Differential Chaos Shift Keying System Research Articles

A Multilevel Code-Shifted Differential Chaos Shift Keying System With Reference Diversity

In this brief, a multilevel code-shifted differential chaos shift keying system with reference diversity (MCS-DCSK-RD) is proposed. In the proposed system, the reference signal with several replicated versions (called reference diversity) are transmitted to reduce the interference of channel noise on the reference signal. We derive the theoretical bit error rate (BER) of the proposed system over the AWGN and multipath Rayleigh channels, and verify its accuracy by simulations. Then, the optimal reference diversity quantity is determined via the theoretical BER. Compared with the multilevel code-shifted differential chaos shift keying (MCS-DCSK) system, the proposed scheme with optimal reference diversity quantity can effectively reduce noise, thus obtain much better BER performance over the additive white Gaussian noise (AWGN) and multipath Rayleigh channels. Also, we further reduce the noise by averaging the received demodulated signals at the receiver, thereby further improving the BER performance of the MCS-DCSK-RD system.

Performance analysis for DCSK system over land mobile satellite channel

In chaos-based digital communications, differential chaos-shift keying (DCSK) system has been widely studied thanks to its non-coherent demodulation without chaotic sequence synchronisation. In respect of the performance evaluation, bit error rate (BER) of the DCSK system was investigated over various transmission environments such as noise, fading, and multi-path-affected channels which are radio-propagation models from simple to complex. In this paper, the idea of applying DCSK for operation in land mobile satellite environments is proposed. A land mobile satellite channel, i.e., Lutz model with two states, is used to evaluate the system performance. Discrete-time models of transmitter and receiver over the studied channel are described. BER analysis is performed by means of Gaussian approximation and discrete integration. The analysed expressions are verified by Monte Carlo simulation. Performance comparison between different DCSK-based schemes over the studied channel is carried out. Obtained results point out that DCSK system can be used as a physical-layer modulation method using chaos for land mobile satellite applications.

High‐data‐rate PO‐CDSK: a high effective chaotic communication scheme

To eliminate the intrasignal interference (ISI), phase-orthogonality correlation-delay-shift-keying (PO-CDSK) alternately chooses quadrature sinusoidal wavelets to modulate the reference signals in different symbol durations and keeps the reference and information-bearing signals orthogonal in one symbol duration. Unfortunately, in PO-CDSK, one data-modulated signal can carry only 1-bit information, resulting in a relatively low data rate. In this brief, the authors design a high-data-rate PO-CDSK system, in which 2-bits information share one time slot but transmitted over the inphase and quadrature channels, respectively. Theoretical BER expression of the proposed system is studied analytically, and simulations are performed over additive white Gaussian noise and Rayleigh multipath fading channels for verification. Results show that, without ISI components, the authors' new system performs much better than differential-chaos-shift-keying (DCSK), CDSK and high-efficiency DCSK systems in BER performance. Besides, the proposed system also achieves doubled spectral and energy efficiencies in comparison with PO-CDSK.

A Framework for the Lower Bound on the BER of DCSK Systems Over Multi-Path Nakagami-m Fading Channels

In this brief, a generalized closed-form approach for the evaluation of the lower bound on the BER of differential chaos-shift-keying (DCSK) systems over multi-path Nakagami- $m$ fading channels is presented. A closed-form lower bound is derived for all configurations of the Nakagami- $m$ channel model which extends to all fading profiles covered by the Nakagami model. In contrast to previous works where very specific models were targeted and only numerical analyses of the DCSK systems were presented, we provide an approach that analytically unifies the performance analysis of DCSK systems over more generalized fading models. A similar analytical development is generalized for Quadrature Chaos Shift Keying (QCSK) and Multi-carrier Differential Chaos Shift Keying (MC-DCSK) systems. A lower bound is applied on the Q-function to extract an exponential expression of the BER. Afterwards, a bound on the exponential function is used to derive a simple polynomial expression which is easily integrable using basic integration techniques for all multi-path Nakagami- $m$ fading channels. The final expression of the newly derived lower bound is forwarded in terms of the Gaussian hypergeometric functions. Comparative simulations conducted for the different systems under consideration show a tight gap between the BER of the simulated systems and their respective lower bounds.

