Reference Chaotic Signal Research Articles

A New Receiver Design for Protograph-Coded Reference Reused DCSK Systems

In this letter, we investigate the performance of protograph-coded reference reused differential chaos shift keying (DCSK) systems to improve the transmission reliability. The traditional protograph-coded DCSK receiver does not take full advantage of the reused chaotic reference signals and hence cannot obtain desirable error performance. To solve this problem, we design a new receiver architecture called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">weighted reference estimation and iterative decoding (WRE-ID)</i> , which can universally improve the performance of protograph-coded reference reused DCSK systems over both multipath Rayleigh fading and additive white Gaussian noise channels. In particular, we put forward the WRE algorithm to estimate reference signal in order to calculate log-likelihood ratio (LLR) more precisely. Furthermore, extrinsic information output from the decoder is utilized to iteratively recalculate the weight of the WRE algorithm. As a further illustration, we derive the LLR expressions of the proposed WRE-ID-aided receiver of a typical protograph-coded reference reused DCSK (i.e., high-efficiency DCSK) system. Analytical and simulated results show that the proposed WRE-ID-aided receiver can always overtake the traditional receivers in reference reused DCSK systems. Hence, the protograph-based reference reused DCSK systems with the proposed receiver are very promising for high-rate high-reliability wireless applications.

A practical type-3 Fuzzy control for mobile robots: predictive and Boltzmann-based learning

This study presents an innovative path-following scheme using a new intelligent type-3 fuzzy system for mobile robots. By designing a non-singleton FS and incorporating error measurement signals, this system is able to handle natural disturbances and dynamics uncertainties. To further enhance accuracy, a Boltzmann machine (BM) models tracking errors and predicts compensators. A parallel supervisor is also included in the central controller to ensure robustness. The BM model is trained using contrastive divergence, while adaptive rules extracted from a stability theorem train the NT3FS. Simulation results using chaotic reference signals show that the proposed scheme is accurate and robust, even in the face of unknown dynamics and disturbances. Moreover, a practical implementation on a real-world robot proves the feasibility of the designed controller. To watch a short video of the scheme in action, visit shorturl.at/imoCH.

Design and Performance Analysis of Frequency Hopping OFDM Based Noise Reduction DCSK System

The reference chaotic signal in the differential chaos shift keying (DCSK) system causes both bit error rate (BER) and security performance degradation. In this paper, a frequency hopping orthogonal frequency division multiplexing based noise reduction DCSK (FH-OFDM-NR-DCSK) system is proposed to enhance both the BER and security performance of the OFDM-DCSK system. This system combines the advantages of both FH-OFDM-DCSK and NR-DCSK. Rather than creating β separate chaotic samples to utilize as a reference sequence, β/P chaotic samples are created and then replicated P times. Moving average filters of size P are applied after the frequency hopper to average the repeated chips of the reference and data-bearing signals. A new frequency hopping pattern is designed depending on the chaotic map on which the matrix pattern is designed efficiently. The performance of the proposed system is examined, and bit error rate analytic equations of the FH-OFDM-NR-DCSK system over an AWGN and two-path Rayleigh fading channel are derived. The simulation results show that the theoretical BER expressions and simulation performance match. The findings show that for the same spreading factor, the proposed system outperforms the DCSK and FH-OFDM-DCSK when P1. This method decreases noise variance and improves BER without adding to the system's complexity.

Design and implementation of enhanced permutation index differential chaos shift keying system

In standard PI-DCSK, information is transmitted by sending reference chaotic signal followed by information bearing signal, which is simply a permutated version of the reference signal. Permutation is performed based on a specific data map. In this paper, a developed version of (PI-DCSK) is presented and tested in AWGN and multipath Rayleigh fading channels environment. Information bearing signal is generated by mapping first set of information bits to the reference bit while the second set is mapped to the permutated-time reversed version of same reference signal. Both versions is added together on the same time slot. At the receiver, each incoming signal undergoes two operations; permutation and time reversal followed by permutation to detect the two different sets of information. This arrangement offers high data rate and reduce the energy requirement utilizing the low cross correlation between the chaotic signal and its time reversed version. The bit error performance is studied using baseband system model and analytically tested using Gaussian Approximation (GA) method. System performance is evaluated analytically to predict the Bit Error Rate (BER) using computer simulations. Results show that system performance is outperform the recent developed one by an average of at 2.25 dB while outperform the other standard chaos based scheme by an average of at same Eb∕N0. Moreover, the analytical form which are developed to predict the BER is validated by simulation.

