Chaos-based Communication Systems Research Articles

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.

Design of A Chaos-based Digital Radio over Fiber Transmission Link using ASK Modulation for Wireless Communication Systems

Secured broadband radio communications are becoming increasingly pivotal for high-speed connectivity in radio access networks, playing a crucial role in both mobile information systems and wireless IoT connections. This paper introduces a chaos-based two-channel digital radio communication system utilizing fiber optic radio transmission technology. The system comprises two radio channels operating at up to 1 Gbps using amplitude shift keying (ASK) modulation, followed by modulation with a chaotic sequence before conversion to the optical domain using the MZM modulator. To compensate for fiber loss, the system utilizes an Erbium Doped Fiber Amplifier (EDFA) and employs the optical links through standard ITU-G.655 optical fibers. Numerical simulation of the designed system is performed using the commercialized simulation software Optisystem V.15 to assess and characterize transmission performance. The results demonstrate the system’s effective operation on two channels with a fiber transmission distance of up to 110 km, maintaining a bit error ratio of less than 10−9. This feature ensures reliable performance for high-speed radio connections, particularly in applications such as fronthaul networks in cloud radio access and wireless sensor network connections.

Some Properties of a Discrete Lorenz System Obtained by Variable Midpoint Method and Its Application to Chaotic Signal Modulation

Various discretization effects caused by applying numerical integration techniques to continuous chaotic systems are broadly studied in nonlinear science. Along with the negative impact on the precision of the various finite-difference schemes, such effects may have surprisingly fruitful practical applications, e.g. pseudo-random number generation, image encryption with improved diffusion and confusion properties, chaotic path planning, and many others. One such application is chaos-based communication systems which gained attention in recent decades due to their high covertness and broadband transmission capability. A crucial problem in the design of chaotic communication systems is the modulation of carrier signals. Due to the noise-like properties of chaotic signals, they can barely be modulated using the same methods as conventional harmonic signals. Thus, developing new modulation techniques is of great interest in the field of chaotic communications. In this study, we investigate the discrete model of the Lorenz oscillator obtained using controllable midpoint numerical integration and develop a novel modulation technique for chaos-based communication systems. We discover and analyze the multistability phenomenon in the dynamics of the investigated finite-difference Lorenz model through bifurcation, the basin of attraction, and Lyapunov spectrum analysis procedures. Using a specially designed testbench, we explicitly show that the proposed modulation method outperforms commonly used parametric modulation and is nearly equal to the state-of-the-art symmetry-based modulation in terms of covertness and noise resistivity. In addition, the proposed modulation technique is much easier to implement using computer arithmetics, especially in fixed-point hardware. The reported results may be efficiently applied to designing advanced chaos-based communications systems or improving the characteristics of existing communication system architectures.

Estimating Optimal Synchronization Parameters for Coherent Chaotic Communication Systems in Noisy Conditions

It is known, that coherent chaotic communication systems are more vulnerable to noise in the transmission channel than conventional communications. Among the methods of noise impact reduction, such as extended symbol length and various digital filtering algorithms, the optimization of the synchronization coefficient may appear as a very efficient and simple straightforward approach. However, finding the optimal coefficient for the synchronization of two chaotic oscillators is a challenging task due to the high sensitivity of chaos to any disturbances. In this paper, we propose an algorithm for finding the optimal synchronization parameter K_opt for a coherent chaos-based communication system affected by various noises with different signal-to-noise ratios (SNR). It is shown, that under certain conditions, optimal $K$ provides the lowest possible bit error rate (BER) during the transmission. In addition, we show that various metrics applied to the message demodulation task propose different noise immunity to the overall system. For the experimental part of the study, we simulated and physically prototyped two chaotic communication systems based on well-known Rossler and Lorenz chaotic oscillators. The microcontroller-based prototype of a chaotic communication system was developed to investigate the influence of noise in the real transmission channel. The experimental results obtained using the designed hardware testbench are in good correspondence with the theoretical propositions of the study and simulation results. The suggested evaluation metrics and optimization algorithms can be used in the design of advanced chaos-based communication systems with increased performance.