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 Analysis of a Wavelet Packet Modulation Based Differential Chaos Shift Keying Communication System

In this paper, a new multicarrier based DCSK system that is combined a wavelet packet modulation (WPM) with differential chaos shift keying (DCSK) and named WPM–DCSK is proposed. WPM–DCSK system is an extension of orthogonal frequency division multiplexing OFDM–DCSK system that aims to replace the fast Fourier transform in OFDM system with wavelet packet transform and improves the spectral efficiency by removing the cyclic prefix and reduced the complexity by using real operation instead of complex operation. WPM–DCSK system has all the benefit of OFDM–DCSK and furthermore improves the limitations and drawbacks of it. The data rate improvement, the energy saving improvement and data-energy- to-bit-energy-ratio factors are derived and compared with DCSK and OFDM–DCSK systems. The validity of the derived analytic expression of the bit error rate of the proposed system is confirmed by the simulation under an additive white Gaussian noise channel.

Design and Performance Analysis of Differential Chaos Shift Keying System With Dual-Index Modulation

In order to sufficiently utilize the time slot resources of the recently proposed pulse-position-modulation differential chaos shift keying (PPM-DCSK), we apply dual-index modulation to differential chaos shift keying and then present two differential chaos shift keying systems with dual-index modulation (DCSK-DIM), where the transmitted bits are partitioned into two orthogonal branches correspond to the in-phase branch and quadrature branch, respectively. Then, by means of the dual-index modulation technique, the mapped bits of in-phase and quadrature branches are modulated into a pair of distinguishable index symbols and thus recycle the time slot resources. At the receiver, two different detection methods are employed to determine the index symbols and demodulate the modulated bits carried by the active time slots. In addition, we derive the theoretical bit error rate (BER) expressions for the proposed DCSK-DIM systems over additive white Gaussian noise and multipath Rayleigh fading channels, respectively. In addition, then the simulation results validate the corresponding theoretical derivations. Finally, compared with other non-coherent chaotic communication systems, the proposed DCSK-DIM systems can achieve an excellent BER performance or data rate. Explicitly, the DCSK-DIM-I system makes a great progress in pursuit of admirable BER performance, while the DCSK-DIM-II system elevates the data rate to great extent.

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

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.

High‐efficiency and noise‐robust DCSK approach based on an analytically solvable chaotic oscillator

A novel high-efficiency and noise-robust differential chaos shift keying (DCSK) communication approach based on an analytically solvable chaotic oscillator (ASCO) is proposed. Due to the special characteristic of the ASCO that provides predictability over specific intervals of every binary symbol period, the proposed communication system requires no reference signal like conventional DCSK systems, which can double the data transmission rate. Meanwhile, the originally transmitted binary information can be recovered by conducting integration processing of the received signal over the specific intervals of every binary symbol period, even under strong noise conditions, which provides a low bit error rate (BER). Simulations are conducted to verify that the proposed DCSK approach provides a much lower BER than conventional DCSK approaches.

