This paper proposes a robust, energy-efficient multi-user OFDM chaotic vector cyclic shift keying (MU-OFDM-CVCSK) system for channels impaired by multi-user interference (MUI), Gaussian, and impulsive noise. The system’s co-designed transceiver uses cyclic shifts of a single reference signal for energy efficiency, while a novel receiver combines low-rank matrix factorization with a truncated-quadratic loss function to suppress both MUI and noise. In particular, the transmitted signal’s cyclical structure enables iterative reference refinement, further enhancing performance. We provide a comprehensive analysis of the algorithm’s convergence, complexity, energy efficiency, power spectral density, peak-to-average power ratio, and derive the bit error rate (BER) expressions. Simulations demonstrate superior BER performance compared to benchmark schemes in challenging interference and noise conditions.

In traditional multi-user orthogonal frequency division multiplexing differential chaos shift keying (MU-OFDM-DCSK) systems, the noisy correlation of reference signals with overlapped information-bearing signals from multiple users degrades the bit error rate (BER). This paper devises a MU-OFDM-DCSK receiver that enhances the BER performance for uplink transmission. In our design, the challenges of reducing multi-user interferences (MUIs) and noise in both reference and information-bearing chaotic signals are addressed via leveraging the low-rank structure of the received signal matrix. By exploiting low-rank matrix factorization, a novel objective function is constructed. Minimization of this function, which corresponds to a least squares optimization, can effectively decode the transmitted data bits, even in the presence of additive white Gaussian noise (AWGN) and MUIs. The BER of our scheme is analyzed and verified in both AWGN and multipath Rayleigh fading channels. Theoretical developments including uniqueness of matrix factorization and algorithm convergence as well as complexity, are also provided. Simulation results demonstrate that our designed receiver yields smaller BER than benchmark schemes.

In this paper, we propose a novel dual index pulse position modulation differential chaotic shift keying (DI-PPM-DCSK) system for wireless covert communication. Unlike conventional PPM schemes, at the transmitter, we propose to modulate index bits with the positions of both the reference and information-bearing signals, thereby incorporating more index bits into each symbol. Thus both energy efficiency and data rate can be improved. Besides, the information-bearing modulated signals are hidden with the artificial noise to enhance the covertness of communications. At the receiver, we propose to demodulate the information bits by calculating the coherence of adjacent symbols. Moreover, we derive analytical expressions for the bit error rate (BER) and covert performance of the system, which are validated through numerical simulations. The results demonstrate that the proposed system achieves superior data rate and BER performance compared to existing counterparts over fading channels. Furthermore, the covertness is validated with both theoretical analysis and simulation results.

In this paper, we propose a pre-coded multi-carrier$M$-ary chaotic vector cyclic shift keying (PC-MC-$M$-CVCSK) transceiver for reliable information transmissions. In this design, we exploit the principle of diagonalization to combat noises and interferences. At the PC-MC-$M$-CVCSK transmitter, we propose to precode the$M$-ary modulated symbols based on the discrete Fourier transform (DFT) and the reverse matrix of an eigenvalue matrix. Meanwhile, the chaotic generator outputs chaotic sequences, which are then cyclically shifted and used to modulate precoded symbols. At the receiver, reverse operations are conducted to recover the data. Moreover, we prove that a circulant matrix can be constructed by selecting the cyclic shift length, while the DFT aided processing will diagonalize the circulant matrix. Thanks to the diagonalization design, the inner product of information-bearing chaotic vectors becomes zero, thus signals can be orthogonalized to suppress interferences. Furthermore, theoretical performances of the proposed transceiver, including the bit error rate (BER), the symbol rate, the energy efficiency and the spectrum efficiency, and the computational complexity are analyzed. Simulation results validate the exact analysis. Furthermore, the results demonstrate that the proposed PC-MC-$M$-CVCSK system outperforms the counterpart schemes, which can provide$M$-ary high symbol rate transmission services with enhanced reliability performances.

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.