In unsourced random access (URA) system, user pilot collisions are a key challenge when multiple users select identical pilot sequences, leading to poor activity detection and decoding performance. To address this issue, this paper develops a two-stage segmented pilot (TSSP) design for collision-resilient URA in massive multiple-input multiple-output (MIMO) system. The proposed scheme enables a substantial enlargement of the effective pilot space without increasing the physical codebook size and detection complexity. First, we construct a probabilistic collision model by leveraging the birthday-problem analogy, which provides theoretical characterization of collision events and closely matches the simulation results. Second, we propose a segmented pilot mapping and decoding framework in which the pilot bits are divided into two interconnected parts linked by common pilot bits. This structured segmentation allows the system to resolve partial collisions and reduce missed detection in high-density access scenarios. Third, we develop a joint-covariance linear minimum mean square error (JC-LMMSE) scheme that exploits the segmented pilot structure to suppress pilot contamination and improve estimation accuracy. Monte Carlo simulations show that the proposed TSSP framework achieves up to 3.5 dB gain in collision scenarios and approximately 1 dB gain in collision-free cases over existing methods, while maintaining comparable computational complexity.

In this paper, we design a novel joint receiver that iteratively performs channel estimation (CE) and symbol detection for channel-coded multi-user multiple-input multiple-output systems with orthogonal time frequency space modulation (MIMO-OTFS). In particular, we first propose a two-stage CE method based on a single superimposed pilot (SP) with inter-user interference canceling (ICCE). The delay-Doppler domain SP is used to estimate path delays, Doppler shifts, and other channel parameters. Then the detected user symbols are utilized to update the channel parameters with mitigating inter-user and multipath interferences. Second, we construct a joint CE and signal detection scheme based on the expectation propagation (EP) algorithm (EP-ICCE). We exploit the relationship between CE and symbol detection, refining the estimated channel matrix with the detected data symbols. Finally, simulation results shows the proposed EP-ICCE can achieve performance gains up to 2 dB over the conventional methods for the different MIMO and modulations.

Non-coherent chaotic communication has gained increasing attention as it provides an efficient solution for reliable communications without requiring channel state information. In this paper, we propose a non-coherent reconfigurable intelligent surface (RIS)-empowered differential chaos shift keying scheme with two-level nested index modulation (RIS-DCSK-TLNIM). In the proposed RIS-DCSK-TLNIM scheme, the reference index and information index are nested to form two-level nested index modulation. This design enhances both the spectral efficiency and bit error rate (BER) performance of RIS-DCSK-TLNIM, albeit at the expense of slightly increased complexity. Furthermore, we propose a joint detection algorithm to recover the information bits transmitted via the reference index, information index, and two distinct-mode signals. We then extend RIS-DCSK-TLNIM into an enhanced system to achieve higher spectral efficiency. Subsequently, we analyze the BER performance, spectral efficiency, and system complexity of RIS-DCSK-TLNIM, and compare these metrics with those of benchmark systems. Comparison results demonstrate that the proposed RIS-DCSK-TLNIM, when configured with a small number of time slots, can achieve more than twice the spectral efficiency and at least a 6 dB gain in BER performance compared to benchmark systems.

Device-to-device (D2D) communications can allow different devices to communicate in short range, which greatly meets the demand of effective transmissions. In this paper, a spectral and energy-efficient carrier index keying-aided$M$-ary differential chaos cyclic shift keying (CIK-MDCCSK) system is proposed for D2D communications, where multiple cyclic-shifted$M$-ary information-bearing signals are superimposed and transmitted by a subcarrier, and extra keying bits are transmitted by indices of the selected subcarriers. Furthermore, a carrier keying detection and$M$-ary de-mapping algorithm is proposed to retrieve the information bits transmitted by$M$-ary symbols and indices of carrier keying. The bit error rate (BER) expressions of the proposed CIK-MDCCSK system are derived over the additive white Gaussian noise (AWGN) and D2D channels, and the optimal power coefficient is deduced for performance enhancement. Then, the spectral efficiency, energy efficiency, and complexity of CIK-MDCCSK are analyzed and compared to benchmark systems to show its superiority. Next, the proposed CIK-MDCCSK system is expanded into its enhanced version for more effective transmission without degrading the BER performance. It is demonstrated by performance comparisons that the proposed CIK-MDCCSK system can achieve more than twice energy efficiency and up to 3 dB gain in BER performance compared to state-of-the-art benchmarks.

