Chaos-based Communication Research Articles

A new 4D hyperchaotic system with high complexity

In chaos engineering, especially for chaos-based communication, chaotic systems require high complex, strong robustness and well-distributed bandwidth. In this paper, we present a new four-dimensional (4D) hyperchaotic system, which satisfies these three significant properties at the same time. Instead of traditional evaluation method of the positive Lyapunov exponents, the complexity of the system is measured by the topological entropy. We find out that it has much larger topological entropy and Kaplan–Yorke dimension compared with the systems reported before, therefore it may have better engineering application value.

A new encoding and switching scheme for chaos-based communication

Many communication systems based on the synchronization of chaotic systems have been proposed as an alternative spread spectrum modulation that improves the level of privacy in data transmission. However, due to the lack of robustness of complete chaotic synchronization, even minor channel impairments are enough to hinder communication. In this paper, we propose a communication system that includes an adaptive equalizer and a switching scheme to alter between a chaos-based modulation and a conventional one, depending on the communication channel conditions. Simulation results show that the switching and equalization algorithms can successfully recover the transmitted sequence in different nonideal scenarios.

Chip Averaging Chaotic ON–OFF Keying: A New Non-Coherent Modulation for Ultra Wide Band Direct Chaotic Communication

This letter proposes a new adaptive threshold modulation scheme, called chip averaging chaotic ON–OFF keying (CA-COOK). This new scheme is applied to non-coherent modulations in ultra-wideband direct chaotic communication. Mainly, the proposed method deals with the “estimation problem” caused by the bit energy variation of the chaotic carrier signal. This is completed by adopting the Cell Averaging Constant False Alarm Rate paradigm used in radar, and each bit period is divided into several chips, where one of those chips is bearing the information. Bit-error-rate performance in additive-white-Gaussian-noise, two-path Rayleigh, and IEEE802.15.4a office NLOS channel models, is analyzed and compared with well-known and challenging chaos-based communication systems. Simulation results show the effectiveness of the proposed CA-COOK.

Chaos-based wireless communication resisting multipath effects.

In additive white Gaussian noise channel, chaos has been shown to be the optimal coherent communication waveform in the sense of using a very simple matched filter to maximize the signal-to-noise ratio. Recently, Lyapunov exponent spectrum of the chaotic signals after being transmitted through a wireless channel has been shown to be unaltered, paving the way for wireless communication using chaos. In wireless communication systems, inter-symbol interference caused by multipath propagation is one of the main obstacles to achieve high bit transmission rate and low bit-error rate (BER). How to resist the multipath effect is a fundamental problem in a chaos-based wireless communication system (CWCS). In this paper, a CWCS is built to transmit chaotic signals generated by a hybrid dynamical system and then to filter the received signals by using the corresponding matched filter to decrease the noise effect and to detect the binary information. We find that the multipath effect can be effectively resisted by regrouping the return map of the received signal and by setting the corresponding threshold based on the available information. We show that the optimal threshold is a function of the channel parameters and of the information symbols. Practically, the channel parameters are time-variant, and the future information symbols are unavailable. In this case, a suboptimal threshold is proposed, and the BER using the suboptimal threshold is derived analytically. Simulation results show that the CWCS achieves a remarkable competitive performance even under inaccurate channel parameters.

Electronic implementation of a practical matched filter for a chaos-based communication system

Presented is an electronic implementation of a matched filter intended for chaos-based communication systems. While implementing the transmitter side of such systems is relatively trivial, the receiver has proven challenging to develop. Most chaotic systems lack a known fixed basis function, making it difficult to develop a matched filter for them. Instead, their receivers rely on more complicated or less effective techniques to compensate for the presence of noise. However, a previously developed manifold piecewise linear chaotic system has been shown to have an exact analytic solution. This solution has enabled the development of a matched filter for use in any communication system based on this chaotic system. The original communication system operated at a fundamental frequency of 84 Hz, much too low for any practical applications. Therefore, newer communication systems have been designed to operate at higher frequencies. In this work, the performance of this matched filter has been evaluated with a 18.4 kHz chaotic oscillator.

Secure communications of CAP-4 and OOK signals over MMF based on electro-optic chaos.

Chaos-based secure communication can provide a high level of privacy in data transmission. Here, we experimentally demonstrate secure signal transmission over two kinds of multimode fiber (MMF) based on electro-optic intensity chaos. High-quality synchronization is achieved in an electro-optic feedback configuration. Both 5 Gbit/s carrier-less amplitude/phase (CAP-4) modulation and 10 Gbit/s on-off key (OOK) signals are recovered efficiently in electro-optic chaos-based communication systems. Degradations of chaos synchronization and communication system due to mismatch of various hardware keys are also discussed.

