Ary Differential Chaos Shift Research Articles

Toward RIS-Aided Non-Coherent Communications: A Joint Index Keying M-ary Differential Chaos Shift Keying System

In reconfigurable intelligent surface (RIS)-aided coherent communications, channel state information (CSI) is often assumed to be perfectly estimated at the receiver. However, perfect CSI cannot be available in practice. Furthermore, the complex and ever-changing channel makes the acquisition of accurate CSI unaffordable because of the large overhead in transmitting pilot signals. Motivated by these considerations, a novel non-coherent RIS-aided joint index keying <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary differential chaos shift keying (RIS-JIK-MDCSK) scheme is proposed in this paper, where the receiver can retrieve information bits by performing non-coherent correlation demodulation without requiring CSI, thereby reducing the system complexity. In RIS-JIK-MDCSK, the states of the reference signal, RIS elements, and information-bearing subcarriers are jointly optimized to devise a joint index keying mechanism, where additional information bits are implicitly transmitted by these state indices, thus increasing the throughput and spectral efficiency. Furthermore, an effective joint index keying detection algorithm is proposed to recover information bits. The analytical bit error rate (BER) of RIS-JIK-MDCSK is derived over a Rayleigh fading channel. Other evaluation metrics, including the throughput, spectral efficiency, and system complexity are also analyzed and compared against benchmark schemes. Numerical simulations are performed to evaluate the superiority of RIS-JIK-MDCSK compared to existing schemes.

Toward Chaotic Secure Communications: An RIS Enabled M-Ary Differential Chaos Shift Keying System With Block Interleaving

Chaotic secure communication systems using chaotic waveforms as their spreading carriers can hide the transmitted information bits over a wide frequency range of chaotic waveform, which disguises the transmitted information waveform as noise. In this paper, a reconfigurable intelligent surface (RIS) enabled <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary differential chaos shift keying with block interleaving (RIS-MDCSK-BI) system is proposed for chaotic secure communications, where an RIS is deployed at the transmitter to assist communications and a pair of block interleaving patterns are used to interleave <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -ary information-bearing signals to enhance security performance. Moreover, we propose a chaotic merging sort algorithm to generate different block interleaving patterns, where these interleaving patterns are encrypted by using the non-periodic and noise-like properties of chaotic signals. To estimate information bits at the legitimate receiver, we propose a sequential detection algorithm and a joint detection algorithm. Then, theoretical bit error rate (BER) performances of the proposed RIS-MDCSK-BI system with the legitimate receiver and the eavesdropping receiver are derived. The security performance metrics, including information leakage and secrecy outage probability, are also analyzed. Monte Carlo simulations are performed to verify the superior BER performance and security performance of the proposed RIS-MDCSK-BI system compared to benchmark systems.

Performance and Capacity Analysis of MDCSK-BICM for Impulsive Noise in PLC

To further mitigate the BER error floor of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M$</tex-math></inline-formula> -ary differential chaos shift keying (MDCSK) modulation for impulsive noise, a low-cost high-reliability coded modulation scheme without equalizations is desirable for impulsive noise. In this paper, a protograph-based low-density parity-check coded MDCSK-based bit-interleaved coded modulation (MDCSK-BICM) scheme is proposed for the scenario with impulsive noise obeying Bernoulli-Laplace distribution. Considering the Gaussian distribution of protograph extrinsic information transfer (PEXIT) and the benchmark of coding design, the U-shaped non-coherent capacity is derived with optimal code rate for square MDCSK, showing that the code rates are stable with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$E_b/N_0$</tex-math></inline-formula> increasing but still much lower than that of DS-16DQAM at code rate <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$&gt;\!0.145$</tex-math></inline-formula> . The derived joint probability density function can be considered as approximately a Gaussian distribution, which is used to improve the impulsive noise fitted PEXIT. Finally, a new code under a novel principle is designed for better bit error rate performance based on the improved PEXIT analysis. Both PEXIT analysis and simulation results demonstrate that the proposed scheme achieves a better BER than that with a traditional scheme, and suggesting a research approach based on simple methods. This basic research work provides a guide to establish a framework and optimize the performance of transmission systems over practical power line communication.