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$M$-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$M$-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.

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 often unaffordable because of the large overhead in transmitting pilot signals. Motivated by these considerations, a novel non-coherent RIS-aided joint index keying$M$-ary differential chaos shift keying (RIS-JIK-MDCSK) system 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 the 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 systems. Numerical simulations are performed to evaluate the superiority of RIS-JIK-MDCSK compared to existing systems.

A Noise Suppression aided Multi-Carrier$M$-ary Differential Chaos Shift Keying (NS-MC-MDCSK) system is proposed here where each information subcarrier transmits an$M$-ary information-bearing signal and the$M$-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$M$-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.

A joint energy and correlation detection aided orthogonal frequency division multiplexing differential chaos shift keying (JECD-OFDM-DCSK) system is presented in this paper, where the reference and information-bearing signals of JECD-OFDM-DCSK are superimposed in the same time slot so that the phase offset between the reference and information-bearing signals is addressed. In JECD-OFDM-DCSK, only some subcarriers are activated and additional information bits are transmitted by the indices of these activated subcarriers, thereby improving the data rate while reducing the energy consumption. The energy efficiency, peak to average power ratio (PAPR) performance and system complexity of JECD-OFDM-DCSK are analyzed and then compared to other systems. The comparison results show JECD-OFDM-DCSK can obtain higher energy efficiency and better PAPR performance compared to its competitors at the cost of higher system complexity. Furthermore, the bit error rate (BER) expressions of JECD-OFDM-DCSK are derived in additive white Gaussian noise (AWGN) and multipath fading channels. Simulation results show that the BER performance of JECD-OFDM-DCSK outperforms that of other OFDM-based DCSK systems. Finally, JECD-OFDM-DCSK performs much better than other systems over the underwater acoustic (UWA) channel, which validates the robustness of JECD-OFDM-DCSK.

Given the high transmission loss, severe Doppler spread and large multipath delay in the underwater acoustic (UWA) channel, the channel estimation and tracking in the conventional orthogonal frequency division multiplexing (OFDM) based UWA systems are severely unaffordable. In this paper, we propose a low-complexity and cost-friendly OFDM-based differential cyclic-shifted differential chaos shift keying (OFDM-DCS-DCSK) system which offers a high data rate, superior robustness and enhanced system security for UWA communications without the need for channel state information (CSI). In the system, the information bits are carried by different step lengths of the cyclic shifts. At the receiver, a low-complexity detection method is used to search the position of maximum from the cyclic correlation values and therefore estimate the information bits. Finally, simulation results demonstrate the proposed OFDM-DCS-DCSK system outperforms its competitors both in bit error rate (BER) performance and in system security.

In this paper, we focus on designing a high-data-rate noncoherent chaotic communication scheme to satisfy the demand of the explosive growth in data traffic. To achieve this goal, a joint time-frequency index modulation assisted multiple-mode DCSK (JTFIM-MM-DCSK) system is proposed, where a pair of distinguished signal modes are modulated into the selected subcarriers and another signal mode is transmitted by the unselected subcarriers. In this configuration, besides the modulated bits used for physical transmission, the carrier index bits and time slot index bits, conveyed by the state of whether subcarriers and time slots are selected or not, are also transmitted implicitly to achieve higher data rate. Moreover, the design of multiple-mode signals ensures that it is taking full advantage of all subcarriers and time slots to transmit the information bits, thereby improving the data rate significantly. The bit error rate (BER) expressions of the JTFIM-MM-DCSK system are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels, which are checked by computer simulations. Finally, the advantage of the JTFIM-MM-DCSK system over other up-to-date noncoherent chaotic communication systems is demonstrated in terms of BER performance through extensive computer simulations.