Highly-secured chaos-based communication system using cascaded masking technique and adaptive synchronization

Highly-secured chaos-based communication system using cascaded masking technique and adaptive synchronization

Prototyping the Symmetry-Based Chaotic Communication System Using Microcontroller Unit

Chaos-based communications are a promising application of chaos theory and nonlinear dynamics. Their key features include concealed transmission, high security, and native broadband signals. Many studies have recently been published devoted to this technology. However, the practical implementations of chaos-based communications are rare due to multiple shortcomings: high hardware requirements, complex signal processing algorithms, and a lack of efficient modulation techniques for chaotic signals. In this study, we consider a simple hardware prototype of a coherent chaos-based communication system based on a novel type of modulation: adaptive symmetry of the finite-difference scheme used in a chaos generator. We explicitly demonstrate the possibility of covertly transmitting data using a chaotic transmitter and receiver implemented in a general-purpose microcontroller unit. A comparison between traditional parameter and symmetry modulation is given through a return map analysis and bit error rate estimation. The communication secrecy is analyzed using quantified return map analysis. The obtained results confirm the possibility of creating chaos-based communication systems based on symmetry modulation.

A filtered Hénon map

In this paper, we use Lyapunov exponents to analyze how the dynamical properties of the Hénon map change as a function of the coefficients of a linear filter inserted in its feedback loop. We show that the generated orbits can be chaotic or not, depending on the filter coefficients. The dynamics of the system presents complex behavior, including cascades of bifurcations, coexistence of attractors, crises, and “shrimps”. The obtained results are relevant in the context of bandlimited chaos-based communication systems, that have recently been proposed in the literature.

Design and Analysis of Multi-User Faster-Than-Nyquist-DCSK Communication Systems over Multi-Path Fading Channels.

In this paper, we present a new multi-user chaos-based communication system using Faster-than-Nyquist sampling to achieve higher data rates and lower energy consumption. The newly designed system, designated Multi-user Faster Than Nyquist Differential Chaos Shift Keying (MU-FTN-DCSK), uses the traditional structure of Differential Chaos Shift Keying (DCSK) communication systems in combination with a filtering system that goes below the Nyquist limit for data sampling. The system is designed to simultaneously enable transmissions from multiple users through multiple sampling rates resulting in semi-orthogonal transmissions. The design, performance analysis, and experimental results of the MU-FTN-DCSK system are presented to demonstrate the utility of the newly proposed system in enabling multi-user communications and enhancing the spectral efficiency of the basic DCSK design without the addition of new blocks. The MU-FTN-DCSK system presented in this paper demonstrates spectral gains for one user of up to 23% and a combined gain of 25% for four () users. In this paper, we present a proof of concept demonstrating a new degree of freedom in the design of Chaos-based communication systems and their improvement in providing wireless transmissions without complicated signal processing tools or advanced hardware designs.

Discovering Chaos-Based Communications by Recurrence Quantification and Quantified Return Map Analyses

Many studies show the possibility of transmitting messages in a protected and covert manner using a noise-like chaotic waveform as a carrier. Among popular chaotic communication system (CCS) types, one may distinguish chaotic shift keying (CSK) and parameter modulation (PM) which are based on the manipulation of the transmitting chaotic oscillators. With the development of direct digital synthesis (DDS), it became possible to modulate chaotic signals by varying the properties of the numerical method used in digital chaos generators. The symmetry coefficient modulation (SCM) is such an approach potentially able to provide higher secrecy. However, the actual security of chaos-based communications is still a questionable and controversial feature. To quantitatively evaluate the CCS security level, a certain numerical metric reflecting the difficulty of breaking a communication channel is needed. Return maps are commonly used to attack chaotic communication systems, but the standard algorithm does not involve any kind of quantification. In this study, we propose a new method for estimating the differences between two return maps based on a two-dimensional (2D) histogram. Then, we investigate the resistance of chaotic shift keying, parameter modulation, and SCM communication schemes against three types of attacks: the proposed quantified return map analysis (QRMA), recurrence quantification analysis (RQA), which had not been previously reported for attacking chaos-based communications, and the classical approach based on spectral analysis. In our experiments we managed to recover the plain binary message from the waveform in the channel when transmitted using all three chaos-based messaging techniques; among them, SCM appeared to be the most secure communication scheme. The proposed QRMA turned out to be the most efficient technique for message recovery: the sensitivity of the QRMA appeared to be 2–5 times higher than that in the case of spectral analysis. The proposed QRMA method can be efficiently used for evaluating the difficulty of hacking chaos-based communication systems. Moreover, it is suitable for the evaluation of any other secure data transmission channel.

