Chaotic Direct Sequence Spread Spectrum Research Articles

Acquisition of Time and Doppler Shift in WFRFT Encrypted Chaotic Direct Sequence Spread Spectrum System

Weighted fractional Fourier transform encrypted chaotic direct sequence spread spectrum (WFRFT-CD3S) signal is aperiodic and complex Gaussian distributed. The aperiodicity and complex Gaussian distribution are conducive to the covert transmission of information but also make it difficult to acquire the WFRFT-CD3S signal. An acquisition method implemented in two steps is proposed to acquire the Doppler-shifted WFRFT-CD3S signal. First, a bidirectional correlation search method is proposed to align the received signal with the local spreading sequence in the time domain. The correlation peak attenuation caused by the Doppler frequency shift is eliminated by differential. Second, the accumulated phase angle caused by the Doppler frequency shift is obtained by the differential correlation value between the aligned received signal and the local spreading sequence. Then, the Doppler frequency shift is estimated by the accumulated phase angle. The detection probability, the false alarm probability, and the root mean square error (RMSE) of the Doppler shift estimation are analyzed theoretically and simulated. The theoretical results are verified by simulation. Theoretical results and simulations show that the detection probability is higher than 0.999, the false alarm probability is less than 0.001, and the RMSE of Doppler shift estimation is lower than 63 Hz when the signal-to-noise ratio is higher than -7.3 dB.

Enhancing the Security of Chaotic Direct Sequence Spread Spectrum Communication Through WFRFT

In this letter, the weighted fractional Fourier transform (WFRFT) is performed on the chaotic sequence to enhance the security of the chaotic direct sequence spread spectrum (CD3S) communication, and a WFRFT-CD3S system that spreads the information bits through the WFRFT-chaotic sequence is proposed. In the proposed system, the transmitter scrambles the phase space trajectory of the chaotic sequence through WFRFT and make the distribution of the transmitted signal be Gaussian-like. The receiver synchronizes the WFRFT-chaotic sequence through bidirectional correlation search and demodulates the information through the synchronized local WFRFT-chaotic sequence. Simulations are implemented to evaluate the security performance, synchronization performance, and demodulation performance of the proposed system.

A Synchronization Approach Based on Bidirectional Correlation Search for Aperiodic Chaotic Direct Sequence Spread Spectrum Signals

The chaotic direct sequence spread spectrum (CD3S) is one of the distinguished techniques providing physical layer secrecy and low probability of intercept (LPI) in wireless communication. Due to the noise-like and aperiodic characteristics of chaotic signals, the synchronization of CD3S signals is a challenging issue. A synchronization approach for aperiodic CD3S signals based on bidirectional correlation search (BDCS) is proposed. Through a joint acquisition of forward frequency domain matched filtering (FDMF) and backward FDMF, the synchronization module aligns received CD3S signals with local chaotic sequences without aid of the pilot signal. The probability distribution of correlator output is derived with additive white Gaussian noise and narrowband jamming. The probability of detection, probability of false alarm, and bit error rate are analyzed mathematically. An approximate solution of the local optimal acquisition threshold coefficient is obtained. These theoretical analyses are verified by numerical simulations, the results of which demonstrate that the proposed synchronization approach enables the CD3S system to resist interception and adapt to the environment with low signal-to-noise and signal-to-jammer ratios.

Unconventional direct acquisition method for chaotic DSSS signals

Considering the wide application of chaotic sequences, especially in chaotic direct-sequence spread-spectrum (DSSS) systems, it is important to guarantee an efficient and synchronous reception of chaotic DSSS signals. However, the sequence characteristics can decrease the performance in different acquisition aspects. Hence, we propose an unconventional direct acquisition method to improve systems that rely on chaotic DSSS signals. The proposed method outperforms similar methods in acquisition characteristics such as accuracy, speed, and detection probability.

