Channel knowledge map (CKM) is a key enabler for environmental awareness in future wireless systems. However, reconstructing high-fidelity CKM from sparse and noisy measurements poses a significant challenge. While Graph Neural Networks (GNNs) have emerged as a potent tool for this task, existing methods often lack physical consistency and generalization due to reliance on single graph structures and purely data-driven approaches. To tackle this challenge, in this paper, we propose a physics-informed multi-view graph neural network (PIMV-GNN) framework. This framework innovatively integrates two mechanisms within a unified GNN backbone: a multi-view learning (MVL) module that builds a rich spatial representation of the complex environment by fusing two complementary graph structures, namely a "spatial line-of-sight" graph and a "physical proximity" graph; and a physics-informed neural network (PINN) module that enforces physical consistency by imposing constraints derived from the Helmholtz equation in the graph domain. Extensive simulations demonstrate that our proposed PIMV-GNN framework significantly outperforms baseline models under various levels of data sparsity and measurement noise. Furthermore, the results reveal a profound synergistic effect between the MVL and PINN modules, where high-quality multi-view features significantly improve the regularization efficiency of the physics-based constraints.

The affine frequency division multiplexing (AFDM) waveform, with its superior capability in separating delay and Doppler shifts, emerges as a promising solution to achieve reliable high-mobility satellite-air integrated communications. However, the secure AFDM waveform design remains a critical challenge when deployed in satellite-air integrated communications. To tackle this issue, in this article, we first analyze the roles of the key parameters in the AFDM waveform, revealing the admissible ranges of these parameters. Afterwards, we propose a time-varying parameter-hopping (PH) AFDM scheme, where the parameters are dynamically adjusted during transmission, which enhances the flexibility of the AFDM waveform. In addition, the scheme can support both basic encryption strategy and advanced encryption strategy for different security requirements in high-mobility satellite-air integrated communications. Specifically, the basic strategy employs a single dynamically hopping parameter, while the advanced encryption strategy, trading the spectral efficiency for a larger parameter space, employs two dynamically hopping parameters. Besides, the anti-eavesdropping performance, quantified by waveform entropy, can be significantly improved through the proposed PH mechanism. Numerical simulations demonstrate the validity of the analysis and the effectiveness of the proposed scheme.

As wireless communication systems evolve toward intelligent operation, the growing complexity of dynamic and non-stationary propagation environments inherent in large-scale and heterogeneous Internet of Things (IoT) scenarios imposes stringent demands on link adaptation robustness. To address these challenges, we propose a joint bandwidth and modulation and coding scheme (MCS) optimization framework that leverages autonomous scenario identification (ASI) and dueling double deep Q-network (D3QN), named as ASI-D3QN. Specifically, a lightweight deep convolutional neural network (CNN) is tailored for ASI to achieve high identification accuracy while maintaining low computational complexity. This design is particularly suited for resource-constrained devices. Then, a D3QN-based optimization strategy is developed to seamlessly integrate ASI-derived environmental context with intrinsic channel metrics. The proposed framework explicitly expands the decision space by integrating signal bandwidth as an additional optimization dimension, facilitating adaptive optimization over multi-dimensional parameters. Finally, an intelligent communication prototype is established to comprehensively validate the proposed approach under representative standardized channel models. Experimental results demonstrate that, compared to existing methods, the proposed ASI achieves at least a 0.27% accuracy improvement with fewer model parameters. Moreover, relative to conventional link adaptation schemes, the ASI-D3QN strategy achieves superior throughput gains in complex dynamic environments.