Reliable Low-Rank Approximation of Matrices Detection Aided Multicarrier DCSK Receiver Design

Multicarrier differential chaos shift keying (MC-DCSK) systems transmit the reference chaotic signal for information recovery to remove the complex synchronization circuit. However, transmission errors in the reference chaotic signal would induce the error propagations when directly used for demodulations. In order to address this issue, we propose a low-rank approximation of matrices (LRAM) detection method to improve the reliability performances. In our design, we exploit the low-rank characteristic of MC-DCSK signals sharing the reference chaotic signal. Instead of directly using the received reference chaotic signal for correlated demodulation, we propose to apply the LRAM method to jointly estimate the reference signal and the information-bearing signal. We use the singular value decomposition and generalized LRAM methods to minimize the distances between the estimates and transmitted data. Thus, the signal-to-noise ratio (SNR) can be improved to achieve lower bit error rate (BER). Moreover, theoretical BER expression is derived and LRAM-aided system is proved to be capable of proving the maximum-likelihood detection for received signals. Simulation results demonstrate the BER performances of our design outperform counterparts over additive white Gaussian noise and fading channels.

PERFORMANCE ANALYSIS OF QUADRATURE CHAOS SHIFT

One of the most famous techniques of non-coherent differential chaos shift keying (DCSK) is Quadrature chaos shift keying (QCSK) system, this system suffered from lowering the data rate and increasing the bit energy during the bit transmission even though its rate doubling the one of the DCSK. Short reference (SR) algorithm is proposed for the QCSK system to design the SR-QCSK communication system that enhances these drawbacks. The main idea of the short reference technique is minimizing the length of the reference chaotic signal (β) at a transmitter by a factor P comparing to produce R samples for the new reference signal while the length of the information-bearing signal remained unchanged, this occurs by duplicating the reference signal P times to get the same length as the conventional QCSK. Therefore, the symbol duration is reduced from 2βTc to (R+β)Tc. The data rate and energy saving improvement factor in a percent form is derived and compared with the QCSK and DCSK systems. Also, the BER analytical expression is derived for the SR-QCSK in additive white Gaussian noise and Rayleigh fading channel. The experimental simulation results proved that the theory derivation gives a good analysis tracking for the BER performance. The SR-QCSK system is compared with other DCSK techniques and the simulation results show that it has a superior performance in the multipath Rayleigh fading channel.

General Iterative Receiver Design for Enhanced Reliability in Multi-Carrier Differential Chaos Shift Keying Systems

In this paper, we present a general iterative receiver for multi-carrier differential chaos shift keying (MC-DCSK) systems. The imperfect channels conditions may induce transmission errors which will degrade the reliability performances. In order to address this issue, we propose an iterative demodulation structure to improve bit error rate (BER) performances by improving the signal to noise ratio (SNR) of reference chaotic signals. At the presented iterative receiver, we propose to evaluate correlation coefficients between the reference chaotic signals and each information-bearing chaotic modulated signal. Then they are used to update and feedback the reference chaotic signal for the next iteration. With the aid of the renewed reference signals, a similar procedure is carried out until the iteration stopping criteria is reached and the threshold decisions are provided. The presented general iterative receiver can be applied to any MC-DCSK systems without introducing any additional modules at transmitters. Theoretical analysis is provided to prove the iteration convergence and to derive the BER performances. Simulation results verify the effectiveness of the theoretical analysis, which demonstrates that better reliability performances can be achieved over additive white Gaussian noise (AWGN) and fading channels compared with counterpart systems.

Design and Performance Analysis of Multilevel Code-Shifted $M$ -Ary Differential Chaos Shift Keying System

The multilevel code-shifted differential-chaos-shift-keying system transmits multiple information-bearing chaotic signals together with a reference chaotic signal in the same transmission symbol duration by orthogonal code sequences of a Walsh matrix. In order to obtain higher bandwidth efficiency (BE), a multilevel code-shifted M-ary differential chaos shift keying (MCS-MDCSK) system is proposed in this brief. We derive the theoretical bit-error-rate (BER) formula for the proposed system over the additive white Gaussian noise channel and the multipath fading channel. Finally, numerical results verify our derivations and superiority of the MCS-MDCSK. The proposed system not only greatly boosts the BE, but also obtains better BER performance.