Joint Code Rate Compatible Design of DP-LDPC Code Pairs for Joint Source Channel Coding Over Implant-to-External Channel

A CM2-S3 transmission link in wireless body area networks (WBAN) is implemented with a joint source channel coding (JSCC) system based on double protograph low-density parity-check (DP-LDPC) code pairs with high reliability and low power consumption. For the practicality and suitability considerations, the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary differential chaos shift keying scheme is introduced to modulate the CM2-S3 channel with better performance than the standard modulations in WBAN. Due to the non-Gaussian-like distribution of the CM2-S3 channel model, the initial joint protograph extrinsic information transfer (JPEXIT) algorithm does not work as a coding analysis tool. To solve this problem, a numerical Gaussian approximation is employed to modify the iterative mutual information function of the JPEXIT for achieving more precise output. Then, a joint code rate compatible (JCRC) method, designed with compatibility in resisting variable channel variances and adapting different source statistics, is proposed for optimizing the DP-LDPC code pairs. Based on the JCRC method, the code searching algorithm is simplified with lower complexity because of the reduced cycle-index. The simulation results show that optimized code pairs have better bit-error ratio performances compared to existing codes, which provides a strong technical support to promote high-quality data transmission in eHealthcare on the physical layer.

Design and Performance Analysis of a Robust Multi-Carrier M-Ary DCSK System: A Noise Suppression Perspective

A Noise Suppression aided Multi-Carrier <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary Differential Chaos Shift Keying (NS-MC-MDCSK) system is proposed here where each information subcarrier transmits an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary information-bearing signal and the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary constellation symbols are constructed by orthogonal Walsh codes to improve the energy efficiency. Exploiting the redundant information available in the received signal, we propose a noise suppression algorithm to suppress channel noise in the reference and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$M$ </tex-math></inline-formula> -ary information-bearing signals. In the proposed algorithm, correlation coefficients detected between the received reference and information-bearing signals are fed back to suppress the noise corrupting the signal received. This method reduces the channel noise significantly and provides an outstanding Bit Error Rate (BER) performance. A performance analysis is performed for the NS-MC-MDCSK system over Additive White Gaussian Noise (AWGN) and multipath fading channels. Finally, the BER performance of the NS-MC-MDCSK system is compared to that of other chaotic communications systems. It is shown that the NS-MC-MDCSK system offers better BER performance than its competitors.

Optimal Design of Joint Protomatrix for DP-LDPC Codes-Based JSCC System Over on-Body Channel

A high-quality data transmission scheme in wireless body area networks is implemented by a joint source-channel coding (JSCC) system with $M$ -ary differential chaos shift keying modulation over an on-body channel. Current DP-LDPC code pairs, which have shown good bit-error ratio performance over additive white Gaussian noise channel and Rayleigh fading channel, cannot perform well over on-body channel. In this paper, the DP-LDPC codes are redesigned for the JSCC system with new methods depending on the on-body channel characteristics. A protomatrix dimension-restrictive searching algorithm for DP-LDPC codes in the JSCC system is proposed according to the on-body channel bandwith and source statistic, which is effective to predesign the dimension of the code pair for a new JSCC system. In this way, the source-channel code rates are appropriately allocated to leave more source redundancy for improving the error floor. Moreover, the joint protomatrix is reconstructed into two kinds of compact structures by simplifying the edge linking relationships and modifying joint protograph extrinsic information transfer algorithm, which decreases the induction of searching entries to further accelerate the code searching speed. The searched code pairs show better bit-error ratio performances compared with existing DP-LDPC codes. The power consumption in the new joint coding system is lower than the separate coding system in WBAN on the physical layer.