Affine frequency division multiplexing (AFDM) is a promising chirp-assisted multicarrier waveform for future high-mobility communications. This paper is devoted to enhanced receiver design for multiple-input–multiple-output AFDM (MIMO-AFDM) systems. Firstly, we introduce a unified variational inference (VI) approach to approximate the target posterior distribution, under which the belief propagation (BP) and expectation propagation (EP)-based algorithms are derived. As both VI-based detection and low-density parity-check (LDPC) decoding can be expressed by bipartite graphs in MIMO-AFDM systems, we construct a joint sparse graph (JSG) by merging the graphs of these two for low-complexity receiver design. Then, based on this graph model, we present the detailed message propagation of the proposed JSG. Additionally, we propose an enhanced JSG (E-JSG) receiver based on the linear constellation encoding model. The proposed E-JSG eliminates the need for interleavers, de-interleavers, and log-likelihood ratio transformations, thus leading to concurrent detection and decoding over the integrated sparse graph. To further reduce detection complexity, we introduce a sparse channel method by approaximating multiple graph edges with insignificant channel coefficients into a single edge on the VI graph. Simulation results show the superiority of the proposed receivers in terms of computational complexity, detection and decoding latency, and error rate performance compared to the conventional ones.

This paper investigates the ambiguity function (AF) of the emerging affine frequency division multiplexing (AFDM) waveform for random integrated sensing and communication (ISAC) signaling under a pulse shaping regime. Specifically, we first derive the closed-form expression of the average squared discrete period AF (DPAF) for AFDM waveform without pulse shaping, revealing that the AF depends on the parameterc1and the kurtosis of random communication data, while being independent of the parameterc2. As a step further, we conduct a comprehensive analysis on the DPAFs of various waveforms, including AFDM, orthogonal frequency division multiplexing (OFDM) and orthogonal chirp-division multiplexing (OCDM). Our results indicate that all three waveforms exhibit the same number of regular depressions in the sidelobes of their DPAFs, which incurs performance loss for detecting and estimating weak targets. However, the AFDM waveform can flexibly control the positions of depressions by adjusting the parameterc1, which motivates a novel design approach of the AFDM parameters to mitigate the adverse impact of depressions of the strong target on the weak target. Furthermore, the closed-form expressions of the average squared DPAFs for pulse-shaped AFDM, OFDM and OCDM waveforms are derived, which demonstrates that the pulse shaping filter generates the shaped mainlobe along the delay axis and the rapid roll-off sidelobes along the Doppler axis. Numerical results verify the effectiveness of our theoretical analysis and proposed design methodology for the AFDM waveform.

Affine frequency division multiplexing (AFDM) exhibits strong robustness against time and frequency dispersion in doubly dispersive channels (DDCs), enabling reliable communication under high mobilities. However, in the multi-user uplink scenario, inter-user channel delay and Doppler differences in the discrete affine Fourier transform (DAFT) domain manifest as inevitable multi-user interference (MUI). To address this issue, building upon the DAFT and AFDM, we propose a novel uplink multiple access scheme termed as DAFT-spread affine frequency division multiple access (DAFT-s-AFDMA). In our proposed scheme, DAFT spreading is performed by each user to multiplex the transmitted symbols over the DAFT domain, which includes a pre-chirp parameter that can be flexibly adjusted to reduce the peak-to-average power ratio (PAPR) of the AFDM system. Accordingly, we derive new guidelines for setting the DAFT parameters and the asymptotically tight upper bounds on the average bit error rate, revealing the insights of PAPR reduction. Furthermore, a low-complexity cross-domain expectation propagation (CD-EP) detector is proposed, capitalizing on the sparsity of DAFT domain effective channel matrix and the corresponding symbol domain constellation constraints to enhance the error performance. Simulation results show that the proposed CD-EP detector outperforms both conventional Gaussian message passing (GMP) and minimum mean square error (MMSE) detectors with a much lower complexity, and also verify the superiority of DAFT-s-AFDMA to plain AFDMA across various scenarios of high-mobility DDCs.

