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.

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

In the past two decades, chaotic modulations have drawn a great deal of attention in low-power and low-complexity wireless communication applications due to their excellent anti-fading and anti-intercept capabilities. Of particular interest is the differential chaos shift keying (DCSK), which is considered as a very promising chaotic modulation scheme that achieves not only good error performance, but also low implementation complexity. In this treatise, we provide an insightful survey on the state-of-the-art research in DCSK-based communication systems through an extensive open literature search. In doing so, we firstly review the principles of DCSK modulation and the significant milestones since its inception. Subsequently, we introduce meritorious variants of DCSK, all of which can outperform the original one in certain aspects. We also present the joint design guidelines when combining DCSK with other critical techniques, e.g., error-correction coding and cooperative communication, in wireless communications under both single-user and multiaccess scenarios. Besides, we summarize research progress in the application of DCSK-based communication systems to ultra-wideband scenarios and their corresponding advantages. Specifically, we restrict our attention to the relevant modulation and system designs, as well as their performance-analysis methodologies. This survey aims not only to allow researchers understanding the development and current status of DCSK-based communication systems, but also to inspire further research in this area.

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A Survey on DCSK-Based Communication Systems and Their Application to UWB Scenarios

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.

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

Motivated by the concept of circuit design in digital circuit, this paper proposes a one-dimensional (1D) nonlinear model (1D-NLM) for producing 1D discrete-time chaotic maps. Our previous works have designed four nonlinear operations of generating new chaotic maps. However, they focus only on discussing individual nonlinear operations and their properties, but fail to consider their relationship among these operations. The proposed 1D-NLM includes these existing nonlinear operations, develops two new nonlinear operations, discusses their relationship among different nonlinear operations, and investigates the properties of different combinations of these operations. To show the effectiveness of 1D-NLM in generating new chaotic maps, as examples, we provide four new chaotic maps and study their dynamics properties from following three aspects: equilibrium point, stability, and bifurcation diagram. Performance evaluations are provided using the Lyapunov exponent, Shannon entropy, correlation dimension, and initial state sensitivity. The evaluation results show that these new chaotic maps have more complex chaotic behaviors than existing ones. To demonstrate the performance of 1D-NLM in practical applications, we use a pseudo-random number generator (PRNG) to compare new and existing chaotic maps. The randomness test results indicate that new chaotic map generated by 1D-NLM shows better performance than existing ones in designing PRNG.

One-Dimensional Nonlinear Model for Producing Chaos

This paper investigates a two-way two-relay network-coded differential-chaos-shift-keying (DCSK) system over multipath Rayleigh fading channels. First, a decode-and-forward protocol is considered, when the two relays first decode the two users' orthogonal transmitted signals and then forward their XORed version back to the users. Based on the equal-gain-combining method at the receiver of each user, the bit-error-rate (BER), achievable diversity order, and throughput are analyzed. It is shown that, as compared to the conventional two-way one-relay network-coded DCSK system, the proposed system achieves lower BER, but reduces the throughput meanwhile. To improve the overall performance and avoid the throughput loss, a novel relay-selection criterion is developed based on the decision metrics used for conventional symbol detection, which can be implemented without requiring the channel state information. According to the criterion, three relay-selection strategies are suggested, namely the max-sum, max-product and max-min relay selections. Both analytical and simulated results show that the proposed relay-selection strategies significantly improve the BER and throughput of the two-way two-relay network-coded DCSK system and achieve higher diversity order. As a further insight, the superiority of the proposed relay-selection strategies is demonstrated in multirelay scenarios. Overall, the proposed system stands out as a promising candidate for low-power and low-complexity short-range wireless-communication applications, such as wireless sensor networks.