Design of a SIMO Deep Learning-Based Chaos Shift Keying (DLCSK) Communication System.

This paper brings forward a Deep Learning (DL)-based Chaos Shift Keying (DLCSK) demodulation scheme to promote the capabilities of existing chaos-based wireless communication systems. In coherent Chaos Shift Keying (CSK) schemes, we need synchronization of chaotic sequences, which is still practically impossible in a disturbing environment. Moreover, the conventional Differential Chaos Shift Keying (DCSK) scheme has a drawback, that for each bit, half of the bit duration is spent sending non-information bearing reference samples. To deal with this drawback, a Long Short-Term Memory (LSTM)-based receiver is trained offline, using chaotic maps through a finite number of channel realizations, and then used for classifying online modulated signals. We presented that the proposed receiver can learn different chaotic maps and estimate channels implicitly, and then retrieves the transmitted messages without any need for chaos synchronization or reference signal transmissions. Simulation results for both the AWGN and Rayleigh fading channels show a remarkable BER performance improvement compared to the conventional DCSK scheme. The proposed DLCSK system will provide opportunities for a new class of receivers by leveraging the advantages of DL, such as effective serial and parallel connectivity. A Single Input Multiple Output (SIMO) architecture of the DLCSK receiver with excellent reliability is introduced to show its capabilities. The SIMO DLCSK benefits from a DL-based channel estimation approach, which makes this architecture simpler and more efficient for applications where channel estimation is problematic, such as massive MIMO, mmWave, and cloud-based communication systems.

Mathematical models of CBSC over wireless channels and their analysis by using the LeNN-WOA-NM algorithm

In recent studies, several chaos-based secure communication (CBSC) systems are developed and are assumed to be effective and promising tools for balancing communications in wireless applications. The reliability of a wireless communication system is dependent on the synchronization between receiving and transmitting nodes. Therefore, it is crucial to analyze the mathematical models for different enhancements through CBSC and avoid the difficulty in synchronization. We have designed a novel computational paradigm that uses weighted Legendre polynomials to construct series solutions for mathematical models of the Lorenz Chaotic Attractor (LCA) and Double Scroll Attractor (DSA) (with filter and without filter) by using Chua’s circuits. We design fitness functions for each system of differential equations. Two optimization techniques, the Whale Optimization Algorithm (WOA) and the Nelder–Mead (NM) algorithm are adopted to optimize the objective functions and calculate the best set of unknown weights. We name our soft computing paradigm, the LeNN-WOA-NM algorithm. We have compared our results with state-of-the-art, and we establish that the LeNN-WOA-NM algorithm is fast, accurate, and reliable. We present graphical and statistical analysis to further elaborate on the performance of our algorithm.

Robust Global Synchronization of a Hyperchaotic System with Wide Parameter Space via Integral Sliding Mode Control Technique