Physical layer security (PLS) has emerged as a promising technology to protect critical and sensitive information against unauthorized devices. To address the key challenge of acquiring channel state information (CSI) of passive eavesdroppers in PLS implementation, we propose a novel sensing-assisted PLS scheme with the aid of reflecting reconfigurable intelligent surface (STAR-RIS). It employs a self-refine sensing scheme utilizing the artificial noise (AN) signals to iteratively estimate the eavesdroppers’ positions for CSI calculation. We aim to maximize the secrecy capacity based on the sensing-estimated CSI while tracking the eavesdroppers in full-duplex (FD) mode with integrated sensing and communication (ISAC) signals comprising artificial noise (AN). This is achieved by jointly designing the beamforming vector of information signals, the beamforming vector of AN signals, and the coefficients of the STAR-RIS. To optimize these coupled variables, we introduce an alternating optimization (AO) scheme to solve the problem recursively. In particular, we tackle the non-convexity of the beamforming optimizations for information and AN signals with the successive convex approximation (SCA) scheme and adopt a semi-definite relaxation (SDR) scheme to design the reflection and refraction coefficients of the STAR-RIS. The numerical results validate that the proposed scheme ensures secure communications against multiple eavesdroppers without any prior eavesdropper channel information. In addition, the proposed scheme can significantly improve SC performance by up to 66. 7% compared to the benchmarks without the sensing-assisted function.

Affine frequency division multiplexing (AFDM) and orthogonal time frequency space (OTFS) are two promising advanced waveforms proposed for reliable communications in high-mobility scenarios. In this paper, we introduce a simple transmit diversity technique, termed cyclic delay-Doppler shift (CDDS), for these two advanced waveforms to achieve ultra-reliable communications in doubly selective channels (DSCs). Two simple CDDS schemes, named modulation-domain CDDS (MD-CDDS) and time-domain CDDS (TD-CDDS), are proposed, which perform CDDS in advance at the transmitter before and after the modulation, respectively. We demonstrate that both of the two proposed CDDS schemes can be implemented efficiently and flexibly by multiplying the transmit vector with a well-designed precoding matrix, which is nothing but a sparse phase-compensated permutation matrix. Moreover, we theoretically and numerically prove that CDDS can provide MIMO-AFDM and MIMO-OTFS with optimal transmit diversity gain when a proper CDDS step is adopted. Compared to the conventional transmit diversity techniques, the proposed CDDS scheme enjoys the advantages of lower channel estimation overhead, implementation complexity, and signal processing latency, making it particularly suitable for ultra-reliable communications in high-mobility scenarios.

This paper investigates the sensing potential of affine frequency division multiplexing (AFDM) in high-mobility integrated sensing and communication (ISAC) from the perspective of radar waveforms. We introduce an innovative parameter selection criterion that establishes a precise mathematical equivalence between AFDM subcarriers and Nyquist-sampled frequency-modulated continuous-wave (FMCW). This connection not only provides a clear physical insight into AFDM's sensing mechanism but also enables a direct mapping from the DAFT index to delay-Doppler (DD) parameters of wireless channels. Building on this, we develop a novel input-output model in a DD-parameterized DAFT (DD-DAFT) domain for AFDM, which explicitly reveals the inherent DD coupling effect arising from the chirp-channel interaction. Subsequently, we design two matched-filtering sensing algorithms. The first is performed in the time-frequency domain with low complexity, while the second is operated in the DD-DAFT domain to precisely resolve the DD coupling. Simulations show that our algorithms achieve effective pilot-free sensing and demonstrate a fundamental trade-off between sensing performance, communication overhead, and computational complexity. The proposed AFDM outperforms classical AFDM and other variants in most scenarios.

Affine frequency division multiplexing (AFDM) is a promising waveform for next generation wireless networks, effectively resisting the channel double selectivity. Conventional embedded pilot (EP) scheme for AFDM requires additional guard symbols, leading to a reduction in spectral efficiency (SE). To address this issue, superimposed pilot (SP)-based schemes have been proposed, improving the SE; however, at the cost of increased computational complexity at the receiver. In this work, we propose an iterative joint channel estimation and data detection scheme for AFDM by harnessing SPs, aiming to enhance the SE while reducing the detection complexity. Simulation results demonstrate that our proposed scheme outperforms the conventional SP-based scheme in both channel estimation and data detection, while achieving a lower computational complexity. Notably, under low data power conditions, our approach surpasses the EP scheme in terms of both SE and data detection accuracy.

