Chaotic Spreading Research Articles

Analysis of Chaos-Based Code Tracking Using Chaotic Correlation Statistics

A new statistical method for examining correlation of chaos-based systems is presented and the proposed method is applied to the analysis of a chaos-based noncoherent tracking loop. The motivation behind this approach is the lack of accuracy in the treatment of chaos-based code tracking when conventional correlation analysis is used. The proposed method has it roots in the chaotic correlation statistics (CCS) of the chaotic spreading code. CCS can be used for chaotic as well as any other nonbinary spreading code. The accuracy of the proposed model is shown to be very high by means of comparison with simulation and implementation results. The distributions of two critical points on S-curve have been derived and shown to closely match the simulation results as well as hardware implementation results. This paper highlights the need for a statistical approach for accurate treatment of nonbinary spreading codes specifically chaos-based spreading codes.

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.

Generation of orthogonal codes with chaotic optical systems

We propose to use an electro-optic oscillator based on two Mach-Zehnder modulators in two different delayed feedback loops to generate two orthogonal chaotic spreading sequences (codes). We numerically demonstrate, for such codes, spectrally efficient multiplexing and demultiplexing of two digital data streams at multi-Gb/s rates using chaos synchronization and covariance-based detection.

Research of chaotic spread spectrum ranging schemes

Chaotic sequence,with its good correlation performance,being sensitive to initial condition and hard to be decrypted,has been used as an ideal spread spectrum code in direct spread spectrum communication system.In order to take full advantages of the chaotic sequences ranging,based on the analysis of the basic principle of the pseudo code ranging and by using the digital matched filter to achieve the chaotic sequences acquisition,two chaotic spread spectrum ranging schemes were designed and their ranging processes,acquisition time and ranging accuracy were analyzed.The results show that taking the chaotic code as the spread spectrum code of ranging is feasible,with the strongpoint of high security,low interception,and it is also suitable for multi-target ranging,etc.

Chaotic spread spectrum-based model design and simulation of multi-user emergency communication system

In view of the present issue that channel noise seriously affects the communication quality of emergency communications,this paper studied the channel noise source and essential characteristics of emergency communication system and proposed a channel model of emergency communication,discussed the principles of interference noise suppression in chaotic spread-spectrum emergency communication system,designed a multi-user simulation model of chaotic spread spectrum emergency communications system,and advanced its Bit Error Ratio(BER) simulation and analysis in typical channel interference noise.The simulation results show that the chaotic spread spectrum communication system can effectively suppress strong noise interference and improve system BER performance in emergency communications significantly.

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.

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.

Channel Identification Using Chaos for an Uplink/Downlink Multicarrier Code Division Multiple Access System

A scheme of chaotic spreading sequence for multicarrier code division multiple access system (MC-CDMA) is proposed to estimate the transmission channel. This system spreads spectrum and identifies the channel, simultaneously. The proposed scheme uses a chaotic sequence generated by a logistic map as a training signal and estimate channel parameters according to dynamics of the chaotic sequence. Encoding data by chaotic sequences is first built and then the orthogonal codes are used to spread the encrypted data for multiusers scheme. At the reception, first the channel parameters are identified using a training chaotic sequence in order to equalize the received data, and then the encrypted information is decoded for the desired user. The studies reveal that the proposed system (chaos plus orthogonal codes) significantly outperforms the Walsh- Hadamard code spreading in MC-CDMA system. The performance of the systemis considered in the multiuser case by means of simulation. The simulation result shows that the proposed chaotic code spreading approach for channel identification achieves significant improvement in the channel identification, comparing to using others training sequence or the least square method.