A Coded DCSK Modulation System Over Rayleigh Fading Channels

Coded modulation (CM) is a bandwidth efficient framework to approach the capacity limit of the differential chaos shift keying (DCSK) systems. In this paper, we propose an M-ary DCSK system operated with CM based on nonbinary protograph low-density parity-check (LDPC) codes over Rayleigh fading channels. First, we investigate the performance of the proposed nonbinary channel coded DCSK (CM-DCSK) and bit-interleaved coded DCSK (BICM-DCSK). In particular, we show that CM-DCSK outperforms BICM-DCSK over Rayleigh fading channels in terms of capacity limit. Compared with BICM-DCSK, CM-DCSK can simplify the receiver structure, since it does not require turbo iteration between the noncoherent detector and channel decoder. Second, guided by the modified extrinsic information transfer (EXIT) analysis, we put forth two new types of nonbinary protograph LDPC codes to approach the capacity limit of CM-DCSK. Both EXIT analysis and simulation results demonstrate that the proposed protograph-coded CM-DCSK achieves a better error performance than BICM-DCSK even with iterative decoding. Furthermore, we show the performance superiority of nonbinary protograph-coded CM-DCSK over a practical ultra-wideband channel. Hence, we conclude that this proposed scheme offers a good alternative for wireless local area network applications.

Design and Performance Analysis of MISO-SRMR-DCSK System over Rayleigh Fading Channels

The major drawback of the differential chaos shift keying (DCSK) system is that equal time and energy are spent on the reference and data signal. This paper presents the design and performance analysis of a short reference multifold rate DCSK (SRMR-DCSK) system to overcome the major drawback. The SRMR-DCSK system is proposed to enhance the data rate of the short reference differential chaos shift keying (SR-DCSK) system. By recycling each reference signal in SR-DCSK, the data slot carries N bits of data and by P times. As a result, compared with SR-DCSK, the proposed system has a higher data transmission rate and evaluates the energy efficiency with respect to the conventional DCSK system. To further improve the bit-error-rate (BER) performance over Rayleigh fading channels, the multiple-input single-output SRMR-DCSK (MISO-SRMR-DCSK) is also studied. The BER expression of the proposed system is derived based on Gaussian approximation (GA), and simulations in Rayleigh fading channels are performed. Simulation results show a perfect match with the analytical expression.

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.

Design and Optimization of Differential Chaos Shift Keying Scheme With Code Index Modulation

Energy usage and data rate of differential chaos shift keying (DCSK) are both inefficient since half of the symbol duration is used to transmit reference. To improve the energy efficiency and data rate, we propose a new chaos modulation scheme which combines DCSK with code index modulation (CIM) referred to as CIM-DCSK. In the proposed scheme, a short reference signal is transmitted first. Then P repeated reference signals, which serve as information-bearing signals, are simultaneously modulated by an information bit and a Walsh code with a specific index which is determined by an extra information symbol. The analytical bit error rate (BER) performance of the proposed scheme is derived and verified by simulations. Further, we improve the performance of the proposed system by applying noise-reduction and optimizing power coefficients on the reference and the information-bearing signals of CIM-DCSK. Simulation and analytical results show that these optimization methods significantly boost the BER performances of the proposed schemes. Finally, the BER performances of the proposed systems are compared with that of the conventional DCSK system and the short reference DCSK (SR-DCSK) system. Numerical results show that the proposed schemes outperform both DCSK and SR-DCSK.

A Generalized Lower Bound on the Bit Error Rate of DCSK Systems Over Multi-Path Rayleigh Fading Channels

This brief presents a generalized closed-form expression of the lower bound on the bit error rate (BER) of differential chaos-shift-keying (DCSK) systems. The analytical expressions are derived for multi-path Rayleigh fading channels. Unlike already existing research work, where numerical integration is the only way forward to derive the average BER for DCSK systems, this brief provides a generalized analytical expression of the lower bound on the BER. In this vein, the bounds of Q-function are used to solve complex integrals of the average BER expressions. Furthermore, a theoretical framework is also provided to generalize the derived analytical expression for the multi-carrier DCSK and the quadrature chaos shift keying systems. For validation of these results, a detailed comparative study with already existing numerical simulations is also provided. In this brief, the analytically derived bound matches the simulation results with a very narrow gap. Therefore, the bound allows the prediction of the actual BER of any chaos-based transmit reference modulation system and its derivatives, with negligible gap.

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

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.

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.

