Multi-carrier Differential Chaos Shift Keying Research Articles

Matrix Reconstruction Algorithm-Assisted Multi-Carrier DCSK Scheme: An Effective Solution for Frequency-Selective Fading Channel

Matrix Reconstruction Algorithm-Assisted Multi-Carrier DCSK Scheme: An Effective Solution for Frequency-Selective Fading Channel

A Noise Reducing Multi-carrier DCSK Communication System Based on Carrier Phase and Code Index Modulation

A Noise Reducing Multi-carrier DCSK Communication System Based on Carrier Phase and Code Index Modulation

Multi-carrier DCSK With Hybrid Index Modulation: A New Perspective on Frequency-Index-Aided Chaotic Communication

To realize high energy-efficient, high spectrum-efficient, and high-throughput data transmission, a multi-carrier differential chaos shift keying communication system with hybrid index modulation, referred to as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">HIM-MC-DCSK system</i> , is proposed in this paper. In the HIM-MC-DCSK system, we intelligently integrate the carrier-number-index technique and carrier-index technique into the MC-DCSK modulation in order to significantly boost the transmission efficiency in wireless communication systems. Especially, we use a pair of orthogonal signals to represent the active and inactive subcarriers in the HIM-MC-DCSK system so as to exploit all the subcarriers to transmit information bits. In addition, the theoretical bit-error-rate (BER) expressions of the HIM-MC-DCSK system are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. Also, the data rate, spectrum efficiency, energy efficiency, and complexity of the proposed system are carefully analyzed. Monte-Carlo simulations not only verify the accuracy of the theoretical analysis but also illustrate the superiority of the proposed system.

Cross Correction and Chaotic Shape-Forming Filter Based Quadrature Multi-Carrier Differential Chaos Shift Keying Communication

In this paper, an improved Quadrature Multi-carrier Differential Chaos Shift Keying (QMC-DCSK) based on Chaotic Shape-forming Filter (CSF) and Cross Correction (CC) is proposed. The chaotic signal generated by CSF is used as reference spreading sequence in QMC-DCSK. Quadrature multi-carriers are used to carry the reference and multiple information bearing signals simultaneously in order to improve the Bit Transmission Rate (BTR). By this way, the proposed system is able to transmit <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2M-1$</tex-math></inline-formula> bits Traditional Data Stream (TDS) during one traditional DCSK bit duration, where <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> is the number of carrier frequencies. Meanwhile, the reference signal transmits Additional Data Stream (ADS) encoded by CSF together with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2M-1$</tex-math></inline-formula> identical or inverse data stream carried by the rest <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2M-1$</tex-math></inline-formula> channels (information bearing signals). By this system configuration, the channel redundance can be used to improved bit error rate (BER) performance of ADS, after decoding TDS. In turn, the TDS reliability can also be improved by checking most ADS polarity of the corresponding carrier. This process is referred to as CC. The contribution of this work lies in the CC operation, by which the reliability of both TDS and ADS is improved significantly. It is the CSF and multi-carrier that make CC possible. The analytical BER is derived for the proposed method. The merits of the proposed system include, first, it improves the BTR as compared to that of QMC-DCSK, because ADS conveys more information bits; second, the ADS reliability is improved dramatically because the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{2}\,M$</tex-math></inline-formula> duplication can be used to improve the signal to noise ratio; third, the TDS reliability is improved as well because the information bits conveyed by each carrier frequency is enhanced and corrected by the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\text{2}\,M$</tex-math></inline-formula> repetitions. By this way, not only TDS and ADS are transmitted (i.e., the higher BTR is achieved), but also both reliability are improved (i.e. the lower BER is achieved). In order to testify the feasibility and superiority of the proposed method, simulation and wireless open-access research platform (WARP) experiment are conducted. The simulation and experiment results show that the proposed method is superior to other comparison methods.

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.