Performance Improvement of DCSK Modulation in Fading Channels Using Coherent Receiver with Channel Estimation

In this paper, we introduce a differential chaos shift keying (DCSK) with correlator receiver (DCSK-CR) scheme that uses a constant chaotic reference signal for all transmitted symbols. For this scheme, the orthonormal basis signals are completely known at the receiver and a coherent correlator-based structure is used to detect the symbols. Although the performance of a coherent receiver is better than that of a non-coherent receiver, the coherent case needs to know the channel state information to detect symbols in fading channels. Taking the chaotic reference signal constant in the proposed DCSK-CR system helps us to estimate the channel state information for detection. We drive the bit error rate (BER) performance of the proposed system in flat Rayleigh fading channels for both cases of errorless and maximum likelihood (ML) estimation of the channel coefficient. Thanks to the coherent structure, numerical results show that the BER performance of the proposed system outperforms the conventional DCSK case from 3 dB (for the ML case) to 8 dB (for the errorless case) in accordance with the channel estimation accuracy. It is shown that changing the chaotic map, initial condition and the chaotic parameter of the system, does not affect the BER performance of the proposed DCSK-CR, as DCSK. However, in contrast to the DCSK system, changing the spread factor in our system model has no effect on the BER.

Permutation Index DCSK Modulation Technique for Secure Multiuser High-Data-Rate Communication Systems

A new noncoherent scheme called Permutation Index Differential Chaos Shift Keying (PI-DCSK) modulation is proposed in this paper. This original design aims to enhance data security, energy and spectral efficiencies, compared to its rivals. In the proposed PI-DCSK scheme, each data frame is divided into two time slots in which the reference chaotic signal is sent in the first time slot and a permuted replica of the reference signal multiplied by the modulating bit is sent in the second time slot. In particular, the bit stream is divided at the transmitter into blocks of $n+1$ bits, where $n$ mapped bits are used to select one of the predefined reference sequence permutations, while a single modulated bit is spread by the permuted reference signal just mentioned. At the receiver side, the reference signal is recovered first, then all permuted versions of it are correlated with the data-bearing signal. The index of the correlator output with maximum magnitude will estimate the mapped bits, while the output content of the corresponding correlator is compared to a zero threshold to recover the modulated bit. Moreover, a new multiple access method based on the proposed scheme is described and analysed. Analytical expressions for the error performance in single-user and multiuser environments are derived for additive white Gaussian noiseand multipath Rayleigh fading channels, respectively. Furthermore, the performance of the proposed PI-DCSK system is analysed and compared with other noncoherent chaotic modulation schemes and is found to be promising.

Design and Analysis of an OFDM-Based Orthogonal Chaotic Vector Shift Keying Communication System

We propose a new non-coherent multicarrier spread-spectrum system that combines orthogonal chaotic vector shift keying (OCVSK) and orthogonal frequency-division multiplexing (OFDM). The system enhances OCVSK by sending multiple groups of information sequences with the same orthogonal chaotic vector reference sequences over the selected subcarriers. Each group carries M information bits and is separated from other groups by orthogonal chaotic reference signals. We derive the information rate enhancement (IRE) and the energy saving enhancement (ESE) factors as well as the bit error rate theory of OFDM-OCVSK under additive white Gaussian noise and multipath Rayleigh fading channels and compare the results with conventional OCVSK systems. For large group numbers, the results show that the IRE and ESE factors approach M×100% and M/(M+1)×100%, respectively, and thus outperform OCVSK systems. The complexity analysis of the proposed scheme as compared with OFDM-DCSK shows a significant reduction in the number of complex multiplications required.

Two-Layer Carrier Index Modulation Scheme Based on Differential Chaos Shift Keying

In this paper, a novel carrier index differential chaos shift keying (DCSK) modulation system is proposed for increased energy and spectral efficiencies. The new system splits all data bits into two groups, which are carried by the chaotic signals and their Hilbert transforms, respectively. For each group, one active subcarrier is selected from all candidate subcarriers according to the index bits, and the signal transmitted via the active subcarrier carries one modulated bit through DCSK modulation. By correlating with the exact or the Hilbert filtered chaotic reference signals, the two data groups can be demodulated separately. In each group, the index bits are determined by the maximum energy comparator, while the threshold verdict helps to estimate the modulated bit. Analytical bit error rate expressions over additive white Gaussian noise and multipath Rayleigh fading channels are derived. Simulations and comparisons are also performed to verify the advantages of this new proposed design.

