Chaotic Carrier Research Articles

Jerk Chaotic System: Analysis, Circuit Simulation, Control and Synchronization with Application to Secure Communication

Dynamical behaviors of 3D Jerk system were examined in terms of equilibrium, stability, dissipative, and phase space attractor in this study. The system’s practical applications were demonstrated through circuit realization and synchronization scheme via active backstepping control with its effectiveness demonstrated in secure communication. The viability of the theoretical model of 3D Jerk system was confirmed using electronic circuit workbench designed in MultiSIM enviroment. A nonlinear feedback controller was designed using the recursive backstepping technique to control and track a desire function. For secure communication application, active backstepping method was adopted to synchronize two identical chaotic systems evolving from different initial conditions. It was demonstrated that when the controller was activated, the systems synchronize successfully. The results of the active backstepping designed controllers were numerically applied in the area of secure communication, with the variable of the drive being encrypted information transmitted through a coupling channel. Using an additive encryption masking scheme, the encrypted signal was a superposition of sinusoidal information specified by period function and chaotic carrier generated from a variable of the Jerk system. The transmitted information signal was successfully retrieved from the chaotic response signal using an inverse function decryption algorithm, thereby confirming the effectiveness and robustness of the designed controller.

Coherent Chaotic Communication Using Generalized Runge–Kutta Method

Computer simulation of continuous chaotic systems is usually performed using numerical methods. The discretization may introduce new properties into finite-difference models compared to their continuous prototypes and can therefore lead to new types of dynamical behavior exhibited by discrete chaotic systems. It is known that one can control the dynamics of a discrete system using a special class of integration methods. One of the applications of such a phenomenon is chaos-based communication systems, which have recently attracted attention due to their high covertness and broadband transmission capability. Proper modulation of chaotic carrier signals is one of the key problems in chaos-based communication system design. It is challenging to modulate and demodulate a chaotic signal in the same way as a conventional signal due to its noise-like shape and broadband characteristics. Therefore, the development of new modulation–demodulation techniques is of great interest in the field. One possible approach here is to use adaptive numerical integration, which allows control of the properties of the finite-difference chaotic model. In this study, we describe a novel modulation technique for chaos-based communication systems based on generalized explicit second-order Runge–Kutta methods. We use a specially designed test bench to evaluate the efficiency of the proposed modulation method and compare it with state-of-the-art solutions. Experimental results show that the proposed modulation technique outperforms the conventional parametric modulation method in both coverage and noise immunity. The obtained results can be efficiently applied to the design of advanced chaos-based communication systems as well as being used to improve existing architectures.

Signal-to-noise ratio degradation analysis for optoelectronic feedback-based chaotic optical communication systems.

Chaotic optical communication encrypts transmitted signals through physical noise; this ensures high security while causing a certain decrease in the signal-to-noise ratio (SNR). Thus, it is necessary to analyze the SNR degradation of decrypted signals after chaotic encryption and the minimum requirements for the SNR of the fiber channel to meet the required bit error rate (BER) performance. Accordingly, an SNR model of decrypted signals for optoelectronic feedback-based chaotic optical communication systems is proposed. Under different channel SNRs, the SNR degradation of 40 Gbit/s phase chaos and intensity chaos models is investigated by simulation and experiment, respectively, with a 15 GHz wideband chaotic carrier. Comparing decrypted signals with original signals, the simulation results show that there is a 2.9 dB SNR degradation for both intensity chaos and phase chaos. Further, in experiments, SNR degradation from 4.5 dB to 5.6 dB, with various channel SNRs for intensity chaos, is analyzed, while there is an SNR degradation from 7.1 dB to 8.3 dB for phase chaos. The simulation and experimental results provide guidance for long-distance transmission chaotic optical communication systems.

Optical cryptographic communications with non-identical chaotic laser systems

"We report secure data transmission performed using chaotic lasers with different external cavity geometries and applying the chaotic masking method based on subcarrier and phase modulations of the chaotic optical carrier. Two semiconductor lasers with similar multimode emission spectra and self-optical feedback provided, respectively, by ring and linear external cavities, were optically coupled and chaotically synchronized into a master – slave scheme. The transmitted message frequency modulates the radio frequency signal which modulates in phase the master chaotic carrier. Based on the robustness of the used encryption method and the synchronization characteristics of the two lasers, the decryption is conducted by the simple radio frequency spectrum monitoring of the slave emission."