Reliable and Efficient Sparse Code Spreading Aided MC-DCSK Transceiver Design for Multiuser Transmissions

In this paper, we propose a Sparse Code Spreading-aided Multi-Carrier Differential Chaos Shift Keying (SCS-MC-DCSK) transceiver to improve the efficiency and reliability performances for multiuser transmissions. With the aim to improve the spectrum efficiency and enhance the reliability, we construct a multi-dimension codebook based on a factor graph matrix to spread information bits in a non orthogonal way, thus the signals could overlap and multiple users are allowed to share all sub-carrier resources via the non orthogonal spreading. The information bits using the same codebook are regarded as a layer, while each user could choose to use one or multiple layers. Then the resultant symbols are spread by the reference chaotic sequence and its quadrature version generated by Hilbert transform in the time domain. At the receiver, reverse operations are conducted, and we propose the Minimum Distance (MD) detection method to retrieve the estimates. Furthermore, theoretical performances, including the Symbol Error Rate (SER), capacity, energy efficiency, spectrum efficiency and computational complexity, are analyzed and compared among the proposed design and benchmarks. Simulation results are then provided to validate the theoretical analysis. Moreover, the Bit Error Rate (BER) performances under different channel conditions demonstrate the superior reliability and efficiency to benchmarks.

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.

Quadrature MC-DCSK Scheme for Chaos-Based Cognitive Radio

In this study, we investigate an enhanced architecture of multicarrier differential chaos-shift keying (MC-DCSK) scheme using quadrature modulation (QM), namely QMC-DCSK. The use of quadrature modulation aims at doubling the data rate over a defined bandwidth and hence improve bandwidth efficiency of the system. In the proposed scheme, the chaotic spreading sequence is transmitted on a predefined frequency while each of the remaining frequencies is phase-shifted at a [Formula: see text] angle in order to produce two quadrature subcarriers located at the same frequency. These subcarriers are modulated by the product of the chaotic spreading sequence and the corresponding bit substreams in parallel. Noncoherent demodulation is carried out in the receiver in order to recover the original data based on the sign of correlation values. Architecture and operation of the conventional and proposed schemes are described. The BER performance over a wireless channel is theoretically derived and then numerically verified. The bit rate, energy and bandwidth efficiencies are evaluated in comparison with those of MC-DCSK. In particular, the application of the proposed scheme to cognitive radio (CR) in the scenario of using multicarrier modulation and chaotic spread-spectrum is discussed and evaluated. The obtained results prove that QMC-DCSK is a fit technique for CR communications.

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.

GCI-DCSK: Generalized Carrier Index Differential Chaos Shift Keying Modulation

A carrier index differential chaos shift keying (CI-DCSK) modulation has been proposed to improve BER performance, spectral efficiency (SE) and energy efficiency (EE) compared to traditional DCSK. CI-DCSK employs a one-to-one mapping between the index symbols and the carrier activation patterns, which limits the numbers of both index carriers and index bits. In this letter, a generalized carrier index differential chaos shift keying (GCI-DCSK) modulation is proposed, which extends the aforementioned CI-DCSK by employing the combinatorial method to index selector and index demapper, where the numbers of both index carriers and index bits are arbitrarily adjustable. Theoretical bit error rate (BER) expressions over both additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels are derived. It is shown that GCI-DCSK can flexibly provide red the desired performance, EE, and SE compared to CI-DCSK, commutation code index DCSK (CCI-DCSK) and permutation index DCSK (PI-DCSK). Besides, in some cases, GCI-DCSK can provide higher SE, larger EE and better error performance than multicarrier DCSK (MC-DCSK) with the same bandwidth.

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.

Noise Reduction Multi-Carrier Differential Chaos Shift Keying System

In multi-carrier differential chaos shift keying (MC-DCSK) system, channel noises pollute both the reference and data signals, resulting in deteriorated performance. To reduce noises in received signals in MC-DCSK, a novel noise reduction MC-DCSK (NR-MC-DCSK) system is proposed in this paper. The proposed system utilizes duplicated chaotic samples, rather than different ones, as the reference. At the receiver side, identical samples can be averaged before correlation detection, which helps decrease the noise interferences and thus brings performance improvement. Theoretical bit error rate (BER) expressions are derived and verified by simulation results for additive white Gaussian noise and multipath Rayleigh fading channels. Finally, comparisons to MC-DCSK and other DCSK-based systems are given to confirm the superiority of the proposed system in BER performance.

