This paper proposes joint sensing and beamforming solutions tailored for extremely large-scale MIMO (XL-MIMO) near-field systems under both static and dynamic scenarios. For static scenarios, we develop a novel Multi-Layer Reconstruction (MLR) mechanism to address the challenges of large-scale near-field dictionary matrix and coarse range grid spacing, and further propose a sparse sensing algorithm, MLR mechanism based Linear Approximation Variational Bayesian Inference (MLR-LA-VBI), to achieve precise user/target position and radar cross section (RCS) sensing with low pilot overhead. Building upon these sensing results, a beamforming scheme is proposed to optimize radiation patterns. For dynamic scenarios, we exploit near-field Doppler-frequency characteristics to propose the modified MLR-LA-VBI (MMLR-LA-VBI) algorithm for sensing and a predictive beamforming framework, where the former serves as the core module of the latter. Our sensing approach enables full motion status sensing of users/targets from a single echo without requiring prior information of the target motion model. By eliminating echo accumulation and leveraging correlations across consecutive coherent processing intervals (CPIs), it achieves high performance with low computational complexity. Moreover, the proposed predictive beamforming framework naturally inherits the aforementioned advantages of MMLR-LA-VBI, and leverages the sensed full motion status to achieve an efficient and seamless beam tracking scheme with Doppler frequency compensation. In addition, theoretical analysis is conducted to characterize the algorithmic complexity, highlighting the advantages of proposed algorithms in terms of efficiency. Finally, simulations and analyses validate the effectiveness of the proposed algorithms in both static and dynamic scenarios.

Reconfigurable intelligent surface (RIS) plays an essential role in alleviating severe path loss in millimeter wave communication systems. Its performance hinges on the precise modeling of high-dimensional cascaded channels. However, traditional modeling approaches require extensive experience in radio propagation, resulting in complex and inefficient processes. To overcome these limitations, we transform the RIS channel modeling into a channel distribution transport mapping problem and introduce a generative model based on rectified flow. Our approach integrates distance information into a diffusion transformer (DiT) architecture through cross-attention mechanisms, resulting in a conditional DiT capable of synthesizing target channels from distance inputs. We further optimize the rectified flow into a single-step generator via reflow techniques. Building on this framework, we design a generative digital twin (DT) channel model that serves as a high fidelity data generator for downstream tasks. The proposed model acts as a virtual replica of the propagation environment, enabling efficient channel data synthesis for training communication algorithms such as channel state information feedback and channel estimation. Simulation results show that our approach generates channels with minimal distribution discrepancy compared to real channels (a maximum mean discrepancy < 0.01), outperforming existing generative methods. Furthermore, the reflow-driven DT channel model achieves the shortest generation time among all evaluated benchmarks.

Extremely large-scale MIMO (XL-MIMO) is regarded as a pivotal enabler for achieving ultra-high spectral efficiency in 6G communications. Near-field channel models, which integrate both line-of-sight (LoS) and non-line-of-sight (NLoS) components, provide accurate characterizations of near-field XL-MIMO channels. However, existing channel estimation schemes encounter severe performance bottlenecks due to the high-dimensional nature of near-field XL-MIMO channels and their structured angular sparsity compared to far-field MIMO systems. To address these challenges, we propose a variance exploding stochastic differential equation (VE-SDE) generator based on an improved diffusion transformer (IDiT) network. The VE-SDE progressively maps the complex XL-MIMO channel distribution to a tractable prior distribution by gradually injecting noise. We utilize the patchify technique to decompose the perturbed angular domain channels into token sequences, which are then processed with diffusion transformer (DiT) blocks, substantially reducing floating-point operations (FLOPs). Additionally, a sparse self-attention mechanism is employed to enhance structured sparsity characterization learning, thereby improving estimation accuracy. Theoretical analysis and numerical experiments show that the VE-SDE generator exhibits strong generalizability and robustness across diverse channel distributions without requiring retraining. Simulation results reveal that the proposed method outperforms state-of-the-art estimation approaches, achieving high-fidelity channel estimation with only 20% pilot density.