Design of a new multi-wing chaotic system and its application in color image encryption

Due to its chaotic carrier function and pseudorandom nature, chaotic systems are frequently applied in the area of secure communication. To render chaotic signals more complicated, a novel multi-wing chaotic system is developed in this study. Initially, a double-wing attractor generated by a novel 3D Lorenz-like chaotic system that comprises two quadratic terms and four linear terms. By inserting a nonlinear feedback controller, the complex system gets transformed into a multi-wing chaotic system. It is noteworthy that the topological shape of the attractor and the number of equilibrium points can both be altered in the particular multi-wing chaotic system. Secondly, the dynamic features of the multi-wing chaotic system are discussed via employing the bifurcation diagram and the Lyapunov exponential spectrum. According to results from simulation, the system displays widely dispersed chaotic characteristics over a large range of parameters. In addition, the complexity analysis findings of chaotic sequences testify that the chaotic sequences have strong complexity. Therefore, the multi-wing chaotic system will have an excellent effect in image encryption. Finally, a scrambling-diffusion encryption scheme is built using the rich chaotic sequences discussed above. The scheme includes two times scrambling of pixel position and once transform of pixel value by the virtue of Galois field (GF). The proposed algorithm has superior efficiency and excellent security according to the results of the feasibility and security analysis. Moreover, the investigation of the multi-wing chaotic system property and its usage in image encryption additionally broadens the applicability of chaos systems and offers some standards for confidential communication.

Conducted electromagnetic interference mitigation in super-lift Luo-converter for electric vehicle applications

In this article, a digital chaotic pulse width modulation (DCPWM)-dependent electromagnetic interference (EMI) noise attenuating procedure has been implemented. With the aid of a field programmable gate array (FPGA), a randomized carrier frequency modulation with a fixed duty cycle has been generated through chaotic carrier frequency, and this process is called DCPWM. Conducted EMI suppression is achieved in a 200 kHz, 40 W elementary positive output super lift Luo (EPOSLL) converter using the DCPWM technique. The results are compared and validated with periodic PWM over DCPWM in simulation and hardware with electromagnetic compatibility (EMC) standards. Besides, 9 dBV (2.81 V) of conducted EMI noise has been minimized in the DCPWM approach against periodic pulse width modulation method for the EPOSLL converter in electric vehicles applications.

Experimental Simulation for Two Optically Filtered Modulation Weights in Laser Diode as a Self-Learning Layer

In this study, the response of a nonlinear laser medium is experimentally studied. In the study, a hybrid version of the input layer that multiplies optically and accumulates electrically is compared with a wholly optical version that multiplies and accumulates optically. This medium is subjected to two different paths of optically filtered and attenuated feedback. With such a system, the variation of feedback weight in one of them is tested in correspondence to the second one. Observations for frequency spectra are carried out to simulate the resultant response with an input layer for a neural network based on chaotic carriers. Chaotic laser emission was observed as a function of several control parameters, which are D.C. bias voltage, branch optical attenuation, and feedback strengths based on filtration with fiber Bragg grating. This learning rule is linear in the difference between each input and output of a neuron. This is an enhancing/inhibiting rule. The thresholds are adjusted in such a way that the output of the neuron is either pushed in the same direction as the input (enhancing) or pushed in the opposite direction (inhibiting).

Experimental demonstration of an 8-Gbit/s free-space secure optical communication link using all-optical chaos modulation.

For the first time, to the best of our knowledge, we experimentally demonstrate a high-speed free-space secure optical communication system based on all-optical chaos modulation. The effect of atmospheric turbulence on optical chaos synchronization is experimentally investigated via a hot air convection atmospheric turbulence simulator. It is shown that, even under moderately strong turbulent conditions, high-quality chaos synchronization could be obtained by increasing the transmission power. Moreover, a secure encryption transmission experiment using a high bias current induced chaotic carrier for 8-Gbit/s on-off-keying data over a ∼10-m free-space optical link is successfully demonstrated, with a bit-error rate below the FEC threshold of 3.8 × 10-3. This work favorably shows the feasibility of optical chaotic encryption for the free-space optical transmission system.

Analytical Model of an Energy Detector for Ultra-Wideband Chaotic Communications

For the ultra-wideband chaotic radio pulses an analytical model of an energy detector is designed and closed-form expressions for the optimal threshold and the detection probabilities are derived. The analytical solution is compared with the results of the numerical simulation. The model proves to be well-suited for the chaotic radio pulses with large base B (or processing gain, or the number of freedom degrees), namely, B ≥ 100. Potential applications areas of the proposed model are ultra-wideband communications with chaotic pulse carriers, e.g., ultra-wideband systems of 802.15.x standards, and multi-element chaotic communication systems.