Design and Analysis of Relay-Selection Strategies for Two-Way Relay Network-Coded DCSK Systems

A novel non-coherent multi-level differential chaos shift keying (DCSK) modulation scheme is proposed in this paper. This new scheme is based on both the transmitted-reference technique and $M$ -ary orthogonal modulation, where each data-bearing signal is chosen from a set of orthogonal chaotic wavelets constructed by a reference signal. Thanks to this signaling design, the new scheme can achieve a higher attainable data rate, lower energy loss in reference transmission, increased bandwidth efficiency, better data security and better bit error rate (BER) performance as compared to the conventional DCSK. Unlike other DCSK-based systems that separate the reference and data-bearing signals using the TDMA scheme, this new system employs I/Q channels to send these two signals in a parallel and simultaneous manner, making the system easily extendable to multi-carriers. This transmission mechanism not only can further increase data rate but also can remove all radio frequency delay lines from detectors. Analytical BER expressions of the proposed system are derived for both additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. Relevant simulation results are given and compared to non-coherent binary/ $M$ -ary DCSK systems. In addition, the impacts of various system parameters on noise performance are discussed. Both theoretical analysis and simulation results confirm the promising benefits of the new design.

System Design and Performance Analysis of Orthogonal Multi-Level Differential Chaos Shift Keying Modulation Scheme

Based on multi-carrier transmission and multi-level chaos shift keying modulation, a novel multi-carrier chaos shift keying (MC-CSK) modulation system is proposed and designed in this paper. The new system adopts multiple subcarriers, on which all chaotic basis signals along with multiple data-bearing signals are transmitted simultaneously. The data-bearing signals and their references, though sharing the same subcarriers, are separated by I/Q channels. As a consequence, the MC-CSK system can achieve higher bit rate and better spectral efficiency compared with the MC-DCSK system. It can also dispense with chaos synchronization and threshold shifting that are required in conventional CSK systems, and achieve a delay-line-free design in both transmitters and receivers. Also, the performance of the proposed system is further improved by normalizing all chaotic basis signals and making them strictly orthogonal using the Gram-Schmidt algorithm. Moreover, the bit error rates (BERs) of the MC-CSK system over additive white Gaussian noise and multipath Rayleigh fading channels are derived. Finally, simulations are performed under different channel conditions and the effects of system parameters on the BER performance are evaluated. Both analytical and simulation results confirm that the MC-CSK system outperforms differential CSK (DCSK) and MC-DCSK systems in BER performance, except a rare case when the number of subcarriers is very small.

Multi-Carrier Chaos Shift Keying: System Design and Performance Analysis

In this brief, a multi-carrier differential chaos shift keying system capable of mitigating channel noise is proposed. In this system, subcarriers are allocated to the reference and data signals in an optimal way, while noise reduction is achieved through reference diversity. To verify its performance, the bit error rate of the proposed system over multipath Rayleigh fading channels is derived, together with a detailed discussion about the determination of the optimal number of reference-carrying subcarriers. Extensive simulations are carried out for performance evaluation, which are further compared to other state-of-the-art systems. Results confirm the superior bit error rate performance of the proposed system, which has only small loss in energy and spectral efficiencies.

Multi-Carrier Differential Chaos Shift Keying System With Subcarriers Allocation for Noise Reduction

The carrier index differential chaos shift keying (CI-DCSK) modulation scheme transmits one reference and a single data-bearing wavelet over different subcarriers within one symbol duration, resulting in a limited bit rate and low spectral efficiency. In this brief, a novel CI-DCSK modulation scheme is proposed by transmitting multiple data-bearing wavelets together with one reference in a parallel way. Different Walsh codes are applied to separate these data-bearing wavelets so that they can share some subcarriers for index modulation and wavelet transmission. By removing or adding some data-bearing wavelets, the proposed scheme can achieve a high and adaptive data rate with better spectral and energy efficiencies. Furthermore, redundancies in the structure of transmitted signals can be exploited for noise reduction. Analytical bit error rate expressions of the proposed system are derived over the AWGN and the multipath Rayleigh fading channels, respectively. Finally, relevant simulations are performed for verification.

Hua Yang

Papers

System Design and Performance Analysis of Orthogonal Multi-Level Differential Chaos Shift Keying Modulation Scheme

Multi-Carrier Chaos Shift Keying: System Design and Performance Analysis

Multi-Carrier Differential Chaos Shift Keying System With Subcarriers Allocation for Noise Reduction

A High Data Rate Solution for Differential Chaos Shift Keying Based on Carrier Index Modulation