Security Enhancement of Fix Chaotic-DSSS in WSNs

The security of the physical layer promises to provide secrecy for wireless communication. The chaotic direct sequence spread spectrum (chaotic-DSSS) is one of the distinguished techniques for providing secrecy in wireless communication. However, conventional chaotic-DSSS requires chip synchronization which makes this system complex to implement in wireless sensor networks (WSNs). This letter suggests using a fix chaotic-DSSS and also proposes a new method, called fake users , to enhance the security of the chaotic-DSSS based WSNs. The performance of the proposed method is theoretically investigated and validated through simulation. The results suggest that the proposed method can significantly improve the security of WSNs.

Chaotic direct-sequence spread-spectrum with variable symbol period: A technique for enhancing physical layer security

In chaotic direct-sequence spread-spectrum (DSSS) technique, chaotic sequences with typical properties such as aperiodic variation, wideband spectrum, good correlation, and initial condition sensitivity have been used as spreading codes in order to improve the security at physical layer. However, a number of recent studies have proved that an intruder can recover chaotic sequences by blind estimation methods and use the sequences to detect symbol period, which will result in the original data being exposed. To overcome this security weakness, this paper proposes a novel chaotic DSSS technique, where the symbol period is varied according to behavior of the chaotic spreading sequence in the communication process. The data with variable symbol period is multiplied with the chaotic sequence to perform the spread-spectrum process. Discrete-time models for the spreading scheme with variable symbol period and the despreading scheme with sequence synchronization are presented and analyzed. Multiple-access performance of the proposed technique in the presence of the additional white Gaussian noise (AWGN) is calculated by means of both theoretical derivation and numerical computation. Computer simulations are carried out and simulated performances are shown to verify the estimated ones. Obtained results point out that our proposed technique can protect the DSSS systems against the detection of symbol period from the intruder, even if he has full information on the used chaotic sequence.

Detectability of Chaotic Direct-Sequence Spread-Spectrum Signals

Chaotic spreading sequences were previously proposed for use in direct-sequence spread-spectrum (DSSS) communications systems, and it was suggested that the nonbinary nature of these sequences would result in an improvement in the low probability of intercept (LPI) performance of the signal. In this letter, we derive the structure of the optimum intercept receivers for chaotic DSSS signals in a statistical framework by exploiting the known probabilistic behavior of spreading sequences. A performance comparison between the optimal receivers and more practical suboptimum detectors—which overlook the multilevel nature of chaotic sequences—is also provided. The results imply that the use of chaotic spreading sequences would not help increase the covertness of DSSS signals.

Chaotic direct sequence spread spectrum for secure underwater acoustic communication

Direct sequence spread spectrum (DSSS) has been widely used in underwater acoustic (UWA) communications. In DSSS communications, spreading sequence’s period and chip rate are important characteristic parameters. However, these characteristic parameters may be detected in hostile environments due to the periodic nature of spreading sequence and their well-known construction process. In this paper, a novel chaotic direct sequence spread spectrum (CD3S) method is proposed for secure UWA communications. In the CD3S communications, chaotic sequences acting as encryption keys are used to encrypt the phases of transmitted signals. Consequently, the application of chaotic sequences disguises these obvious characteristic parameters of spread spectrum (SS) signals. It is difficult for unauthorized users to detect or intercept CD3S signal without knowledge of corresponding chaotic sequences. Hence, CD3S signal has a lower probability of detection and interception. Moreover, CD3S can achieve similar bit error ratio (BER) performance compared with DSSS in actual UWA communications. Also, the receivers that are suitable for DSSS communication can also be applied to CD3S communication. Numerical simulations demonstrate its excellent performance and potential applications in confidential UWA communications.

Blind Demodulation of Chaotic Direct Sequence Spread Spectrum Signals Based on Particle Filters

Applying the particle filter (PF) technique, this paper proposes a PF-based algorithm to blindly demodulate the chaotic direct sequence spread spectrum (CDS-SS) signals under the colored or non-Gaussian noises condition. To implement this algorithm, the PFs are modified by (i) the colored or non-Gaussian noises are formulated by autoregressive moving average (ARMA) models, and then the parameters that model the noises are included in the state vector; (ii) the range-differentiating factor is imported into the intruder’s chaotic system equation. Since the range-differentiating factor is able to make the inevitable chaos fitting error advantageous based on the chaos fitting method, thus the CDS-SS signals can be demodulated according to the range of the estimated message. Simulations show that the proposed PF-based algorithm can obtain a good bit-error rate performance when extracting the original binary message from the CDS-SS signals without any knowledge of the transmitter’s chaotic map, or initial value, even when colored or non-Gaussian noises exist.