A New APSK-Based M-Ary Differential Chaos Shift Keying Modulation System

In this letter, a new amplitude phase shift keying (APSK) based ${M}$ -ary differential chaos shift keying (A- ${M}$ -DCSK) system is proposed. The theoretical symbol error rate (SER) and bit error rate (BER) expressions of A- ${M}$ -DCSK system for two constellations are derived and verified for both AWGN and multipath Rayleigh fading channels. Numerical results reveal that A- ${M}$ -DCSK system provides near or better BER with much lower peak-to-average power ratio (PAPR) as compared to quadrature amplitude modulation (QAM) based ${M}$ -DCSK (Q- ${M}$ -DCSK) system. Furthermore, A- ${M}$ -DCSK system shows better robustness against channel estimation error than Q- ${M}$ -DCSK system. At last, with APSK constellation rotation, the BER of A- ${M}$ -DCSK system is enhanced with a slightly increased PAPR.

Closed-Form BER Expressions of M-Ary DCSK Systems Over Multipath Rayleigh Fading Channels

In this letter, we derive a closed-form bit error rate (BER) of $M$ -ary differential chaos shift keying ( $M$ -DCSK) systems over multipath Rayleigh fading channels via approximating Gaussian $Q$ -function by polynomials. The approximation is made piecewisely using polynomials of different degrees and Remez algorithm is applied to achieve the minimax approximation. Our method can be extended into the existing non-coherent transmit-reference chaos-based modulation systems, e.g., short-reference DCSK and multi-carrier DCSK systems. The derived closed-form BERs are compared with the simulated ones in order to verify the efficiency of proposed approximation scheme.

Design and Analysis of Joint Source Channel Coding Schemes Over Non-Standard Coding Channels

Although a mountain of work on joint source-channel coding (JSCC) scheme over standard coding channels (a combination of BPSK modulation and AWGN channels) have been studied deeply, there has been no knowledge about JSCC over non-standard coding channels. In this paper, a JSCC scheme based on double protograph low-density parity-check (DP-LDPC) codes is proposed over non-standard coding channels which consists of M -ary differential chaos shift keying (DCSK) and Rayleigh fading channels is proposed, named as JSCC-DCSK system. A joint protograph extrinsic information transform (JPEXIT) algorithm is proposed to analyze the decoding threshold of DP-LDPC codes on the non-standard coding channels. Considering the effects from the source redundancy left by source coding and the non-linear property of non-standard coding channels, the design of DP-LDPC structure is discussed, and new design principles from a global perspective are proposed. Several DP-LDPC codes for different source statistic are designed by the aid of JPEXIT algorithm and verified by Monte Carlo simulation. The appropriate number of the turbo iteration is determined to keep the bit error rate (BER) of system performance and the complexity of the receiver at a low level.

Design and Performance Analysis of a New $M$ -Ary Differential Chaos Shift Keying With Index Modulation

A new M-ary differential chaos shift keying with index modulation (IM-MDCSK), which has the advantages of high data rate and low energy consumption, is proposed in this paper. In the proposed scheme, each data frame is divided into several time slots where the reference signal is placed in the first time slot and the rest time slots with specific indices are provided for information bearing signals. More exactly, the information bearing signals with active indices are modulated by M-ary DCSK symbols, and the active indices are determined by mapped bits via the combination number mapping method. At the receiver, the absolute values of decision variables in all branches are used to find the indices of active time slots, while M-ary DCSK demodulation is applied to recover the modulated bits. Moreover, we derive the analytical bit-error-rate (BER) expressions for the proposed scheme over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels, and then simulation results verify our theoretical derivations. Finally, the performance of IM-MDCSK scheme is compared with M-ary DCSK and other up-to-date chaotic modulation schemes based on index modulation (IM). IM-MDCSK scheme is proved to be competitive and preeminent.