Bit-Error-Rate Evaluation of High-Efficiency Differential-Chaos-Shift-Keying System Over Wireless Channels

A high-efficiency differential-chaos-shift-keying (HE-DCSK) system has been proposed previously for the improvement of both bit-rate and bit-error-rate (BER) performance in comparison with the conventional DCSK system. This improvement made HE-DCSK be a promising solution for chaos-based communications. However, the performance of this system was just investigated under an additive white Gaussian noise (AWGN) channel. This is main motivation for our work to evaluate the performance of HE-DCSK over a typical wireless channel which is simultaneously affected by white noise, fading, multipath, and delay spread. The operation of the transmitter and receiver over the wireless channel is modeled and described. The BER performance is evaluated by theoretical analysis using Gaussian approximation and discrete integration. The numerical results obtained by Monte Carlo simulations are presented to verify the analyzed performance. Obtained results point out that the HE-DCSK system not only performs better than other DCSK-based ones under wireless channels but also can exploit the multipath characteristic to improve the performance.

Class of novel broadband chaos‐based coherent communication systems

As opposed to chaotic communication systems where a message signal directly modulates a broadband chaotic signal, it is also possible to indirectly utilise a chaotic signal to form a chaos-based communication system. This study proposes a class of novel broadband chaos-based coherent communication systems and demonstrates that their theoretical probability of error expressions match those of their counterpart conventional narrowband systems in the additive white Gaussian noise and the Rayleigh flat fading channel. The results are confirmed with the corresponding empirical bit error rate (BER) simulations. It is demonstrated that the chaos-based quadrature phase shift keying system offers an overall best performance while the chaos-based amplitude shift keying and frequency shift keying equivalent systems offer a possibility of performance optimisation. Most importantly, it is shown that the proposed systems outperform the chaotic communication systems in terms of BER while also being more practicable. The proposed systems thus hold high promise as the chaotic communication systems pose implementation difficulties, lack robust synchronisation techniques and are generally considered of academic interest only.

White Gaussian Chaos

A discrete-time white Gaussian noise (WGN) is a random process with impulsive autocorrelation function. Also, the random variables obtained by sampling the process at any time instants are jointly Gaussian. WGN is widely used to model noise in engineering and physics. In this letter, we propose a way to generate chaotic signals that behave like WGN, due to the features of its autocorrelation function and its invariant density. From the tent map and by using as conjugacy map transformations commonly employed to random variables, we obtain a white Gaussian chaos (WGC) map. Numerical simulations are shown to illustrate the technique. WGC can be an interesting choice for chaos generator in chaos-based communication systems.

Synchronization and chaotic communication in nonlinear circuits with nonlinear coupling

In this paper, an experimental realization of chaotic synchronization through nonlinear coupling is presented. This proposed novel method is illustrated in the inductor-free analog model of the Chua’s circuit with threshold nonlinearity. By choosing a different nonlinear coupling, i.e., max (x), min (x), pair of diodes, superdiode and threshold-limited control in bidirectionally coupled systems, we observe different kinds of synchronization. The dynamics of the coupled chaotic system is corroborated through numerical and experimental studies. Further, we show the feasibility of the proposed model for chaos-based secure communication via a threshold-limited coupling. The communication performance of different signal, namely sine and pulse amplitude modulation signal, is demonstrated and verified using multisim circuit simulation.

Design and Analysis of an OFDM-Based Short Reference Quadrature Chaos Shift Keying Communication System

In this paper, a new non-coherent chaos-based digital communication system combined short reference Quadrature chaos shift keying with orthogonal frequency division multiplexing named (OFDM-SRQCSK) is presented. This system is an extension of short reference Quadrature chaos shift keying (SR-QCSK) modulation by sending parallel information sequences with one chaotic reference sequence over the selected subcarrier frequencies. The proposed system enhanced the spectral efficiency and the energy saving of the conventional QCSK and SR-QCSK systems. In the proposed system, the information rate and energy saving improvement factors are derived comparing with QCSK system. Furthermore, the bit error rate (BER) analytic expressions for OFDM-SRQCSK system are derived in additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. The simulation results proved that the BER analytics match the Monte-Carlo simulations with average relative differences about 0.07 and 0.1 dB under AWGN and multipath fading channel respectively.