Combined Equalization and Demodulation of Chaotic Direct Sequence Spread Spectrum Signals for Multipath Channels

Due to the inherent noise-like characteristic of chaotic signals and their sensitivity to the initial value, chaotic direct sequence spread spectrum (CD3S) signals have the advantages of a low probability of intercept (LPI) and a high level of security. Demodulation of non-cooperated CD3S signals is then a challenging issue. If the signal is sent though multipath channels, it is even more difficult for the receiver to demodulate it blindly. Based on the existing theories and methods, we focus more on signals passing through multipath channels. This paper presents an approach to achieve blind equalization and demodulation of CD3S signals through multipath channels. Multiple unscented Kalman filters (UKFs) are used to equalize and demodulate the CD3S signals for the unknown channel. This method can effectively demodulate the signals without any knowledge of the chaotic transmitter’s parameters, initial value, state equation, or the channel coefficients, even when the signal is severely distorted by the multipath channel. Simulation results demonstrate that this method gives faster convergence and better demodulation performance than existing methods for various channel conditions.

Hardware implementation for blind demodulation method for chaotic direct sequence spreadspectrum signals

In this paper, we design a field-programmable gate array (FPGA)-based hardware implementation for blind demodulation method for chaotic direct sequence spread spectrum (CD3S) signals. Both transmitter and receiver are designed. The transmitter can produce ten chaotic maps as the spreading sequence. In the receiver, the mathematic model of unscented Kalman filter (UKF) chaotic fitting is built and simplified for hardware implementation. The hardware structure of the receiver is based on this simplified model. For real time fitting different chaotic maps, a dynamic adjustment strategy of range-differentiating factor is proposed. The additove white Gausian noise (AWGN) and multipath channel experiments verify the anti-noise and anti-multipath performance of the UKF chaotic fitting method on one hand. On the other hand, the experiments verify the method can demodulate CD3S signals spread by all ten chaotic maps effectively.

Breaking a chaotic direct sequence spread spectrum communication system using interacting multiple model-unscented Kalman filter

In this paper, a new method to break chaotic direct sequence spread spectrum (CD3S) communication systems is proposed. Here, the CD3S communication system transmitting different information symbols is considered as a combination of two subsystems which are driven by two different chaotic dynamic models, respectively. At every single time moment, the CD3S signal can be regarded as generated by the subsystem corresponding to the information symbol transmitted. Then, based on the multiple model form of CD3S signals, an interacting multiple model unscented Kalman filter with model switching detection mechanism is exploited to track the CD3S signals. The l(2)-norm of tracking errors is used to choose the model which best matches the intercepted signals. Thus, the information symbols are recovered indirectly. Compared with the existing methods, the proposed algorithm can: (1) reduce the influence of a low spreading factor; (2) calculate the spreading factor using the length of time intervals between model switching; and (3) be more effective under scenarios of low signal-to-noise ratio or multipath fading. Simulation results verify the superiority of the proposed method.

Breaking chaotic direct sequence spreading spectrum communication systems using DM-UKF chaotic fitting method

In this paper, a dual model unscented Kalman filter chaotic fitting breaking method is proposed to break chaotic direct sequence spread spectrum communication systems in the cases of low spreading factor, low signal-to-noise ratio or severe multipath fading. Based on the characteristic that the range of information symbol is a finite set, the proposed algorithm fits the original chaotic signal through different filters which work in parallel. The fitting errors are used to choose the optimum matching filter, thus to estimate the information symbols. Furthermore, an error-controlling-factor is introduced to increase the distance of model based tracking errors, which can not only facilitate the information extracting process, but also reduce the influence of noise and multipath fading. Theoretical analysis and simulation results prove that the proposed algorithm is superior to the existing breaking method.