Multi-Carrier $M$-ary DCSK System With Code Index Modulation: An Efficient Solution for Chaotic Communications

A new multi-carrier $M$ -ary differential chaos shift keying system with code index modulation, referred to as CIM-MC- $M$ -DCSK , is proposed in this paper. In the proposed CIM-MC- $M$ -DCSK system, the reference and information-bearing signals for each subcarrier can be transmitted simultaneously by using the orthogonal sinusoidal carriers, where the information-bearing signal adopts the $M$ -DCSK modulation to further increase the data rate. With an aim to making full use of the system energy resources, the reference signals in all subcarriers are coded by a Walsh code to carry additional information bits. The analytical bit-error-rate (BER) expressions of the proposed CIM-MC- $M$ -DCSK system are derived over additive white Gaussian noise as well as multipath Rayleigh fading channels. Furthermore, a noise-reduction scheme and a hierarchical-modulation scheme are designed for the proposed system. In particular, the former scheme can significantly improve the BER performance while the latter scheme can provide different quality of service for the transmitted bits according to their different levels of importance. Simulation results verify the accuracy of the analytical expressions and the superiority of the proposed systems.

Efficient and robust M ‐ary differential chaos shift keying scheme with code index modulation

In this study, a new chaos modulation scheme which combines M -ary differential chaos shift keying (DCSK) with code-index modulation (CIM-MDCSK) is proposed. In the CIM-MDCSK scheme, the two Walsh codes that are used to generate two orthogonal chaos components are selected from the candidate codes, whose code indices are determined by information symbols. Thus, the information bits are conveyed not only by M -ary DCSK signal but also by the indices of the Walsh codes. Theoretical symbol error rate (SER) and bit error rate (BER) of the proposed scheme are derived and confirmed by simulations. Furthermore, by applying the noise-reduction to reference signals of CIM-MDCSK, the SER/BER expressions are also derived. Simulation results show that the proposed CIM-MDCSK outperforms DCSK and M -ary DCSK based on Hilbert transform. Especially, the CIM-MDCSK with noise-reduction shows significant advantages. Moreover, the performance of CIM-MDCSK scheme is compared with direct sequences spread-spectrum system with code-index modulation over flat and frequency selective fading channel. The proposed CIM-MDCSK can offer good performance over frequency selective fading channel with a low complexity non-coherent receiver which does not require any channel state information and channel equalisation.

Design and performance analysis of generalised carrier index M ‐ary differential chaos shift keying modulation

In this study, two generalised carrier index M-ary differential chaos shift keying (CI-MDCSK) schemes are proposed, which combine index modulation with multicarrier M-ary DCSK (MC-MDCSK). At the transmitter, two different index selectors based on two different mapping rulers are employed to select active carriers, where the modulated bits are transmitted by the active carriers through M-ary DCSK modulation, which is based on the Hilbert transform and constellation theory. At receiver, maximum or minimum energy detection is employed to determine the active carriers, where the bits carried on these active carriers are demodulated. The analytical bit error rate (BER) expressions over additive white Gaussian noise as well as multipath Rayleigh fading channels are derived. Simulations are performed with different numbers of carriers and different constellation sizes. Both analytical and simulation results show the superiority of the new schemes in BER performance or spectral efficiency (SE) compared with the MC-MDCSK scheme. Moreover, compared with conventional DCSK, CI-MDCSK schemes owns both better BER performance and SE in some cases, where the constellation is not greater than 8.