Code-Shifted Differential Chaos Shift Keying with Code Index Modulation for High Data Rate Transmission

In the general code-shifted differential chaos shift keying (GCS-DCSK) system, multiple bit-streams are simultaneously carried by CS-DCSK signal using Walsh codes. However, its data rate is limited by the available Walsh codes in the Walsh code matrix due to orthogonality constraint of GCS-DCSK signal. In this paper, we propose a new GCS-DCSK scheme with code index modulation (CIM-CS-DCSK), which can achieve higher spectrum efficiency using code index modulation to carry additional bits. In the proposed scheme, the reference chaotic signal is the same as that of GCS-DCSK, and the multiple information bearing signals are simultaneously modulated by the information symbols and the selected Walsh codes with specific indices, which are determined by an integer sequence mapped from information symbols via the natural numbers to $k$ -combinations mapping method. We derive bit error rate of the proposed scheme over the additive white Gaussian noise channel. The numerical results not only verify our analysis but also show the advantage of the proposed scheme over GCS-DCSK. Through analyzing and comparing the numbers of carried bits per transmitted symbol of CIM-CS-DCSK and GCS-DCSK, it is shown that the proposed scheme can obtain higher data rate than GCS-DCSK with the same resource constraints.

Efficient Amplitude Shift Keying-Aided Orthogonal Chaotic Vector Position Shift Keying Scheme With QoS Considerations

In this paper, we present an efficient amplitude shift keying (ASK)-aided orthogonal chaotic vector PSK (ASK-OCVPSK) non-coherent modulation scheme with considerations of different quality of service (QoS) demands. In our ASK-OCVPSK design, the reference chaotic signal is generated recursively from the shifted chaotic vectors orthogonalized by the Gram–Schmidt transform buffered in the shift register. Then, we embed the information on both the position and the amplitude of the chaotic sequence. The binary information bitstream is divided into two segments, which are modulated, respectively, by the parallel concatenated position shift keying (PSK) scheme and the ASK scheme. Next, the ASK symbol is further modulated by the PSK modulated chaotic vector, and the resultant symbol is transmitted together with the reference chaotic vector. Notably, with the aid of the shift register, only one chaotic vector is transmitted and the reference chaotic sequences can be easily regenerated recursively at the receiver for information recovery. Furthermore, we derive the theoretical bit error rate (BER) expressions for the proposed system over additive white Gaussian noise (AWGN) channel. Then, the spectrum efficiency and the complexity of the proposed scheme are analyzed and compared with those of the counterpart schemes. Simulations are performed over the AWGN channel and multipath Rayleigh fading channel, and the results demonstrate that the theoretical BER matches the simulation results. Moreover, the results verify that the presented scheme are more efficient and more reliable than the counterpart schemes and can provide different BER performances without changing the modulator structure to meet the different QoS demands of the users.

Multilevel code‐shifted differential‐chaos‐shift‐keying system

The M-ary differential-chaos-shift-keying (M-ary DCSK) system offers a good noise performance over an additive white Gaussian noise (AWGN) channel in the category of non-coherent detection chaotic systems. However, the way that the M-ary DCSK system utilises the available Walsh codes results in a relatively low bandwidth efficiency (BE). Moreover, the number of delay elements required at the transmitter and receiver increases exponentially with the number of bits per symbol. To overcome the aforementioned problems, the authors propose a multilevel code-shifted DCSK (MCS-DCSK) system in this study. In the proposed MCS-DCSK system, the reference chaotic signal and the information-bearing chaotic signals are orthogonal and are transmitted in the same time slot. They show that the MCS-DCSK system significantly outperforms the M-ary DCSK system in terms of BE and complexity. They also derive analytical bit-error-rate expressions for the MCS-DCSK system over additive white Gaussian noise and multipath fading channels, and verify them with simulation results.