Anti-jamming performance analysis of optimal chaotic spread spectrum sequences

In order to improve the anti-jamming performance of Direct Sequence/Code Division Multiple Access (DS/CDMA) system based on chaotic sequences,an optimization algorithm for choosing chaotic sequences was proposed.The optimal improved Logistic-map chaotic sequences were applied to DS/CDMA system,and the anti-jamming performances were studied under different kinds of jamming such as single-frequency interference,partial-band interference,and impulsive interference.The results show that the optimal improved Logistic-map chaotic sequences have larger capacity,excellent anti-jamming ability,and lower Bit Error Rate (BER).Compared with the Gold sequence,with the same BER,SNR can be improved at least 2 dB,so they are more suitable for DS/CDMA system and anti-jamming technology.

$M$-DCSK-Based Chaotic Communications in MIMO Multipath Channels With No Channel State Information

We consider chaotic digital communications in multiple-input-multiple-output (MIMO) wireless multipath fading channels. In particular, we focus on systems that employ M -ary differential chaos shift keying (M-DCSK). We consider two transceiver schemes, both of which require no channel state information at either the transmitter or the receiver. The first one employs a distinct chaotic sequence at each transmit antenna to spread the same data symbol and transmits omnidirectionally. At each receive antenna, the corresponding differential detection statistic is formed, and these statistics are then combined with equal gain for symbol detection. The second scheme employs a single chaotic spreading sequence and makes use of adaptive transmit and receive beamforming. The beamformers are updated by using a simple stochastic gradient method that is based on the received signal power and a finite-rate feedback strategy. Simulation results show that both schemes can effectively exploit the spatial diversity of the underlying MIMO system, and the adaptive beamforming scheme significantly outperforms the omnidirectional transmission.

Channel Identification Using Chaos for an Uplink/Downlink Multicarrier Code Division Multiple Access System

A scheme of chaotic spreading sequence for multicarrier code division multiple access system (MC-CDMA) iproposed to estimate the transmission channel. This systespreads spectrum and identifies the channel, simultaneously. The proposed scheme uses a chaotic sequence generated by a logistic map as a training signal and estimate channel parameters according to dynamics of the chaotic sequence. Encoding data by chaotic sequences is first built and then the orthogonal codes are used to spread the encrypted data for multiusers scheme. At the reception, first the channel parameters are identified using a training chaotic sequence in order to equalize the received data, and then the encrypted information is decoded for the desired user. The studies reveal that the proposed system (chaos plus orthogonal codes) significantly outperforms the Walsh-Hadamard code spreading in MC-CDMA system. The performance of the system is considered in the multiuser case by means of simulation. The simulation result shows that the proposed chaotic code spreading approach for channel identification achieves significant improvement in the channel identification, comparing to using others training sequence or the least square method.

Performance Analysis of MIMO MC-DS/CDMA System Using Chaotic Spreading Sequence

1 Abstract— This paper presents a novel chaotic spreading sequence for multiple input multiple output multi-carrier direct sequence code division multiple access (MIMO MCDS/CDMA) systems. The effect of multiple access interference can be mitigated by choosing the spreading sequences with appropriate cross-correlation properties. The performance of the system is analysed in multiuser scenario with the aid of simulation. The simulation results show that the proposed chaotic code spreading approach achieves a significant improvement in system utility and combats multiple access interference (MAI). The analysis reveals that the proposed system achieves significant performance improvement compared to Walsh Hadamard spreading code in MIMO MCDS/CDMA systems. Index Terms—MC-DS/CDMA, Chaotic code, MIMO, Spreading sequence, MAI

Performance Analysis of Complex CDMA Using Complex Chaotic Spreading Sequence with Constant Power

A performance of the complex chaotic spreading sequences with constant power is investigated in a chip-synchronous complex CDMA with a complex scrambling. We estimate a signal-to-interference ratio (SIR) and a bit error rate (BER). An exact invariant measure of the complex chaotic spreading sequence can be obtained. Therefore, the SIR can be calculated analytically. The result can be used as one of the criteria for evaluating the performance of the complex CDMA using the chaotic spreading sequences.