This paper investigates an intelligent reflecting surface (IRS)-aided wireless-powered communication network (WPCN) for maximizing the weighted sum rate (WSR). To reduce the complexity of traditional model-driven algorithms and improve convergence in data-driven deep learning approaches, a novel hybrid block coordinate descent (BCD) algorithm motivated by the dilation extraction and context attention (DECA) neural network (NN) is proposed. Specifically, the WSR maximization problem is firstly reformulated as a more tractable form, enabling the BCD algorithm to efficiently optimize the decoupled variables within the constraints. Meanwhile, at each BCD iteration, the DECA NN accelerates IRS phase shift optimization by facilitating the majorization-minimization (MM) algorithm to solve the computationally intensive fractional programming problem. Moreover, by leveraging dilation convolution and high-speed attention mechanisms, the DECA NN significantly outperforms existing deep learning benchmarks in both precision and convergence speed. Numerical results show that the proposed hybrid framework delivers performance comparable to the traditional BCD algorithm with dramatically reduced time consumption, while consistently maintaining robust performance under imperfect CSI and exhibiting strong transferability across diverse communication scenarios.

Cell-free massive multiple-input multiple-output (MIMO) systems have emerged as a transformative architecture for sixth generation (6G) communication networks, where distributed access points (APs) collaborate to simultaneously serve all user equipments (UEs). However, in time division duplex (TDD) systems, the reciprocity of uplink channel and downlink channel is disrupted by hardware imperfections in radio frequency (RF) chains, leading to significant degradation in system performance. This paper begins with a theoretical analysis of the downlink performance under a conjugate beamforming scheme, considering scenarios with and without channel calibration. A key theoretical insight highlights the limitation of conventional least squares (LS) calibration method, which fails to achieve high calibration accuracy even with an unlimited number of pilot observations. To overcome this limitation, we propose a novel channel calibration approach based on a diffusion model, designed to successively refine the calibration vector obtained from the LS calibration method. Furthermore, to address the shortcomings of conventional denoising diffusion probabilistic model (DDPM) training architectures, we introduce an innovative bridge-based diffusion model that maps the distribution of LS calibration vectors to their perfect counterparts. The proposed diffusion neural network architecture employs a conditional generative process, integrating a message passing neural network (MPNN) to incorporate domain-specific calibration insights. Numerical results demonstrate the superior performance of our proposed calibration method compared to existing methods, with supplementary experiments and in-depth analyses confirming the efficacy of the proposed successive refinement design.

The multiple-input multiple-output dual functional radar communication (MIMO-DFRC) system is a promising platform for future integrated sensing and communication applications. Ensuring reliable performance of both radar and communication functions, the beam selection is a critical technology in MIMO-DFRC systems. However, the beam selection problem is known to be NP-hard, and efficiently addressing it remains an open issue, especially in distributed systems. In this paper, we address the beam selection problem for a MIMO-DFRC system by formulating it as a semi-Markov decision process and propose a novel hierarchical reinforcement learning (HRL) algorithm. In our approach, codebook-based beam selection for transmitting and receiving BS is controlled by an agent deployed in the cloud. Inspired by the mechanism of hierarchical codebook beam training, we employ an option-based policy that enables the agent to explore different layers of the codebook and extract context information across multiple discrete time steps. We utilize an invalid action masking technique to overcome the dynamic action space problem caused by the option-based policy. Simulation results demonstrate that the HRL-based algorithm outperforms existing beam selection methods and achieves remarkable performance even under conditions of a high probability of false alarm and low signal-to-noise ratio. Furthermore, we find that the proposed algorithm exhibits promising capabilities to learn a more efficient policy beyond the full hierarchical codebook training trajectory.