A new multicarrier M-ary orthogonal chaotic vector shift keying with index modulation (MC-MOCVSK-IM) is presented in this paper. In this design, information bits are conveyed not only by the multiple groups of M-ary information bearing signals, but also by the specific indices of the selected reference signals which depend on the incoming mapped bits. Benefiting from the favorable features of multicarrier modulation, M-ary modulation and index modulation, MC-MOCVSK-IM system is capable to offer higher energy efficiency and spectral efficiency at some expense of hardware complexity. In addition, the analytical bit error rate (BER) expressions of MC-MOCVSK-IM system are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels. The BER performance comparison between MC-MOCVSK-IM system and other non-coherent chaotic communication systems is carried out to highlight the superiority of MC-MOCVSK-IM system in terms of BER performance. Considering the dramatically increased demand for high-data-rate transmission and the harsh environment of future wireless communication, MC-MOCVSK-IM system shows strong robustness and offers competitive solutions for high-data-rate non-coherent chaotic communication systems.

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.

In this study, an M ‐ary code‐shifted differential chaos shift keying system with in‐phase and quadrature code index modulation (I/Q‐CIM‐CS‐MDCSK) is presented. In the proposed system, the information bits are conveyed not only by the M ‐ary constellation symbols, but also by the specific Walsh codes indices corresponding to the in‐phase and quadrature branches of M ‐ary information bearing signals. Since the reference signal and the multiple M ‐ary information bearing signals are overlapped and transmitted within the identical time slot in a parallel manner, the spectral efficiency of the I/Q‐CIM‐CS‐MDCSK system is enhanced significantly. In addition, the analytical bit error rate (BER) expressions for the presented system are derived under the additive white Gaussian noise and multipath Rayleigh fading channels. Finally, the BER performance of the proposed system is compared to other chaotic communication systems. The results manifest that the I/Q‐CIM‐CS‐MDCSK system is a promising and competitive chaotic communication scheme.

In this paper, a dual-mode differential chaos shift keying with index modulation (DM-DCSK-IM) is proposed. In the proposed system, the bit stream is partitioned into two subblocks, where the first subblock is the mapped bits used to select the active time slot, which presents the time slot's constellation mode, and the second subblock is the modulated bits, which are further divided into two groups and modulated by a pair of distinguishable modem-mode constellations, respectively. Unlike the recently proposed pulse-position-modulation differential chaos shift keying (PPM-DCSK), since both the active and inactive time slots are applied to convey the information bits, the data rate of the proposed system can be promoted significantly. In order to detect the active time slots and recover the mapped bits as well as modulated bits correctly, we propose an effective detection algorithm for the proposed system. Furthermore, the theoretical bit error rate (BER) expressions are derived over additive white Gaussian noise (AWGN) and multipath Rayleigh fading channels, and the simulation results validate the accuracy of our derivations. Finally, the BER performance of the proposed system is compared with the other non-coherent chaotic communication systems, and the results indicate that the proposed system can offer competitive and satisfactory BER performance.

In this paper, an M -ary orthogonal multilevel differential chaos shift keying system with code index modulation (CIM-OM-MDCSK) is proposed. In the proposed system, the multiple information bearing signals are modulated by the selected Walsh codes with specific indices and the M -ary information signals which are composed of modulated bits, chaotic signals, and their Hilbert transform. Since the reference signal along with the information bearing signals are overlapping in time domain and orthogonal in code domain by using Walsh code sequences, the spectral efficiency of the CIM-OM-MDCSK system is improved largely. By combining the M -ary modulation, orthogonal multilevel modulation, and code index modulation, the proposed CIM-OM-MDCSK system can achieve high data rate and superior bit error rate (BER) performance compared to its rivals. Moreover, we derive the BER expressions of the proposed system over additive white Gaussian noise and multipath Rayleigh fading channels. Finally, we make a performance comparison between the proposed system and other state-of-the-art non-coherent chaotic communication systems. The results confirm the competitive benefits of the proposed system.