Balance analysis of four digital chaotic spread spectrum sequences

The research on the balance of chaotic sequence has important significance to spread-spectrum communication. The relationship between the balance and the parameter of four typical chaotic maps (Chebyshev, improved Logistic, Logistic and Tent) was discussed. The new numeric ranges of initial value and fractal parameter were decided, which provided reference for the generation of chaotic spread-spectrum sequence. Through the graphs of the four chaotic sequences' balance and the error-bit rate performance of these systems with the four chaotic sequences' map parameters, the new numeric ranges were validated. Both simulation results and the analysis show that the balance of Chebyshev is the best.

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.

基于双混沌置乱和扩频调制的彩色图像盲水印算法

基于双混沌置乱和扩频调制的彩色图像盲水印算法

M-ary chaotic spread spectrum Pattern time delay shift coding scheme for multichannel underwater acoustic communication

Pattern time delay shift coding scheme uses the time delay shift values of the Pattern to code the information whose anti-ISI (intersymbol interference) ability is related to the kind and duration of the Pattern. Spread spectrum communications is competent for long-range underwater acoustic communications for its spread spectrum gain, but the low communications rate seriously restricts its application. The proposed new scheme is adapted to the underwater acoustic environment, which integrates the spread spectrum with Pattern time delay shift coding and works at M-ary mode spread spectrum and several communications channels. The scheme could achieve good performance of the spread spectrum and also improve the data transfer rate. The results of lake trial show that the M-ary chaotic spread spectrum Pattern time delay shift coding scheme is robust and feasible.

Chaos-based multi-user time division multiplexing communication system

A chaos-based multi-user time division multiplexing (TDM) communication system has been proposed and its benchmark performance compared to that of the chaos-based direct sequence code division multiple access (DS-CDMA) system in the noisy and Rayleigh fading channels. The benchmark performance of the systems is investigated in terms of the bit error rate (BER) under the assumption of perfect synchronisation. The chaotic spreading signals, used to encrypt the binary messages, are generated using the logistic map. The degradation in performance of the systems in the Rayleigh fading channel when compared with the noisy channel is demonstrated. Furthermore, it is shown that in both noisy and Rayleigh fading channels, the chaos-based multi-user TDM system outperforms the chaos-based DS-CDMA system for a large number of users in the system, whereas the chaos-based DS-CDMA system yields better performance for low user numbers. The overall BER performance degradation for the chaos-based DS-CDMA multi-user system in noisy and Rayleigh fading channels is characterised by the flattening of the BER curves at low levels of noise due to the prevailing effects of the interuser interferences.

Performance Analysis and Optimization of Multi-User Differential Chaos-Shift Keying Communication Systems

Bit-error rate (BER) performance of a generalized multi-user differential chaos-shift-keying (DCSK) digital communication system is analyzed and optimized in this paper using baseband models. The generalized version of DSCK involves use of multiple nonrepeating chaotic spreading segments and energy adjustments and allows considerable system optimization. Theoretical BER analysis of correlation decoders based on a mathematical two-stage exact conditional approach is given as the foundation of subsequent performance studies. The consequent fully theoretical BER result gives an odd-symmetric spreading map condition for the BER to be unaffected by the mix of transmitted bits. The basis of the theoretical result is used to improve on the traditional simple Gaussian approximation (SGA) approach to the calculation of BER; this is inaccurate because it does not recognise the chaotic dynamics of DCSK. To overcome this drawback, a dynamically improved Gaussian approximation (DIGA) is developed. The DIGA approach is compared with the SGA approach, with simulation results demonstrating its accuracy and efficiency, certainly for more than five to ten users. Not only does the DIGA approach provide a more accurate BER than the SGA approach, its simple form also makes optimization of the DCSK system practically possible. The BER lower bound for the multi-user DCSK system is deduced from the DIGA approach. It is shown how the parameters and structure of the multi-user DCSK communication system can be optimized to achieve this lower bound. The work gives an exact theoretical basis of DCSK and covers several aspects which have not been treated in earlier research or have been inexactly treated.