Breakability of chaotic direct sequence spreading spectrum secure system under multi-path fading channel

Blind demodulation (breaking) of chaotic direct sequence spread spectrum (CD3S) signals is a challenging and leading issue under multipath fading channel in the field of chaotic communication. Until now, there are neither equalization methods to remove the impact of the channel, nor the immediate breaking methods. Based on the existing study, the breakability of CD3S signals is analyzed under multipath fading channel by using unscented Kalman filter (UKF) chaotic fitting in this paper. Beginning with the state space equation for the CD3S signals in UKF chaotic fitting, the channel influence on the tracking error is analyzed in the process of UKF chaotic fitting, then the range of the message state estimation is derived, and finally a sufficient condition theorem is proposed for the CD3S signals to be broken. Simulation results show that CD3S signals can be broken successfully under the proposed condition with excellent performance of bit error rate (BER), no matter whether the channel characteristic is either time-invariant or time-variant.

A novel unified equalization and demodulation of chaoticdirect sequence spread spectrum signal based on state estimation

A novel unified algorithm based on state estimation was proposed for equalization and demodulation of chaotic direct sequence spread spectrum (CD3S) signal through a non-ideal channel. The algorithm uses the state equations of the channel and the CD3S signal, as well as the reciprocal relationship between equalization and demodulation. Multiple extended kalman filters (EKF) were used for equalizing the channel while demodulating the binary message simultaneously by implementing them in reciprocal interaction. This algorithm could not only overcome the impact brought about by non-ideal channel, such as multipath interference and channel noise, but also demodulate the binary message from CD3S signal. This unified approach utilizes the information more adequately and has better real-time performance than independent approaches. Simulation results demonstrated that the proposed algorithm has a fast convergence rate, and is resistant to the multipath effect without knowledge of channel characteristic and the noise, so the efficient and reliable transmission of the CD3S signal through the non-idea channel is realized.

Breaking a chaotic secure communication scheme

The chaotic direct sequence spread spectrum (CD3S) has been extensively studied and accepted as an approach of chaotic secure communication. However, we find that CD3S is insecure and present the results of breaking CD3S. A modified unscented-Kalman-filter chaos fitting method is proposed. With the proposed method, an intruder can use a different chaotic system to fit the transmitter's chaotic system and break the CD3S scheme without any knowledge of the chaotic transmitter's structure, parameters or initial value, even under the following conditions: (A) the chaotic spreading sequence is complex and generated by two chaotic maps; (B) there exists noise in the CD3S signal; (C) the CD3S signal is constructed in frames. Simulation results verify the method.

Breaking a chaotic direct sequence spreading spectrum secure communication system

In this paper, a novel method is proposed for the breaking of chaotic direct sequence spread spectrum (CD3S) secure communication system. Chaotic fitting is defined based on the concept of generalized synchronization, then the method based on unscented Kalman filter and chaotic fitting is presented based on the principle of CD3S and the characteristic that the information symbol varies slowly. Furthermore, addressing to the tracking error induced by the processing noise and chaotic fitting error, a modified unscented Kalman filter based on tracking-error-controlled factor is suggested. The CD3S is unmasked according to the error-amplitude of the tracking-error. We can extract the binary message signal from the CD3S signal without knowing either the structure or the parameters of the chaotic transmitter. Simulation results verify the method.

Detection performance of chaotic spreading LPI waveforms

Low probability of intercept (LPI) performance of a direct-sequence (DS) spread-spectrum (SS) system with chaotic spreading sequences is investigated in this paper. Several intercept receivers, including energy detectors, synchronous and asynchronous, coherent and noncoherent structures, which are typically used to detect binary DS SS signals, are examined here to detect the presence of chaotic DS SS signals. A simple detection approach using a binary correlating function to detect nonbinary chaotic sequences is proposed. The expressions of detection probabilities of chaotic spreading signals using those intercept receivers are derived. Comparisons between systems using chaotic and binary sequences are given in terms of the LPI performance, and the performance improvement with chaotic spreading sequences is observed.