On-chip optoelectronic feedback in a micropillar laser-detector assembly

Implementing time-delayed feedback in optoelectronic circuits allows one to uncover the rich physics and application potential of nonlinear dynamics. Important feedback effects are, for instance, the generation of broadband chaos, or laser self-pulsing. We explore the effect of optoelectronic feedback in an ultracompact microlaser–microdetector assembly operating in the regime of cavity quantum electrodynamics (cQED). This system is used to generate self-pulsing at MHz frequencies in the emission of a microlaser, which is qualitatively explained by a rate equation model taking cQED effects into account. The results show promise for exploring chaos in ultracompact nanophotonic systems and for technological approaches toward chaos-based secure communication, random number generation, and self-pulsed single photon sources on a highly integrated semiconductor platform.

Photon number distribution and second-order degree of coherence of a chaotic laser: analysis and experimental investigation

The researches on higher-order coherence and quantum statistics of light field are the important researching issues in quantum optics. In 1956, Hanbury-Brown and Twiss (HBT) (Hanbury-Brown R, Twiss R Q 1956 Nature 177 27) revolutionized optical coherence and demonstrated a new form of photon correlation. The landmark experiment has far-reaching influenced and even inspired the quantum theory of optical coherence that Glauber developed to account for the conclusive observation by HBT. Ever since then, the HBT effect has motivated extensive studies of higher-order coherence and quantum statistics in quantum optics, as well as in quantum information science and cryptography. Based on the HBT scheme, the degree of coherence and photon number distribution of light field can be derived from correlation measurement and photon counting technique. With the rapid development of the photoelectric detection technology, single-photon detection, which is the most sensitive and very widespread method of optical measurement, is used to characterize the natures of light sources and indicate their differences. More recently, HBT scheme combined with single-photon detection was used to study spatial interference, ghost imaging, azimuthal interference effect, deterministic manipulation and detection of single-photon source, etc. Due to broadband RF spectrum, noiselike feature, hypersensitivity to the initial conditions and long-term unpredictability, chaotic laser meets the essential requirements for information security and cryptography, and has been developed in many applications such as chaos-based secure communications and physical random number generation, as well as public-channel secure key distribution. But the research mainly focused on macroscopic dynamics of the chaotic laser. Moreover, the precision of measurement has reached a quantum level at present. Quantum statistcs of light field can also uncover profoundly the physical nature of the light. Thus, it is important to exploit the higher-order degree of coherence and photon statistics of chaotic field, which contribute to characterizing the field and distinguishing it from others. In this paper, photon number distribution and second-order degree of coherence of a chaotic laser are analyzed and measured based on HBT scheme. The chaotic laser is composed of a distributed feedback laser diode with optical feedback in fiber external cavity configuration. The bandwidth of the chaotic laser that we obtain experimentally is 6.7 GHz. The photon number distribution of chaotic laser is fitted by Gaussian random distribution, Possionian distribution and Bose-Einstein distribution. With the increase of the mean photon number, the photon number distribution changes from Bose-Einstein distribution into Poissonian distribution and always accords with Gaussian random distribution well. The second-order coherence g(2)(0) drops gradually from 2 to 1. By changing the bias current (I = 1.0Ith-2.0Ith) and feedback strength (010%), we compare and illustrate different chaotic dynamics and g(2)(0). From low frequency fluctuation to coherence collapse, the chaotic laser shows bunching effect and fully chaotic field can be obtained at the broadest bandwidth. Furthermore, the physical explanation for sub-chaotic or weakening of bunching effect is provided. It is concluded that this method can well reveal photon statistics of chaotic laser and will open up an avenue to the research of chaos with quantum optics, which merges two important fields of modern physics and is extremely helpful for the high-speed remote chaotic communication.

Time-Scale Independent Permutation Entropy of a Photonic Integrated Device

A new measure of complexity, time-scale independent permutation entropy, has been developed and applied to fully characterize the relative complexity of the emission of a four-section photonic integration chip (PIC) laser. The new technique allows the relative complexity of dynamics with different characteristic time scales to be compared. The analysis reveals the range of possible outputs the PIC device can produce over a three-dimensional operating parameter space. From the perspective of using such devices as synchronized transmitter and receiver pairs in chaos-based secure communication applications, a region of uninterrupted, highly complex, unpredictable dynamics has been identified for the device. Regions surrounding this desired complex state show intermittency, pulse packages, and limit-cycle oscillations. The effect of varying the laser's biasing current, feedback strength, and feedback phase reveals the extent of the short-cavity regime and provides insight to the fundamental physics driving the integrated device dynamics.

