We present a novel constellation-splitting criterion in the multiple parameters weighted-type fractional Fourier transform (MP-WFRFT) modulations. First, the signal superposition characteristics are studied and the related four theorems are put forward and proved. Second, to get the expected constellation pattern, we build the optimization model with the defined constraints. Then, the genetic algorithm is adopted to optimize the designed model. Finally, numerical results are presented to validate the proposed theorems, and the bit error rate performance shows that the MP-WFRFT can be utilized to guarantee the communication security.

We present a novel modulation recognition for Weighted-type Fractional Fourier Transform (WFRFT)-based systems using 4th-order Cumulants. Firstly, the constellation characteristics of the basic digital modulations ASK, PSK and QAM are analyzed, and the corresponding relationships between the neighboring constellation points’ distance and the constellation size are deduced. Secondly, the closed-form expression of the 4th-order Cumulants(C42) for WFRFT-based systems with ASK, PSK, and QAM are derived. Finally, through the first and second order derivatives of C42, we prove that the optimal WFRFT order αr can be obtained through the minimisation of C42. Simulation results show that the novel recognition for WFRFT-based system is feasible and can reach an accuracy of almost 90% when energy per bit-to-noise power spectrum density ratio (Eb/N0) is greater than 6.

This paper presents a novel combinatory strategy to embed weighted-type fractional Fourier transform (WFRFT) precoding signals into transform domain communication system (TDCS). The original data can be divided into two parts. One part is modulated with the cyclic code shift keying in the traditional TDCS. The other part is first disguised as other higher order baseband modulations MPSK through WFRFT proceding process, then will further be embedded into the traditional TDCS system. A double-random scheme is designed to dynamically generate the pseudo phase for WFRFT rotation and TDCS basic function’s phase. Theoretical analyses show that the higher spectral efficiency can be obtained while causing little effect on its original communication quality. The final simulations demonstrate that the constellation precoding method can help disguise the original signals into other higher order baseband PSK modulations with a controllable Gaussian-like noise. Besides, owing to the dynamically double-random phase generation scheme, the proposed combinatory WFRFT-TDCS system can gain better anti-eavesdropping capacity while maintaining its own communications’ quality with regards to bit error rate performances.

In this paper, a power and time slot allocation method is proposed for the weighted fractional data carrying artificial noise (DCAN) to secure satellite transmission. We first introduce a data carrying artificial noise based on weighted fractional fourier transform (WFRFT) to achieve physical layer security in satellite transmission which outperforms the traditional artificial noise method when the channel state information (CSI) is not precise at the transmitter. Then, we formulate an optimization problem to optimize the power allocation among the main signal and the weighted fractional DCANs in three steps by adopting the fractional programming, the alternative research and difference of convex functions (DC) programming respectively. We further divide the transmission time into different time slots and assign them to the main signals by solving a maximum weighted sum problem to ensure the transmission security with limited transmission power. Simulation results show that the proposed power and time allocation method outperforms the DCAN based on WFRFT with average power allocation when the number of the transmitted signals increases. Meanwhile, the proposed power allocation method is superior to the method based on perfect CSI or the assumption of massive transmission antennas, which may be not possible at the satellite.

The Doppler effect causes frequency offset and spectrum spread of communication signals, which increases the difficulty of feature extraction when identifying the modulation mode in aeronautical wireless channels. To improve the signal modulation recognition capability of the single monitoring node in Wireless Sensor Networks (WSN), a method based on the bidirectional convolution gated recurrent deep neural network (Bi-CGDNN) with an attention mechanism is proposed in this paper. We design the framework with different types of network layers, realizing frequency offset suppression and feature mapping. In addition, quadrature sampling signals and instantaneous feature statistics are collected to generate the dataset. Thus, the waveform features and phase-frequency information of the signals can be used for combinatorial analysis. In particular, the attention mechanism is introduced to optimize the framework for better feature perception and higher recognition rates. Experimental results show that our method achieves great recognition effects at different maximum Doppler frequencies. The recognition rate reaches 98.1% at the signal-to-noise ratio (SNRs) of 8dB with the Doppler frequency of 200Hz.

This study investigates the information security problem in amplify‐and‐forward (AF) satellite transmission with eavesdroppers at both the transmitter and the receiver. Two multi‐antenna earth stations aim to exchange messages through a multi‐antenna satellite in two hops. The satellite channels (both uplink and downlink) are assumed to be shadowed‐Rician fading. In the first hop, the multiple term weighted fractional Fourier transform (MWFRFT) is adopted to secure the messages from the eavesdropper at the transmitter. To overcome the simplicity of parameters in MWFRFT, the authors enhance the MWFRFT with frequency hopping and propose the frequency hopping multiple term weighted fractional Fourier transform (FH‐MWFRFT) to improve the secrecy. In the second hop, the satellite broadcasts the signal to the receiver after null space beamforming (NSBF). Since the energy at the satellite is confined, the NSBF is simplified by applying the singular value decompose to avoid the complicate optimisation calculations at the satellite. The one‐way and two‐way transmission scenarios with full channel state information (CSI) and statistic CSI are both considered in this study. Simulation results demonstrate the proposed method could achieve a better security at the transmitter while maintain a similar secrecy performance to the optimisation method at the legitimate receiver.