In high-mobility scenarios, affine frequency division multiplexing with index modulation (AFDM-IM) has attracted significant attention due to its ability to convey information by combining active subcarrier indices with constellation symbols. Motivated by the spatial multiplexing concept in multiple-input multiple-output (MIMO) systems, in this paper, we propose the MIMO-AFDM-IM scheme to enhance spectral efficiency (SE) and bit error rate (BER) performance. Three detection methods are introduced to address the exponential complexity of Maximum Likelihood (ML) detection in MIMO-AFDM-IM. These methods aim to strike a balance between detection accuracy and computational complexity. Additionally, the average bit error probability (ABEP) of the MIMO-AFDM-IM scheme is derived to assess its performance. Computer simulations are carried out under time-varying multipath conditions, and the results demonstrate the superiority of the proposed MIMO-AFDM-IM over MIMOAFDM and AFDM-IM across various system configurations.

This paper investigates affine frequency division multiplexing (AFDM) with practical digital-to-analog conversion (DAC) and analog-to-digital conversion (ADC) filters over doubly-dispersive channels. Firstly, we derive the input-output relationship for AFDM with practical DAC and ADC filters, thereby characterizing the discrete affine Fourier transform (DAFT) domain channel. Subsequently, the equivalent sampled DAFT channel matrix is visualized. Additionally, an analysis of the auto-ambiguity function of the AFDM pilot signal is conducted, focusing on the impact of various DAC and ADC filters. The selection of these filters exerts a significant influence on the sidelobe behavior in the time-delay domain of the sub-ambiguity function. Simulations demonstrate that AFDM with practical DAC/ADC outperforms OFDM and OCDM in bit error rate under identical conditions, while the root-raised cosine filter enhances spectral efficiency.

Spectrum competition and hardware complexity inherent in communication and radar systems can be alleviated by a dual-function radar communication (DFRC) systems. However, enhancing detection capabilities for maneuvering or weak targets remains a significant challenge, as traditional radar signal accumulation algorithms are not directly applicable to DFRC systems. This article proposes a novel method that integrates signal accumulation and parameter estimation for target detection in DFRC systems. The approach employs an orthogonal frequency division multiplexing (OFDM) waveform within a multiple-input-multiple-output (MIMO) framework, enabling the detection of high-speed or weak targets through a computationally efficient signal accumulation process. The proposed method comprises three key steps: first, the designed signals combined with the multiple signal classification (MUSIC) algorithm for target angle estimation in the spatial domain. Second, a two-step signal accumulation process is introduced, which separately extracts range and velocity information for weak or high-speed targets. Third, acceleration is derived based on velocity information and accumulation time. We present explicit expressions and detailed analyses of various performance metrics, including accumulation output response for high-speed targets, multiple target scenarios, and cases with low-signal-to-noise ratio (SNR). Additionally, Cramér-Rao bounds (CRBs) for azimuth, range cell, and velocity cell estimation in DFRC MIMO-OFDM systems are derived. Simulation results validate the proposed method, demonstrating its superior target detection performance compared to existing techniques.

Taking into account the flexible deployment and Line-of-Sight (LoS) communication links of uncrewed aerial vehicles (UAVs), this article proposes a multi-UAV-assisted vehicular edge computing networks (VECNs) architecture to provide instantaneous computation support at multiple congestion road segments. Given that the computation resources of a single UAV are insufficient, and offloading tasks directly to the cloud computing center (CCC) in intelligent transportation systems (ITSs) introduces significant latency, multiple UAVs with precached service or content caching data are deployed optimally for the vehicle users. In order to address the tradeoff between system costs and service efficiency, we propose a novel cost-efficient layered optimization scheme, in which the number and deployment positions of UAVs are jointly optimized. According to the varying vehicular network environments and the dynamic requirements of vehicle users, we design a hierarchical reinforcement learning algorithm, combining double deep Q network (DDQN) and multiagent deep deterministic policy gradient (MADDPG), the former is used to optimize the number of UAVs, and the deployment of UAVs are optimized via the MADDPG. Simulation results demonstrate the effectiveness of the proposed scheme in lowering total task completed latency and increasing the system profits. The service efficiency in dealing with the vehicle users’ requirements also be improved.