Dual-Channel Secure Communication Based on Wideband Optical Chaos in Semiconductor Lasers Subject to Intensity Modulation Optical Injection

Chaotic optical communication was initially proposed to provide advanced physical layer security for optical communication. Here, we propose and numerically demonstrate an optical chaos communication scheme based on semiconductor lasers subject to intensity modulation optical injection for secure transmission of quadrature amplitude modulation (QAM) messages. In this scheme, two chaotic sources were generated with different modulation parameters and acted as chaotic carriers at the transmitter side, which were subsequently used to drive two receivers in two separate channels. Numerical results demonstrate that this scheme allows for broadband chaos generation and high-quality chaos synchronization can be achieved to simultaneously encrypt two messages for secure communication; a 20 GBaud 16-QAM message was recovered correctly with a transmission distance in standard single mode fiber (SMF) over 120-km, while the other 20 GBaud 64-QAM message was limited to a 20-km fiber transmission distance. The system performance was systematically evaluated by analyzing the bit error ratio (BER) of the recovered message versus the masking coefficient and the transmission distance. Furthermore, our simulations justify the robustness against the mismatch of parameters. Therefore, we hope that this scheme can be experimentally implemented for high-speed chaos communication and secure key distribution.

Modeling of a multi-parameter chaotic optoelectronic oscillator based on the Fourier neural operator.

A model construction scheme of chaotic optoelectronic oscillator (OEO) based on the Fourier neural operator (FNO) is proposed. Different from the conventional methods, we learn the nonlinear dynamics of OEO (actual components) in a data-driven way, expecting to obtain a multi-parameter OEO model for generating chaotic carrier with high-efficiency and low-cost. FNO is a deep learning architecture which utilizes neural network as a parameter structure to learn the trajectory of the family of equations from training data. With the assistance of FNO, the nonlinear dynamics of OEO characterized by differential delay equation can be modeled easily. In this work, the maximal Lyapunov exponent is applied to judge whether these time series have chaotic behavior, and the Pearson correlation coefficient (PCC) is introduced to evaluate the modeling performance. Compare with long and short-term memory (LSTM), FNO is not only superior to LSTM in modeling accuracy, but also requires less training data. Subsequently, we analyze the modeling performance of FNO under different feedback gains and time delays. Both numerical and experimental results show that the PCC can be greater than 0.99 in the case of low feedback gain. Next, we further analyze the influence of different system oscillation frequencies, and the generalization ability of FNO is also analyzed.

Security-enhanced watermark embedding and transmission based on synchronized chaotic semiconductor lasers

In this paper, we propose and numerically demonstrate a chaotic watermarking encryption and secure transmission scheme based on two synchronized response lasers (RLs) subject to identical injection from a driving laser (DL). In this proposed system, the chaotic signal from DL can be optimized after passing through a phase modulator and a dispersion component, then the chaotic signal with large bandwidth and low time delay signature is obtained. Simultaneously injecting this chaotic signal into two identical RLs, high-quality chaos synchronization between two RLs can be realized. Both synchronized chaotic signals are, respectively, divided into two parts. One is used to generate shared keys required by the watermarking encryption, and the other is used as chaotic carrier to realize the secure message transmission. After introducing the synchronized optical chaos into the watermarking encryption algorithm, the normalized correlation of the extracted watermark without long-distance transmission is 0.9554 and can still maintain above 0.9 over 200 km transmission fiber. The message transmission and watermark extraction have good robustness to the fiber parameter mismatches, and excellent performances can be maintained even within 20% mismatches range. In our method, synchronized high-quality optical chaotic signals from two RLs are used to watermark embedding and transmission, and double encryption can be realized, which can open a new path for future high-speed and security-enhanced watermark embedding and transmission.

Double-Stream Differential Chaos Shift Keying Communications Exploiting Chaotic Shape Forming Filter and Sequence Mapping