Capacity of the non‐coherent DCSK system over Rayleigh fading channel

Capacity bounds are calculated for the differential chaos shift keying (DCSK) system with non-coherent detectors, including differentially coherent detector and energy detector, over additive white Gaussian noise (AWGN) and Rayleigh fading channels. Through theoretical analysis and numerical simulations, it is found that the capacity characteristics of the non-coherent DCSK system are significantly different from those of the coherent case. It is shown that there are different capacity bounds corresponding to different spreading factor values. Optimal code rates are found, which minimise the required bit signal-to-noise ratio for a reliable communication system, and they are increasing with the increase of the spreading factor value over an AWGN channel while decreasing over a Rayleigh fading channel. As compared with the AWGN channel, the performance over a Rayleigh fading channel is much more sensitive to the code rate. The new results are useful as benchmark for designing capacity-approaching codes for the non-coherent DCSK system.

Very high efficiency differential chaos shift keying system

In this study, a new non-coherent communication system, i.e. very high efficiency differential chaos shift keying system, is proposed. This system is a generalised form of the high efficiency differential chaos shift keying (HE-DCSK) system, with an arbitrary number (N) of transmitted bits per frame. The major advantage of this new proposition is its ability to significantly improve the spectral efficiency compared with DCSK and HE-DCSK. The theoretical bit error rate of this system is found using the Gaussian approximation method under different communication channels: additive white Gaussian noise and two-ray Rayleigh fading channels. Simulations in both environments show a perfect match with the analytical expressions for large spreading factors. Simulation results for the two-ray Rayleigh fading channel show clearly the diversity gain compared with the single-ray Rayleigh channel.

NR-DCSK: A Noise Reduction Differential Chaos Shift Keying System

One of the major drawbacks of the conventional differential chaos shift keying (DCSK) system is the addition of channel noise to both the reference signal and the data-bearing signal, which deteriorates its performance. In this brief, we propose a noise reduction DCSK system as a solution to reduce the noise variance present in the received signal in order to improve performance. For each transmitted bit, instead of generating $\beta$ different chaotic samples to be used as a reference sequence, $\beta/P$ chaotic samples are generated and then duplicated $P$ times in the signal. At the receiver, $P$ identical samples are averaged, and the resultant filtered signal is correlated to its time-delayed replica to recover the transmitted bit. This averaging operation of size $P$ reduces the noise variance and enhances the performance of the system. Theoretical bit error rate expressions for additive white Gaussian noise and multipath fading channels are analytically studied and derived. Computer simulation results are compared to relevant theoretical findings to validate the accuracy of the proposed system and to demonstrate the performance improvement compared to the conventional DCSK, the improved DCSK, and the differential-phase-shift-keying systems.

Design of a Short Reference Noncoherent Chaos-Based Communication Systems

Data rate and energy efficiency decrement caused by the transmission of reference and data carrier signals in equal portions constitute the major drawback of differential chaos shift keying (DCSK) systems. To overcome this dominant drawback, a short reference DCSK system (SR-DCSK) is proposed. In SR-DCSK, the number of chaotic samples that constitute the reference signal is shortened to $R$ such that it occupies less than half of the bit duration. To build the transmitted data signal, $P$ concatenated replicas of $R$ are used to spread the data. This operation increases data rate and enhances energy efficiency without imposing extra complexity onto the system structure. The receiver uses its knowledge of the integers $R$ and $P$ to recover the data. The proposed system is analytically studied and the enhanced data rate and bit energy saving percentages are computed. Furthermore, theoretical performance for AWGN and multipath fading channels are derived and validated via simulation. In addition, optimising the length of the reference signal $R$ is exposed to detailed discussion and analysis. Finally, the application of the proposed short reference technique to the majority of transmit reference systems such as DCSK, multicarrier DCSK, and quadratic chaos shift keying enhances the overall performance of this class of chaotic modulations and is, therefore, promising.