A Multi-Carrier $M$ -Ary Differential Chaos Shift Keying System With Low PAPR

An improved multi-carrier $M$ -ary differential chaos shift keying (MM-DCSK) system is presented, where differential modulation and demodulation are carried out across multiple carriers in the frequency domain, so channel estimation is not needed. For one data frame transmission, only one non-information-bearing reference sub-carrier signal is required, and the reference of each information-bearing sub-carrier is its previous sub-carrier signal, thus high energy efficiency is attained. If channel response changes during a frame period, the time diversity is achieved. In addition, the peak-to-average power ratio (PAPR) is considered, and it is found that adjacent symbols with a large Euclidean distance achieve a low PAPR. Accordingly, a low-complexity PAPR reduction algorithm is proposed based on symbol-interleaving with only one inverse fast Fourier transform processor. The simulation results demonstrate that the system with the proposed algorithm dramatically reduces the PAPR. Analytical bit-error-rate expressions are derived and verified by simulations over additive white Gaussian noise and multi-path fading channels.

A New Hierarchical $M$ -ary DCSK Communication System: Design and Analysis

Multiresolution $M$ -ary differential chaos shift keying (MR- $M$ -DCSK) modulation using non-uniformly spaced phase constellation is a promising technique that can satisfy different bit-error-rate (BER) requirements within one symbol over multipath fading channels. However, the BER performance always deteriorates as the modulation order $M$ becomes larger. To overcome this shortcoming, a new hierarchical square-constellation-based $M$ -DCSK communication system using non-uniformly spaced distance constellation is proposed, which can be easily extended to other-constellation scenarios, e.g., rectangular, star, and asymmetrical square constellations. Furthermore, an adaptive transmission scheme is designed by modifying the distance between the two constellation points in the last hierarchical level. In addition, theoretical BER expressions of the proposed systems are derived over multipath Rayleigh fading channels, which are consistent with the simulated results. Analytical and simulated results show that the proposed system not only can provide lower energy consumption as compared with the conventional MR- $M$ -DCSK system but also can efficiently adjust BER performance based on the signal-to-noise ratio information. Therefore, the proposed system can serve as a desirable alternative for energy-efficient short-range wireless-communication applications.

Non-Coherent Capacity of $M$ -ary DCSK Modulation System Over Multipath Rayleigh Fading Channels

Non-coherent capacity bounds for the $M$ -ary differential chaos shift keying (DCSK) modulation system are derived and analyzed over multipath Rayleigh fading channels, deriving conditions on the channel state information/non-channel state information (CSI/NonCSI) and soft-decision/hard-decision (SD/HD), respectively. Meanwhile, the inter-symbol interference is modeled and analyzed mathematically. Through numerical simulations and analyses, it is found that: 1) the influences of the spreading factor $\beta $ , multipath number $L$ , modulation dimension $M$ , CSI/NonCSI, and SD/HD on the non-coherent capacity bounds are significant; 2) there is a relatively broad range of code rates corresponding to the optimal system power in U-shaped capacity curves of the non-coherent reception; and 3) the U-shaped non-coherent capacity bounds are proven to exist by investigating the mechanism of the low density parity check coded the $M$ -ary DCSK system. These results are useful as benchmarks for designing power-efficient coded $M$ -ary DCSK systems.

Design and Performance Analysis of a New Multiresolution &lt;inline-formula&gt; &lt;tex-math notation="LaTeX"&gt;$M$&lt;/tex-math&gt;&lt;/inline-formula&gt;-Ary Differential Chaos Shift Keying Communication System

A new multiresolution $M$ -ary differential chaos shift keying (DCSK) modulation scheme is proposed in this paper. It is a promising technique for providing a different quality of service for transmitted bits within a symbol according to their different bit error rate (BER) requirements based on the principle of nonuniformly spaced constellations. The new system not only is simple but also provides better antimultipath fading performance against various spreading factors, inheriting the advantages of the conventional DCSK system. Furthermore, the proposed scheme and its multicarrier version further increase spectral efficiency and use lower energy consumption at the same bandwidth as compared with the conventional DCSK and its multicarrier system. Explicit BER expressions of the new system are derived and analyzed over additive white Gaussian noise and multipath Rayleigh fading channels. All simulation results verify the prominent advantages of the new scheme and the accuracy of the new analytical approach.

$M$-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.