A new Differential Chaos Shift Keying modulation scheme exploiting Chaotic Shape-forming Filter and Sequence Mapping (CSF-SM-DCSK) is being proposed. The new CSF-SM-DCSK system employs a novel sequence mapping rule and includes a data correction module to achieve a good trade-off between the low Bit Error Rate (BER) performance and high transmission rate. It transmits two data streams simultaneously and preserves the simplicity and robustness of DCSK method. Channel one, transmitting a Low Priority Stream (LPS), generates the chaotic carrier by a Chaotic Shape-forming Filter (CSF) at the transmitter and applies a coherent Matched Filter (MF) at the receiver to recover the information. Channel two, transmitting a High Priority Stream (HPS), relies on conventional DCSK modulation, while the reference and information-bearing parts are transmitted simultaneously with orthogonal sine and cosine carriers. This double-stream solution eliminates the need for analog RF delay lines and doubles the data transmission rate. Before feeding the LPS data stream into the modulator, each LPS bit is encoded into a symbol sequence using sequence mapping. This approach, together with the coherent MF reception, equips the LPS channel with an extremely high robustness against channel noise and multipath propagation. To handle every possible redundancy in the received signal and to minimize the possibility of making wrong decisions, a data correction block is also introduced. Initially, a rough estimation of the received HPS DCSK bit is done at the receiver, then this estimation is used to remove the DCSK modulation from the received information-bearing signal. The three inputs of data correction blocks are: (i) the reference and (ii) the information-bearing parts of the received signal in their original form, and (iii) the received information-bearing signal where the DCSK modulation is removed. The data correction block improves the BER performance while the increased channel capacity, enabled by the double-stream approach, improves the spectral efficiency. Analytical expressions are derived to predict the BER performances in additive white Gaussian noise channel for both the LPS and HPS channels. Computer simulations are used to show that the system performance of the CSF-SM-DCSK modulation scheme proposed in this work is superior to that of the already published solutions. In addition to the computer simulations, the new chaos-based wireless communications system has been implemented on a wireless open-access research platform to experimentally demonstrate the feasibility and the superiority of CSF-SM-DCSK.

Field-programmable gate array design of image encryption and decryption using Chua’s chaotic masking

<span>This article presents a simple and efficient masking technique based on Chua chaotic system synchronization. It includes feeding the masked signal back to the master system and using it to drive the slave system for synchronization purposes. The proposed system is implemented in a field programmable gate array (FPGA) device using the Xilinx system generator tool. To achieve synchronization, the Pecora-Carroll identical cascading synchronization approach was used. The transmitted signal should be mixed or masked with a chaotic carrier and can be processed by the receiver without any distortion or loss. For different images, the security analysis is performed using the histogram, correlation coefficient, and entropy. In addition, FPGA hardware co-simulation based Xilinx Artix7 xc7a100t-1csg324 was used to check the reality of the encryption and decryption of the images.</span>

Chen system-based chaotic transceiver for frequency output quartz transducers

The application of unidirectional synchronization of two coupled Chen systems is exhibited in this work. In spite of the high dependence on initial conditions, which means that two initially close phase trajectories with time become uncorrelated, it is possible to synchronize two dynamic systems to make them evolve identically. Data transmission using chaos requires mixing an information signal with a chaotic carrier. This procedure performs data encryption and spreads the spectrum of an information signal, which increases information security and reliability. Thus, the prospect of using devices with chaotic dynamics in modern telecommunication and telemetry applications is due to several factors, including high information capacity, various frequencies, and confidentiality of messages. The proposed scheme is considered to be used in a measuring transducer design that requires sensors to operate at a long distance from the rest of the scheme. We propose an application of a chaotic oscillator as a transceiver module for a quarts sensor transducer, which could be used in a telemetry application. The process of producing non-periodic but determined oscillations by the non-linear Chen system and signal transmission application, based on it, are the subject of the research. The complete synchronization of two unidirectionally connected Chen systems and its signal transmission application are considered. The goal is to develop a transceiver extension for the quartz measuring transducer scheme to ensure the stable operation of sensors at a long distance from the rest of the scheme. The result of the research: a chaos synchronization scheme was applied to transmit a frequency-modulated signal, obtained from a difference-frequency block of the quartz sensor transducer. Additionally, the mathematical model and numerical modeling of the Chen dynamical system has been done. The numerical solution of the system's differential equations was obtained using Matlab software. To study the change in the dynamic regime depending on the parameters of the model, the spectrum of Lyapunov exponents was calculated and bifurcation diagrams were constructed. The circuit design of the Chen oscillator was built using Multisim software, which uses the PSpice model to simulate electrical components. A model of an analog signal transmission system with chaotic mixing of a frequency output signal with a chaotic carrier has been proposed as an extension of the use of quartz transducers in measuring devices.

Coherent chaotic optical communication of 30 Gb/s over 340-km fiber transmission via deep learning.

Chaotic optical communication has attracted much attention as a hardware encryption method in the physical layer. Limited by the requirements of chaotic hardware synchronization, fiber transmission impairments are restrictedly compensated in the optical domain. There has been little experimental demonstration of high-speed and long-distance chaotic optical communication systems. Here, we propose a method to overcome such limitations. Using a deep-learning model to realize chaotic synchronization in the digital domain, fiber transmission impairments can be compensated by digital-signal processing (DSP) algorithms with coherent detection. A successful transmission of 30 Gb/s quadrature phase-shift keying messages hidden in a 15 GHz wideband chaotic optical carrier was experimentally demonstrated over a 340-km fiber link. Meanwhile, the chaotic receiver can be significantly simplified without compromising security. The proposed method is a possible way to promote the practical application of chaotic optical communications.