Multi-carrier differential chaos-shift keying with repeated spreading sequence

This paper proposes a multi-carrier differential chaos-shift keying (MC-DCSK) system using repeated spreading sequence (RSS), namely RSS-MC-DCSK, for chaos-based wireless communications. In the proposed system, instead of transmitting the chaotic spreading sequence on a predefined subcarrier as in conventional MC-DCSK, a DCSK-modulated signal, of which each two-bit duration consisting of reference and data-bearing sequences is sent via this subcarrier. Meanwhile, a repeated spreading sequence is produced by copying the reference sequence of the DCSK-modulated signal to the same and next bit periods. The parallel bit streams are multiplied with this RSS and the resulting signals are then conveyed by corresponding subcarriers. In the receiver, the signal retrieved from the predefined subcarrier is DCSK-demodulated and simultaneously used to recover the repeated spreading sequence. The correlative demodulation is performed for all the signals retrieved from the remaining subcarriers to decode the data. The structure and operation of the proposed system are described. Bit error rate (BER) performance under a multipath Rayleigh fading channel is theoretically analyzed and then verified by numerical simulations. In addition, the BER performance, energy and spectral efficiencies of RSS-MC-DCSK are evaluated in comparison to those of MC-DCSK.

Design and analysis of a DCSK-based cognitive radio system using hybrid underlay/overlay transmission

In this paper, we present a hybrid Underlay/Overlay DCSK-based Cognitive Radio (DCR) system using the Cognitive Radio techniques and abilities of a Multi-Carrier DCSK (MC-DCSK) scheme together, which can be extended to many other similar non-coherent scenarios. In this scheme, secondary user (SU) employs the spectrum holes as a dedicated frequency to transmit reference signals in overlay mode and uses remaining common frequencies to transmit data bearing signals by an underlying approach. We derived an analytical BER expression for the DCR scheme over a frequency selective fading channel and adopted it as our optimization criterion. To formulate the optimization problem, we proposed a sub-carrier grouping approach in order to implement our min–max fairness strategy, considering the power budget and interference temperature constraints. The proposed DCR scheme not only employed spectrum holes, but also improved BER performance of the conventional multi-user MC-DCSK system significantly considering the power allocation policy and robustness against frequency selective channel. Finally, simulation results validated the advantages of the proposed scheme.

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.

Carrier Index Differential Chaos Shift Keying Modulation

A new carrier index differential chaos shift keying (DCSK) modulation method combining index modulation (IM) with multicarrier DCSK (MC-DCSK) is proposed. Two schemes employing two different index selectors and detectors to implement IM and demodulation are introduced. The new designed index selectors are one-to-one mappings between the index symbols and the carrier activation patterns, which can avoid the disaster caused by the previous designed selectors. Analytical bit error rate expressions of the two systems are derived over the additive white Gaussian noise as well as multipath Rayleigh fading channels. Simulation results verify the superiority of one scheme in energy efficiency and another scheme in spectral efficiency, respectively, compared with MC-DCSK.

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.

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.

Analog Network Coding for Multi-User Multi-Carrier Differential Chaos Shift Keying Communication System

This paper presents the design and performance analysis of an analog network coding (ANC) scheme for multi-user multi-carrier differential chaos shift keying (MC-DCSK) modulation. The incentives to employ the MC-DCSK system are to achieve a better spectral efficiency and more efficient energy consumption compared to that of a conventional DCSK system. The proposed scheme considers a network comprising L user nodes (L ≥ 2) and a single relay node R. In this scheme, called the ANC-based two-way relay system, all users transmit their signals to the relay in the first time slot, and the relay forwards the superposition of the received signals each of the user nodes in the second time slot. At the receiver end, each user mitigates the overall interference by subtracting its own data signal from the received combined signal and then starts the decoding process. The system design is analytically studied, and the corresponding theoretical bit error rate expression for the multipath fading channel is derived. Additionally, the conventional ANC-DCSK scheme is analyzed and compared to the proposed ANC-based MC-DCSK scheme to show the improvement in the performance of our approach. Finally, to validate the accuracy of the methodology, the simulation results are compared to the related theoretical expressions.