Connected and automated vehicles (CAVs) have emerged as an efficient solution to improve the driving experience in the intelligent transportation systems (ITSs), in which the targeted vehicle (TV) can switch between the human-driven (HD) and autonomous-driven (AD) modes to act as server or terminal in vehicular edge computing networks (VECNs). However, due to the dynamic nature of traffic networks and the moving of vehicles, distribution of computational resources is imbalanced and variable, it is a challenge to design the cooperative resource management scheme for the whole journey of vehicle users. In this article, we propose a joint driving model selection and resource management scheme for TV in each road segment, to maximize the vehicle users’ satisfaction of the whole journey. For the complex formulated joint optimization problem, we design a three-stage hierarchical optimization (3SHO) framework, using deep Q-network (DQN) for driving mode optimization in the first stage and deep deterministic policy gradient (DDPG) for optimizing resource management under different selected driving modes. And a terminal-server matching mechanism is introduced to enable dynamic service quality improvement for TV. Specially, we design a new user satisfaction function with the quality of service, traffic revenue, and the gap between expected and actual revenues of users are considered. Experimental results showcase the robust convergence of the 3SHO algorithm, the adeptness to dynamic traffic networks, and the capacity to enhance user satisfaction significantly.

Dual-function radar-communication (DFRC) systems are key to addressing spectrum congestion and hardware constraints in future 5G/6G networks. Among various DFRC waveform candidates, OFDM stands out for its flexibility, but its high range sidelobes pose challenges for weak target detection in cluttered environments. In this work, we propose a novel waveform optimization framework that jointly minimizes the peak sidelobe level (PSL), maintains a low symbol error rate (SER), and enforces constant envelope constraints. To solve the resulting non-convex, NP-hard problem efficiently, we introduce a Block-wise Majorization-Minimization (BWMM) algorithm that iteratively refines the phase of each OFDM symbol to suppress both auto- and cross-correlation sidelobes. Theoretical analysis and simulation results validate that the proposed BWMM-PSL method significantly enhances radar sensing performance while preserving communication reliability.

This paper explores a novel integrated localization and communication (ILAC) system using the affine Fourier transform multicarrier (AFT-MC) waveform. Specifically, we consider a multiple-input multiple-output (MIMO) AFT-MC system with ILAC and derive a continuous delay and Doppler shift channel matrix model. Based on the derived signal model, we develop a two-step algorithm with low complexity for estimating channel parameters. Furthermore, we derive the Cramér-Rao lower bound (CRLB) of location estimation as the fundamental limit of localization. Finally, we provide some insights about the AFT-MC parameters by explaining the impact of the parameters on localization performance. Simulation results demonstrate that the AFT-MC waveform is able to provide significant localization performance improvement compared to orthogonal frequency division multiplexing (OFDM) while achieving the CRLB of location estimation.

Affine frequency division multiplexing (AFDM) is a promising chirp-based waveform designed for communications in high-mobility scenarios. In this paper, the pulse shaping for AFDM over doubly selective channels (DSC) is investigated. We first develop the pulse-shaped AFDM (PS-AFDM) system, where different transmit pulses and receive pulses can be used for each chirp carrier. Based on that, we formulate the impacts of pulse shaping on the input-output relationship of PS-AFDM system with fractional delay and fractional Doppler shifts. In particular, we reveal that there exists inter-pulse interference (IPI) within the pilot region and inter-region interference (IRI) between the pilot region and the data region in the AFDM/PS-AFDM received symbols. To provide an instructive guideline for interference suppression, we elaborate how the adopted transmit and receive pulses determine the IPI and IRI. Furthermore, we demonstrate that applying the pulse-shaping window with low sidelobe levels in PS-AFDM can suppress the IPI and IRI, facilitating the channel estimation and signal detection processes significantly. Simulations verify that the proposed PS-AFDM systems can achieve lower overhead and higher accuracy channel estimation compared to the conventional AFDM systems.