The inherent property of invariance to structural and parametric uncertainties in sliding mode control makes it an attractive control strategy for chaotic dynamics control. This property can effectively constrain the chaotic property of sensitive dependence on initial conditions. In this paper, the trajectories of two identical four-dimensional hyperchaotic systems with fully-known parameters are globally synchronized using the integral sliding mode control technique. Based on the exponential reaching law and the Lyapunov stability principle, the problem of synchronizing the trajectories of the two systems was reduced to the control objective of asymptotically stabilizing the synchronization error state dynamics of the coupled systems in the sense of Lyapunov. To verify the effectiveness of the control laws, the model was numerically tested on a hyperchaotic system with a wide parameter space in a master-slave configuration. The parameters of the hyperchaotic system were subsequently varied to evolve a topologically non-equivalent hyperchaotic system that was identically coupled. In both cases, the modeled ISM control laws globally synchronized the dynamics of the coupled systems after transient times, which sufficiently proved the invariance property of the ISMC. This study offers an elegant technique for the modeling of an ISMC for hyperchaotic coupling systems. As an open problem, this synchronization technique holds promises for applications in robot motion control, chaos-based secure communication system design, and other sensitive nonlinear system control.

PAPR suppressing matrix transform and dual layered phase sequencing design for a chaos-based multi-carrier CDMA VLC system.

In this paper, we propose a chaos-based visible light communication system, wherein multiple users can access the network via the multi-carrier code division multi-access (MC-CDMA). By utilizing the high security property of chaotic sequences being aperiodic and sensitive to initial values, secure access can be achieved. However, the multi-carrier transmission suffers from high peak to average power ratio (PAPR) due to the superposition of multiple carriers, which reduces the lifetime of the light-emitting diodes (LEDs). In order to suppress the PAPR, we propose a joint matrix transform and dual layered phase sequencing (MT-DLPS) scheme. By reducing the autocorrelations of signals, the PAPR can be reduced. Moreover, the computation complexity is analyzed. Simulations are then conducted to validate that the PAPR is effectively reduced while maintaining satisfactory bit error rate (BER) performances.

Trading off security and practicability to explore high-speed and long-haul chaotic optical communication.

Recent demonstrations of chaos-based secure communication have proven the feasibility of secured transmission of high-speed (tens of Gbit/s) signals over certain distances (∼100-km), which bring hope for secure communication from theoretical analysis to practical applications. So far, the chaos-based secure communication system with chaos-masking (CMS) encryption is considered as one of the most important and feasible schemes. In this paper, an optical chaotic carrier generated by an opto-electronic oscillator is used to encrypt 112-Gbit/s message by CMS encryption for data transmission over a 1040-km single-mode-fiber. The message is successfully decrypted by combining coherent detection and our proposed blind decryption algorithms, which can successfully separate the chaotic carrier and the message with the bit-error-rate (BER) below the forward error correction (FEC) threshold. Experimental results show that the coherent detection combined digital signal processing algorithms may be a possible way to promote the practical applications of chaotic optical communication in the future. In addition, this paper reveals that the security of the CMS encryption may be not high enough for those systems requiring rigorous confidentiality. Subsequently, we further discuss the bottlenecks encountered in current high-speed chaotic optical communication systems and analyze how to improve and weight the security and practicability.

Artificial intelligence enhances the performance of chaotic baseband wireless communication

Some new findings for chaos-based wireless communication systems have been identified recently. First, chaos has proven to be the optimal communication waveform because chaotic signals can achieve the maximum signal to noise ratio at receiver with the simplest matched filter. Second, the information transmitted in chaotic signals is not modified by the multipath wireless channel. Third, chaos properties can be used to relief inter-symbol interference (ISI) caused by multipath propagation. Although recent work has reported the method of obtaining the optimal threshold to eliminate the ISI in chaos-based wireless communication, its practical implementation is still a challenge. By knowing the channel parameters and all symbols, especially the future symbol to be transmitted in advance, it is almost an impossible task in the practical communication systems. Owning to Artificial intelligence (AI) recent developments, Convolutional Neural Network (CNN) with deep learning structure is being proposed to predict future symbols based on the received signal, so as to further reduce ISI and obtain better bit error rate (BER) performance as compared to that used the existing sub-optimal threshold. The feature of the method involves predicting the future symbol and obtaining a better threshold suitable for time variant channel. Numerical simulation and experimental results validate our theory and the superiority of the proposed method.

