoelectronic Entropy Sources

During the last 4 years, chaotic waveforms for random number generation found a deep interest within the community of analogue broadband chaotic optical systems. Earlier investigations on chaos-based RNG were proposed in the 90s and early 2000, however mainly based on piecewise linear (PL) 1D map, with bit rate determined by analog electronic processing capabilities to provide the PL nonlinear function of concern. Optical chaos came with promises for much higher bit rate, and entropy sources based on high complexity (high dimensional) continuous time (differential) dynamics. More specifically in 2009, Reidler published a paper entitled “An optical ultrafast random bit generator”, in which they presented a physical system for a random number generator based on a chaotic semiconductor laser. This generator is claimed to reach potentially the extremely high rate of 300 Gb/s. We report on analysis and experiments of their method, which leads to the discussion about the actual origin of the obtained randomness. Through standard signal theory arguments, we show that the actual binary randomness quality obtained from this method, can be interpreted as a complex mixing operated on the initial analogue entropy source. Our analysis suggests an explanation about the already reported issue that this method does not necessarily require any specific deterministic property (i.e., chaos) from the physical signal used as the source of entropy. The bit stream randomness quality is found to result from “aliasing” phenomena performed by the post-processing method, both for the sampling and the quantization operations. As an illustration, such random bit sequences extracted from different entropy sources are investigated. Optoelectronic noise is used as a non deterministic entropy source. Electro-optic phase chaotic signal, as well as simulations of its deterministic model, are used as deterministic entropy sources. In all cases, the extracted bit sequence reveals excellent randomness.

Synthesizing antipodal chaotic waveforms

Chaotic waveforms are natural information carriers since a correspondence can be established between the symbolic dynamics of a chaotic oscillator and the symbols of a message. Message symbols can be efficiently encoded in a chaotic waveform by applying vanishingly small perturbations to an oscillator to guide its symbolic dynamics to follow a desired course. Recently, two chaotic hybrid dynamical systems were shown to have matched filters enabling robust reception of chaotic communication waveforms in the presence of noise. The first of these, the exact shift oscillator, produces waveforms with desirable properties similar to antipodal signaling, but a physical implementation may be difficult to control using small perturbations. The second oscillator, the exact folded-band oscillator, produces less optimal waveforms but is more easily controlled. Here we introduce a method for generating waveforms of the exact shift oscillator by summing waveforms from a bank of easily controlled exact folded-band oscillators. We show that any solution of the exact shift oscillator can be so constructed using only three folded-band oscillators. Thus, this scheme allows us to realize the advantages of both chaotic systems while overcoming their individual disadvantages, thereby enabling practical chaos communications.

Enhancing Privacy of Chaotic Communications by Double Masking

In this paper, we numerically demonstrate that the performances of private transmission using chaotic lasers can be substantially improved by double masking the message by a suitable scheme. In addition to standard optical chaos, our method makes use of the chaotic voltage waveform available across the transmitter laser junction. With respect to the standard setup, the new one requires only one more electrical amplifier and a passive adder at the transmitter, while the receiver remains unchanged. It has been found that with this new scheme, synchronization quality is significantly improved for the twin lasers, while this is not the case for an unmatched laser pair. This results in an increased bit error rate differential between the authorized user and an eavesdropper, thus enhancing privacy. Simulations have been performed with the Lang-Kobayashi model.