This paper proposes a novel design algorithm for dual-function radar communication (DFRC) Orthogonal Frequency-Division Multiplexing (OFDM) waveform. The algorithm achieves a tradeoff between detection performance and communication bit error rate (BER) performance. Firstly, the algorithm modulates communication information on the phase of the subcarrier coefficient of OFDM waveform using M-phase-shift keying (MPSK) schemes such as Binary-PSK (BPSK). Subsequently, the waveform minimises the weighted integrated sidelobe level (WISL) of the transmit waveform and the receive mismatch filter while ensuring the BER. Additionally, constraints are placed on constant amplitude, mainlobe energy and signal-to-noise ratio (SNR) loss. To address the non-convex optimization issues arising from algorithm design, a Weight Alternating Direction Method of Penalty (W-ADPM) network-based approach simultaneously optimises the transmit waveform and receives mismatched filters. The simulation experiments demonstrate that the proposed algorithm has better convergence performance for the proposed waveform compared to the Alternating Direction Method of Multipliers (ADMM) algorithm. Besides, compared to traditional matched filters, the jointly transmitted and received mismatched filters proposed in this paper provide better WISL cross-correlation performance while ensuring the BER.

Dual-function radar-communication (DFRC) systems offer a promising solution to mitigate spectrum competition and hardware complexity in 5G/6G communication. Orthogonal Frequency Division Multiplexing (OFDM) technology has been commonly employed in current DFRC signals. However, many DFRC signal sequences exhibit poor range sidelobes, making them unsuitable for weak target detection. In this paper, we design encrypted sparse transmitting waveforms to encrypt signals. In the time domain, the DFRC signal's Peak Side Level (DPSL) is minimized to enhance radar detectability, while simultaneously constraining the communication Bit Error Ratio (BER) and the constant envelope value of the signal to maintain communication quality. To address the non-convex optimization problem, we develop a Block Successive Upper-bound Minimization (BSUM) framework, which alternately updates each communication phase location. This framework aims to lower the dual-function cross- and auto-correlation peak sidelobe levels, referred to as the Block Successive Upper bound Minimization for DFRC DPSL (BSUM-DPSL) algorithm. The proposed algorithm's effectiveness is theoretically validated, and simulation results demonstrate that the effectiveness of designed MIMO-OFDM waveform in comparison with other waveforms.

Analogous to orthogonal time frequency space (OTFS), affine frequency division multiplexing (AFDM) emerges as a promising solution for achieving ultra-reliable communication under time-varying channels with large Doppler shifts. To apply this new modulation technique for next-generation communications, there is an expectation that it will be easily integrated into current systems without major modifications. In this paper, we propose a low-complexity waveform called simplified-AFDM (S-AFDM), which is more compatible with existing techniques by reducing the parameter settings in AFDM. First, We provide a general framework and formulate the input-output relation of the S-AFDM system in the discrete affine Fourier transform (DAFT) domain. Furthermore, we present a detailed analysis of the diversity order of S-AFDM in single-input single-output (SISO) setting with maximum likelihood (ML) detection. Numerical results demonstrate that the proposed modulation scheme exhibits the same performance of classic AFDM with commonly used detectors, while halving its addtional modulation complexity superimposed on the orthogonal frequency division multiplexing,

The key to friendly collaboration in vehicular communication systems lies in the reliable communication between vehicles. The current systems, which employ fixed transmission schemes, significantly constrain system capacity in respect of spectrum. Besides, considering the dynamic environment of vehicular communications, the requirement for real-time scenario identification is particularly urgent. Hence, in order to improve the reliability of communications, this paper proposes an adaptive modulation and coding (AMC) technique driven by deep learning (DL)-based scenario identification (SI) in vehicular communication systems, namely SI-AMC. In contrast to the traditional AMC technique, our proposed SI-AMC attains a refined channel response estimation through the pre-discrimination of scenario features, thereby further enhancing vehicular communication performance. During the transmission process, the SI-AMC scheme achieves environment adaptability through rate-adaptive adjustments. Moreover, in terms of SI, we creatively design an enhanced convolutional neural network structure which ex-ploits a novel activation function and regularization strategies to enhance the robustness of the model. Simulation results show that the accuracy of SI reaches up to 97.86 % and the throughput of the entire link in vehicular communications is effectively promoted. Code and the model will be released at https://github.com/communicationDLl/SI-AMC.