Wireless Chaos-Based Communication System: Literature Review

Since the early 1990s, a slew of chaotic-based communication systems have been proposed, all of which take advantage of chaotic waveform properties. The inspiration stems from the substantial benefits that this form of nonlinear signal offers. Many communication schemes and applications have been specifically designed for chaos-based communication systems to achieve this goal, with energy, data rate, and synchronization awareness being taken into account in most designs. However, non-coherent chaos-based systems have recently received a lot of attention in order to take advantage of the benefits of chaotic signals and non-coherent detection while avoiding the use of chaotic synchronization, which has poor performance in the presence of additive noise. This paper provides a thorough examination of all wireless radio frequency chaos-based communication systems. It begins by describing the difficulties of chaos implementations and synchronization processes, then moves on to a thorough literature review and study of chaos-based coherent techniques and their applications.

Secure chaotic communication based on extreme multistability

Extreme multistability is the coexistence of a large number of attractors which can be reached by varying initial conditions. In this paper we show how this fascinating phenomenon can be used for secure communication. The main advantage of the communication system based on extreme multistability over a conventional chaos-based communication system is its exceptionally high security. The proposed system consists of two identical six-order oscillators; one in the transmitter and another one in the receiver, each exhibiting the coexistence of a large number of chaotic attractors. The oscillators are synchronized using a private channel through one of the system variables, while the information is transmitted via a public channel through another variable. The information is encrypted by varying the initial condition of one of the state variables in the transmitter using a chaotic map, adhering message packages in a staggered form to the coexisting attractors within the same time series of another state variable, which leads to switching among the coexisting chaotic attractors. To ensure communication security, the duration of the packages is shorter than synchronization time, so that synchronization attacks are ineffective.

Multi‐carrier chaotic communication scheme for underwater acoustic communications

Multi-carrier (MC) and spread-spectrum (SS) are two good technologies for underwater acoustic (UWA) communications. In this study, the authors propose a novel MC chaos modulation scheme, which combines code-shifted differential chaos shift keying (CS-DCSK) with orthogonal frequency division multiplexing (OFDM), namely MC-CS-DCSK. The proposed scheme exploits the orthogonal characteristic of the Walsh code to superimpose the chaotic reference chips and the information bearing chips in the same time/frequency unit. Besides, a cyclic-shift interleaver is used on chips to harvest frequency diversity. To the in-depth understanding of the proposed system, the bit error rate (BER) of the proposed system under Gaussian channels and multipath Rayleigh fading channels are derived and verified by simulation. Furthermore, the spectral efficiency of the proposed system is analysed and compared with some existing chaos-based communication systems. Finally, they study BER performance of the system under UWA channels and compare it with traditional MC direct sequence SS and OFDM-based MC-DCSK systems. Simulation results show that the system has good robustness under time-varying UWA channels.

Multiscroll chaotic system with sigmoid nonlinearity and its fractional order form with synchronization application

In this paper, a multiscroll snap oscillator with hyperbolic tangent function is proposed. There is no limitation in the number of scrolls and it can be increased by proper choice of a specific function. The Lyapunov exponents of the proposed system are obtained to testify the chaotic behavior of the system. Fractional order multiscroll system is derived from its integer order model by using the Adams–Bashforth–Moulton algorithm. A new scheme is applied in order to investigate the synchronization of the multiscroll systems. The main objective of the paper is to propose a multiscroll attractor and show that the number of scrolls can be controlled by the only nonlinear function. Such systems are less investigated in the literatures and has many real time applications like image and voice encryption, random number generators, chaos based communication systems and so on.

Spectral characteristics of a general piecewise linear chaotic signal generator

The Power Spectral Density (PSD) of the transmitted signals is a fundamental aspect in the performance evaluation of general communication systems. This way, when it comes to chaos-based communication systems, it is relevant to analytically obtain the PSD of chaotic signal generators. In particular, a number of results for piecewise-linear maps were recently obtained. In the present paper, we deduce the PSD for a general family of such maps composed by an arbitrary number of segments, with positive or negative slopes. Numerical examples illustrate the analytical results and show the diversity of attainable spectra.