Exploiting Reservoir Computing for Optical Secure Communication

Abstract A reservoir computing (RC) based on vertical cavity surface emitting laser (VCSEL) subjected to optical feedback is adopted to realize chaos synchronization in optical chaotic communication. Combined with the application of chaos masking (CMS) technology in chaotic secure communication, chaotic signal generated by distribution feedback (DFB) laser after optical feedback and optical injection, that is used as chaotic carrier of hiding original information, and act as target signal of the RC. Then masked information is used for RC training and transmission. Next, utilizing the weights and error offsets trained out by RC at transmitter, carrier can be reconstructed by RC at receiver. Finally, message is acquired by subtracting the reconstructed carrier from received masked signal. Taking image data transmission in 10 km fiber as an example, the chaos synchronization between the carrier signal and the constructed carrier signal is 0.9935, Q-factor is 10 and bit error rate (BER) is 5×10-28 with simulation.

Three-loop electro-optical phase chaotic secure communication system with time-delay signatures concealment and key space enhancement

A novel three loops electro-optical phase (TLEOP) chaotic secure communication system is proposed, which consists of three mutually coupled electro-optical phase chaotic feedback loops. A pseudo-random binary sequence (PRBS) is introduced in the proposed system scheme. The scheme improves the complexity of the chaotic carriers and completely the time-delay signatures (TDSs) of the system with a small feedback gain coefficient that is easy to reach. The PRBS or the original messages and the chaotic carriers are nonlinearly coupled together and participate in the generation of the chaotic carrier which further improves the complexity and the security of the chaotic system. Multiple TDSs effectively enlarge the key space of the system (about 1012). The synchronization performance of the proposed TLEOP system is discussed. The results show that the TDSs are suitable as the secret key of the system because of the high sensitivity of the chaos synchronization to time-delays. Since the mismatch of the feedback gain coefficient caused by environmental changes has little effect on the chaos synchronization, the proposed system has strong robustness. The proposed scheme has great application prospects in chaotic secure communication.

Capacity expansion of chaotic secure transmission system based on coherent optical detection and space division multiplexing over multi-core fiber.

We propose and experimentally study a coherent optical chaotic secure transmission system through a multi-core fiber (MCF). The messages are encrypted by the chaotic carrier and transmitted through the outer cores of the MCF, whereas the chaotic carrier signal is concealed by transmitting through the center core. The MCF provides large transmission capacity expansion and security enhancement against eavesdroppers due to its physical structure. In addition, the designed optical chaos self-homodyne coherent detection strategy has high detection sensitivity and simple physical structure. Due to the prevalence of devices and digital signal processing (DSP) algorithms used in this system, it can be well compatible with a commercial coherent optical communication system. Error free 40 Gb/s/core encrypted 16 quadrature amplitude modulation (QAM) signal transmission over 10 km 7-core fiber is achieved, and 20 Gb/s quadrature phase shift keying (QPSK) signal transmission over a 100 km standard single-mode fiber (SSMF) is demonstrated to verify the long-distance transmission capability. The sensitivity to the secret key is also studied.

Investigation on the complex and tunable laser chaos generated by the microresonator optical combs injection

A novel method to generate high complexity and wavelength-tunable laser chaos is proposed by injecting nonlinear frequency combs from a microresonator (MR) into a semiconductor laser. The nonlinear dynamics and chaotic characteristics are simulated. The results show that chaos with permutation entropy of 0.997, spectral entropy of 0.953, spectrum bandwidth of 32.4 GHz, the flatness of 0.38 dB/GHz can be generated. Compared with the conventional optical feedback injection system and the phase conjugate feedback injection system, the MR injection system can generate better chaos with bandwidth enhancement and complexity improvement at lower bias currents. The time delay signature introduced by the MR can be completely concealed, which provides support for chaotic secure communication. Furthermore, the microresonator injection (MRI) system is flexible and expandable. Laser chaos with tunable wavelength can be generated by changing the working wavelength of the slave laser. And if multiple lasers with free spectral range interval are connected to MR parallelly, up to 93 high-performance chaotic carriers with a cross-correlation as low as about 0.1 can be realized in short, conventional, and long wavelength bands simultaneously. This scheme provides a foundation for multiple parallel chaotic carriers and large-capacity chaotic secure communication.