Deep-learning-based modulation recognition methods can extract the features of signals automatically with the usage of the deep neural network (DNN). However, the background noises might lower the recognition accuracy and induce longer convergence time. In order to improve the recognition accuracy and to reduce the computational complexity, in this article, we propose to construct the dataset based on spectral correlation function (SCF), which has the special property of relatively being insensitive to background noises. Moreover, we propose to add a convolutional neural network denoising module to combat the noises for better feature extraction performances. Furthermore, in order to reduce the dataset size, we propose to use the two-dimensional (2-D) cross-section SCF profiles for the DNN. Then, we propose a DNN architecture based on the back-propagation neural network. Thanks to the noise resistant SCF feature extractions and the intelligent denoising as well as DNN-based classification design, the recognition accuracy can be improved. Simulation results show that the proposed method can effectively classify modulation schemes at the signal-to-noise ratio (SNR) as low as $-$10 dB. Moreover, the proposed intelligent system achieves higher recognition accuracy than counterpart schemes in low-SNR regions.

Chaos communications have widely been applied to provide secure and anti-jamming transmissions by exploiting the irregular chaotic behavior. However, the real-valued chaotic sequences imposed on the information induce interferences to the user data, thereby leading to reliability performance degradations. To address this issue, in this paper, we propose to utilize the intelligent and feature extraction capability of the deep neural network (DNN) to learn the transmission patterns to demodulate the received signals. In our design, we propose to construct the long short-term memory (LSTM) unit aided intelligent DNN-based deep learning (DL) demodulator for orthogonal frequency division multiplexing-aided differential chaos shift keying (OFDM-DCSK) systems. After learning and extracting features of information-bearing chaotic transmissions at the training stage, at the deployment stage, the received signals can be recovered efficiently and reliably. Thanks to the recursive LSTM-aided DL design, correlations between information-bearing chaotic modulated signals can be exploited to enhance reliability performances. Simulation results demonstrate with the proposed DL demodulation design, and the intelligent OFDM-DCSK system can achieve more reliable performances over additive white Gaussian noise (AWGN) channel and fading channels compared with benchmark systems.

In this paper, we propose a novel two-dimensional frequency and time diversity aided orthogonal frequency division multiplexing based differential chaos shift keying (OFDM-DCSK) system. Our aim is to provide secure and robust transmissions for practical wireless systems, where perfect channel state information (CSI) may not be available at the receiver, by exploiting the natural high security of chaotic sequences and frequency diversity gains brought by the frequency hopping (FH). In our design, the information bits are firstly modulated by chaotic chips, then non-repetitive FH operations are performed on both reference chips and chaotic modulated symbols. After the inverse fast Fourier transform (IFFT), the non-repetitive reference chips and chaotic modulated symbols are respectively transmitted over different subcarriers. Subsequently, the receiver recovers the information using the received reference chaotic chips which naturally embed the channel frequency response (CFR) of all subcarriers. We then analyze the energy and spectral efficiencies, derive the bit error rate (BER) and information leakage expressions, and provide a detailed complexity analysis of the proposed scheme. Simulation results verify the effectiveness of our derivations and demonstrate that the proposed system achieves better BER and security performances compared with the benchmark system, especially when the CSI is imperfect or unknown.

Chaos-based communications can be applied to high-speed vehicular information transmissions thanks to the anti-jamming and anti-interference capabilities of chaotic transmissions. In traditional practical chaotic systems, reference chaotic signals are required to be delivered to remove complex chaotic synchronization circuits. However, the direct transmission of reference signals will degrade the security performances, while interferences and noises imposed on the reference signals due to imperfect channel conditions will deteriorate the reliability performances. In order to enhance the reliability and security performances over vehicular channels such as the railway channel and the channels undergoing fast fadings, in this paper, we propose a deep learning (DL) aided intelligent OFDM-DCSK transceiver. In this design, no reference chaotic signals are delivered, and we propose to utilize the time-delay neural network (TDNN) to learn the chaotic maps, followed by the long short-term memory (LSTM) units to extract and exploit the correlations between chaotic modulated signals, and multiple fully connected layers (FCLs) to estimate the user bit data. With the aid of the constructed deep neural network (DNN), after the offline neural network training, the receiver can recover the transmitted information with lower bit error rate (BER) and enhance security performances. Theoretical performance is then analyzed for the proposed intelligent transceiver. Simulation results validate the proposed design, and demonstrate that the intelligent DL-based OFDM-DCSK system can achieve better BER and security performances over fast fading and railway channels compared with the benchmark systems.

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.