Orthogonal time frequency space (OTFS) is a promising waveform that modulates information in the delay-Doppler domain and enables robust transmission performance in high-mobility scenarios. However, similar to other multi-carrier schemes, OTFS has a non-negligible issue of high peak-to-average power ratio (PAPR), which may lead to signal distortion and performance degradation when using a power amplifier. In this paper, we employ a parameter-adjustable expanded precoding scheme, and generalize the precoding matrix into a scalable form, composed of a periodically expanded transformation matrix and an energy conservation matrix. The PAPR can be flexibly reduced by varying the dimension of the precoding matrix with only a slight increase in system complexity, thus improving the cost-efficiency of the system. Simulation results demonstrate that the proposed expanded precoding scheme can achieve a minimum reduction of 3 dB in PAPR and enhance the bit error rate (BER) performance of OTFS.

On the heels of orthogonal time frequency space (OTFS) modulation, the recently discovered affine frequency division multiplexing (AFDM) is a promising waveform for the sixth-generation wireless network. In this paper, we study the widely-used embedded pilot-aided (EPA) channel estimation in multiple-input multiple-output AFDM (MIMO-AFDM) system with fractional Doppler shifts. We first formulate the vectorized input-output relationship of MIMO-AFDM, and theoretically prove that MIMO-AFDM can achieve full diversity in doubly selective channels. Then we illustrate the implementation of EPA channel estimation in MIMO-AFDM and unveil that serious inter-Doppler interference (IDoI) occurs if we try to estimate the channel gain, delay shift, and Doppler shift of each propagation path. To address this issue, the diagonal reconstructability of AFDM subchannel matrix is studied and a low-complexity embedded pilot-aided diagonal reconstruction (EPA-DR) channel estimation scheme is proposed. The EPA-DR scheme calculates the AFDM effective channel matrix directly without estimating the three channel parameters, eliminating the severe IDoI inherently. Since the effective channel matrix is necessary for MIMO-AFDM receive processing, we believe this is an important step to bring AFDM towards practical communication systems. Simulation results validate the effectiveness of the proposed EPA-DR scheme.

In non-terrestrial networks (NTN), optimal planning of the optimization problem of 3-dimensional (3D) trajectory is a key research topic. In this article, the optimization problem of the unmanned aerial vehicle (UAV) aided wireless sensor networks is addressed. To maximize the energy efficiency (EE) performance, we formulate the 3D trajectory optimization problem as a non-convex optimization and divide it into two sub-problems, the UAV's horizontal trajectory optimization problem with given altitude and the UAV's altitude optimization problem with given horizontal location. By combining with the discrete linear state-space approximation method, the energy-efficient algorithm with given transmit power of each sensor is proposed. Numerical results show that the proposed methods achieve significant improvements compared to the existing; EE schemes.

In simultaneous transmit and receive wireless communications, digital self-interference (SI) cancellation is required before estimating the remote transmission (RT) channel. Considering the inherent connection between SI channel reconstruction and RT channel estimation, we propose a multi-layered M-estimate total least mean squares (m-MTLS) joint estimator to estimate both channels. In each layer, our proposed m-MTLS estimator first employs an M-estimate total least mean squares (MTLS) algorithm to eliminate residual SI from the received signal and give a new estimation of the RT channel. Then, it gives the final RT channel estimation based on the average of the estimation values obtained from each layer. Compared to traditional minimum mean square error estimator and single-layered MTLS estimator, it demonstrates that the m-MTLS estimator has better performance of normalized mean squared difference. Besides, the simulation results also show the robustness of m-MTLS estimator even in scenarios where the local reference signal is contaminated with noise, and the received signal is impacted by strong impulse noise.

Optimization problem of transmit power and straight trajectory is addressed in unmanned aerial vehicle (UAV) aided wireless sensor networks. To maximize the energy efficiency (EE) performance, we formulate the transmit power and straight trajectory optimization problem as a non-convex optimization and solve it by iterative method. To facilitate the analysis, we derive an analytical expression of upper bound of the aggregated throughput with straight UAV flight. Based on the upper bound, the original optimization problem can be addressed by solving an alternating sequence of trajectory optimization (TO) and power optimization (PO) sub-problems with closed-form expressions. Furthermore, we propose an alternative algorithm for power allocation and straight trajectory optimization problem and analyze the computing complexity. Numerical results show that the proposed method achieves a significant improvement compared to the existing EE schemes.