Chaos Communication: A Case of Statistical Engineering

The paper gives a statistically focused selective view of chaos-based communication which uses segments of noise-like chaotic waves as carriers of messages, replacing the traditional sinusoidal radio waves. The presentation concerns joint statistical and dynamical modelling of the binary communication system known as “chaos shift-keying”, representative of the area, and leverages the statistical properties of chaos. Practically, such systems apply to both wireless and optical laser communication channels. Theoretically, the chaotic waves are generated iteratively by chaotic maps, and practically, by electronic circuits or lasers. Both single-user and multiple-user systems are covered. The focus is on likelihood-based decoding of messages, essentially estimation of binary-valued parameters and efficiency of the system is in terms of the probability of bit decoding error. The emphasis is on exact theoretical results for bit error rate, their structured approximations and engineering interpretations. Design issues, optimality of performance, interference and fading are other topics considered. The statistical aspects of chaotic synchronization are involved in the modelling of optical systems. Empirical illustrations from an experimental laser-based system are presented. The overall aim is to show the use of statistical methodology in unifying and advancing the area.

Synchronizations and secure communication applications of a third degree Malasoma system with chaotic flow

Chaos-based secure communication systems are alternative of standard spread-spectrum systems that enable spreading the spectrum of the information signals and encrypting information signals with simple and inexpensive chaotic circuitry. In secure communication area, like Lorenz, Chua, Rossler, Duffing etc., classical systems are widely used. Malasoma chaotic system is topologically simple but their dynamical behaviors are very rich and its synchronization and secure communication applications has not seen in literature. This paper aims for introducing a new chaotic system which is able to use as alternative to classical chaotic systems into secure communication fields. Mentioned novel model is also supported with electronic circuit model simulations that aim for being a synchronization circuit model using P-C method as chaotic masking communication circuit model. Modelling, synchronization and secure communication applications of Malasoma are realized respectively in MATLAB-Simulink environment. Retrieved results show that this novel chaotic system is able to use in secure communication fields.

Frequency-translated differential chaos shift keying for chaos-based communications

In this paper, an efficient, differential chaos shift keying (DCSK) method, known as frequency-translated DCSK (FT-DCSK), is proposed. Ordinary DCSK is difficult to incorporate using CMOS integrated circuits because of the long wideband delay line that is required to separate reference and data chaotic sequences into two time-shifted slots of each frame. Another disadvantage of DCSK is the repetition of chaotic sequence in reference and data slots, which decreases data security and bandwidth efficiency. In the proposed method, the usage of a delay line is avoided by frequency translation of the reference chaotic sequence over the frame time. Frequency translation is achieved by amplitude modulation of two orthogonal sine carriers with reference chaotic sequences. As a result, the FT-DCSK scheme avoids the usage of wideband delay lines and increases the bandwidth efficiency. The analytical expression for bit error rate (BER) performance is derived and compared with simulation results. Finally, the obtained performance results are compared with similar modulation schemes. The proposed FT-DCSK scheme exhibits promising performance based on BER results.

Effect of Gain Nonlinearity on Time Delay Signature of Chaos in External-Cavity Semiconductor Lasers

The effects of gain nonlinearity on the time delay signature (TDS) of both intensity and phase chaos in semiconductor lasers (SLs) with optical feedback are investigated numerically. The SLs subject to single-path feedback are mainly considered, and SLs with dual-path feedback are also discussed for the sake of generality. The TDS is evaluated via both auto-correlation function (ACF) and permutation entropy function. It is found that the TDS is more sensitive to nonlinear gain factor (NGF) for large injection current and low feedback strength. For given feedback strength, the peak heights of ACF for both intensity and phase chaos around TDS can be decreased by using SL with low NGF, especially when the injection current is relative high. Furthermore, with low NGF, successful TDS concealment can be achieved in wider region in the parameter planes of feedback strength and injection current. Hence, careful selection of an internal parameter is an effective candidate for TDS concealment in wider parameter region, which is complementary to the existing techniques by controlling the external parameters, and thus is highly desirable for expanding the key space for chaos-based secure communication.

A digital bandlimited chaos-based communication system

In recent years, many communication systems that use a function to encode an information in a chaotic signal were proposed. Since every transmission channel is bandlimited in nature, it is required to determine and to control the chaotic signal spectrum. This way, a bandlimited chaos-based communication system (CBCS) was proposed using digital filters and chaotic synchronization. As the filters modify the original chaotic system, it is necessary to study how their insertion affects chaotic synchronization. In this work, we present a digital discrete-time bandlimited CBCS system analysis, considering practical settings encountered in conventional communication systems. The proposed system is based on master–slave chaotic synchronization and the required conditions for its synchronization is obtained analytically for a general K-dimensional chaos generator map. The performance of this system is evaluated in terms of bit error rate. As a way to improve the signal to noise ratio, we also propose to filter the out-of-band noise in the receiver. Numerical simulations show the advantages of using such a scheme.

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.