Design and Performance Analysis of a Multiuser OFDM Based Differential Chaos Shift Keying Communication System

In this paper, a multiuser OFDM-based chaos shift keying (MU OFDM-DCSK) modulation is presented. In this system, the spreading operation is performed in time domain over the multicarrier frequencies. To allow the multiple access scenario without using excessive bandwidth, each user has $N_P$ predefined private frequencies from the $N$ available frequencies to transmit its reference signal and share with the other users the remaining frequencies to transmit its $M$ spread bits. In this new design, $N_P$ duplicated chaotic reference signals are used to transmit $M$ bits instead of using $M$ different chaotic reference signals as done in DCSK systems. Moreover, given that $N_P , the MU OFDM-DCSK scheme increases spectral efficiency, uses less energy and allows multiple-access scenario. Therefore, the use of OFDM technique reduces the integration complexity of the system where the parallel low pass filters are no longer needed to recover the transmitted data as in multicarrier DCSK scheme. Finally, the bit error rate performance is investigated under multipath Rayleigh fading channels, in the presence of multiuser and additive white Gaussian noise interferences. Simulation results confirm the accuracy of our analysis and show the advantages of this new hybrid design.

고속통신을 위한 FM-QCSK 카오스 통신 시스템

The FM-QCSK(: Frequency Modulated Quadrature Chaos Shift Keying) system is one of the most efficient systems in chaotic literature. One of the problems in this system is that half the bit duration is used for sending a chaotic reference signal which leads to increase the energy losses and reduces the data rate. In this paper, a novel scheme to enhance the performance of FM-QCSK system has been proposed. With the proposed scheme, FM-QCSK would be able to operate at higher data rates with reduced BER(: Bit Error Rate) and energy consumption. The basic modification introduced by the proposed scheme is the use one reference chaotic signal to transmit multi information signals in both in-phase and quadrature-phase channels. The results showed that the proposed scheme have achieved more than 3 dB gains in SNR for AWGN channels respectively at $BER

Multicarrier chaotic communications in multipath fading channels without channel estimation

A multi-carrier chaotic shift keying(MC-CSK) communication scheme with low probability of interception(LPI) is proposed in this article. We apply chaotic spreading sequences in the frequency domain, mapping a different chip of a chaotic sequence to an individual orthogonal frequency division multiplexing(OFDM) subcarrier. In each block size of $M$ OFDM symbols, we use one pilot OFDM symbol inserted time-spaced in all-frequency to transmit the reference chaotic signal and use the other M-1 OFDM symbols to transmit the information-bearing signals each spreaded by the reference chaotic signal. At the receiver, we construct a differential detector after DFT and recover the information bits from the correlations between the pilot OFDM symbol and the other M-1 OFDM symbols in each block size of M. Performance analysis and computer simulations show that the MC-CSK outperforms differential chaos shift keying(DCSK) in AWGN channels with high bandwidth efficiency for the block size of M=2 and that the MC-CSK exploits effectively the frequent diversity of the multipath channel.

Design of Enhanced Differential Chaos Shift Keying Scheme

In this paper, a new noncoherent Differential Chaos Shift Keying is proposed and named Extended -Differential Chaos Shift Keying (E-DCSK). Each pair of bits is modulated using two different versions of the same chaotic reference signal; the first information bit is modulated with the chaotic reference signal block while the next information bit is modulated after reversing samples' order of the same reference block. This saves the transmitted signal energy in addition to reduce the repeated components in the signal spectrum. Bit-error performance in additive-white-Gaussian-noise of the proposed system is analyzed and compared with the other chaos based communication systems. Results show that the bit-error rate performanceof the E-DCSK is often better than other schemes when spreading factorisrelatively low. Also, clear matching between theoretical analysis and simulation result is observed.

Pseudo-Random Binary Sequence Selection for Delay and Add Direct Sequence Spread Spectrum Modulation Scheme

Recently, correlation delay shift keying (CDSK) has been proposed as a modulation scheme for noncoherent detection which inherits the advantages of conventional spread-spectrum communications using a chaotic reference signal. The CDSK modulation scheme transmits the sum of a chaotic reference signal with its delayed modulated version. In this paper, we consider the utilisation of pseudo-random binary sequences (PRBS) instead of chaotic reference signals. This new modulation scheme is defined as the delay and add direct sequence (DADS) modulation scheme. DADS offers some interesting properties compared to CDSK, mainly the possibility to select some PRBS which improves the BER performance. To this end, a new criterion for PRBS selection is proposed. Theoretical analysis and simulation results show that the BER performance of CDSK is comparable to DADS with arbitrary PRBS, however the DADS performance can be improved by 3 dB with PRBS selection.