This paper considers low-complexity transmit beamforming schemes for signal-to-interference-plus- noise ratio (SINR) balancing problem in the Gaussian multiple-input single-output multi-receiver wiretap channel (MISO-MRWC). The formulated max-min-fair problem are shown to be non-convex. To overcome the computational complexity, we develop the leakage-based and zero forcing (ZF) based beamforming algorithms for finding the local optimum transmit beamformers. Extensive simulation results illustrate that the proposed beamforming algorithms achieve low computational complexity without serious performance deterioration.

This paper studies the beamforming design for sum secrecy rate (SSR) maximization in the Gaussian multiple-input single-output multi-receiver wiretap channel (MISO-MRWC). The optimization problem of finding the optimal beamforming algorithm is non-convex and intractable to solve using low-complexity methods. Motivated by the thinking of zero-forcing (ZF) and signal-to-leakage-plus-noise ratio (SLNR), we propose three low-complexity beamforming algorithms for finding a local SSR optimum. The simulation results show that the SLNR-based beamforming algorithm outperforms the other two algorithms with ZF preprocessing.

In this paper, we address physical layer security for amplify-and-forward (AF) multi-antenna relay systems in the presence of multiple eavesdroppers. A robust joint design of cooperative beamforming (CB) and artificial noise (AN) is proposed with imperfect channel state information (CSI) of both the destination and the eavesdroppers. We aim to maximize the worst-case secrecy rate subject to the sum power and the per-antenna power constraints at the relay. Such joint design problem is non-convex. By utilizing the semidefinite relaxation (SDR) technique, S-procedure and the successive convex approximation (SCA) algorithm, the original non-convex optimization problem is recast into a series of semidefinite programs (SDPs) which can be efficiently solved using interior-methods. Simulation results are presented to verify the effectiveness of the proposed design.

In this paper, we investigate the secrecy performance for a multiple-input multiple-output (MIMO) wiretap channel in the presence of a multiantenna eavesdropper. In particular, the legitimate transmitter uses transmit antenna selection (TAS) to transmit on a single antenna with the largest signal-to-noise ratio (SNR) while both the legitimate receiver and the eavesdropper adopt maximal ratio combining (MRC) for reception. We derive exact closed-form expressions for the probabilities of achieving positive secrecy rate and secrecy outage in the case of imperfect feedback due to feedback delay and/or feedback error. Furthermore, we derive the asymptotic secrecy outage probability at high SNR, which accurately reveals the secrecy diversity loss due to imperfect feedback. Simulation results are provided to verify our analytical results and illustrate the impact of imperfect feedback on the secrecy performance of such a wiretap system.

A novel approach for ensuring confidential wireless communication is proposed and analysed from a geometrical perspective. In this method, both the legitimate receiver and transmitter generate artificial noise (AN) to impair the eavesdropper's channel. The authors use the concept of insecure region to characterise the security performance when the eavesdropper's channel is unknown. The insecure region is defined as the region where the eavesdropper may decode the secret message. With the aim of minimising the size of the insecure region, an optimum power allocation strategy between the information bearing signal and the AN is proposed. Simulation results show that the proposed method achieves a good performance.

This paper studies masked beamforming schemes for secure communication in broadcast multiple-input multiple-output (MIMO) systems with a passive multiple-antenna eavesdropper. Assuming no information about the eavesdropper is available at the transmitter, we aim to maximize the transmit power of the artificial noise while meeting mean square error (MSE) constraints at the legitimate receivers and the total power constraint at the transmitter. Based on imperfect channel state information (CSI) of the legitimate receivers at the transmitter, we present a worst-case robust masked beamforming algorithm. By exploiting alternating iterative optimization, the proposed algorithm recasts the non-convex optimization problem as two semidefinite program (SDP) based subproblems, which are solvable with interior-point methods. Simulation results are provided to illustrate the secrecy performance of the proposed algorithm.