As a revolutionary paradigm for intelligently controlling wireless channels, intelligent reflecting surface (IRS) has emerged as a promising technology for future sixth-generation (6G) wireless communications. While IRS-aided communication systems can achieve attractive high performance gain, existing schemes require plenty of IRS elements to mitigate the “multiplicative fading” effect in cascaded channels, leading to high complexity for real-time beamforming and high signaling overhead for channel estimation. In this paper, the concept of sustainable intelligent element-grouping IRS (IEG-IRS) is proposed to overcome those fundamental bottlenecks. Specifically, based on the statistical channel state information (S-CSI), the proposed grouping strategy intelligently pre-divide the IEG-IRS elements into multiple groups based on the beam-domain grouping method, with each group sharing the common reflection coefficient and being optimized in real time using the instantaneous channel state information (I-CSI). Then, we further analyze the asymptotic performance of the IEG-IRS to reveal the substantial capacity gain in an extremely large-scale IRS (XL-IRS) aided single-user single-input single-output (SU-SISO) system. In particular, when a line-of-sight (LoS) component exists, it demonstrates that the combined cascaded link can be considered as a “deterministic virtual LoS” channel, resulting in a sustainable squared array gain achieved by the IEG-IRS. Finally, we formulate a weighted-sum-rate (WSR) maximization problem for an IEG-IRS-aided multiuser multiple-input single-output (MU-MISO) system and a two-stage algorithm for optimizing the beam-domain grouping strategy and the multi-user active-passive beamforming is proposed. Simulation results validate the superiority of our proposed two-stage algorithm in low pilot overhead conditions and show that in the context of an XL-IRS aided MU-MISO system, the proposed IEG-IRS can achieve a significant WSR gain, thus overcoming this performance drawback associated with high complexity and signaling overhead.

Beamforming enhances signal strength and quality by focusing energy in specific directions. This capability is particularly crucial in cell-free integrated sensing and communication (ISAC) systems, where multiple distributed access points (APs) collaborate to provide both communication and sensing services. In this work, we first derive the distribution of joint target detection probabilities across multiple receiving APs under false alarm rate constraints, and then formulate the beam selection procedure as a Markov decision process (MDP). We establish a deep reinforcement learning (DRL) framework, in which reward shaping and sinusoidal embedding are introduced to facilitate agent learning. To eliminate the high costs and associated risks of real-time agent-environment interactions, we further propose a novel digital twin (DT)-assisted offline DRL approach. Different from traditional online DRL, a conditional generative adversarial network (cGAN)-based DT module, operating as a replica of the real world, is meticulously designed to generate virtual state-action transition pairs and enrich data diversity, enabling offline adjustment of the agent’s policy. Additionally, we address the out-of-distribution issue by incorporating an extra penalty term into the loss function design. The convergency of agent-DT interaction and the upper bound of the Q-error function are theoretically derived. Numerical results demonstrate the remarkable performance of our proposed approach, which significantly reduces online interaction overhead while maintaining effective beam selection across diverse conditions including strict false alarm control, low signal-to-noise ratios, and high target velocities.

Accurate sensing channel estimation is fundamental to high-performance integrated sensing and communication (ISAC), as it supplies critical information for target detection and localization. Despite extensive research, most existing approaches rely on the unrealistic assumption of ideal hardware conditions. However, hardware impairments are often inevitable due to the use of cost-efficient circuit components. This highlights the necessity for robust estimation techniques that remain reliable under imperfect conditions. To this end, we propose a self-supervised model-fusion network (SMF-Net) tailored for sensing channel estimation in hardware-impaired ISAC systems. To suppress distortions induced by hardware non-idealities, we design a two-stage cascaded convolutional neural network that leverages the spectral bias of neural networks, i.e., their tendency to learn high response frequency details in shallow layers and low frequency information in deep layers, to better separate different types of distortions present in corrupted channel estimates. By analyzing domain-specific features of the distorted channel components, we introduce a hybrid-domain denoising strategy that effectively exploits spatial correlations and angular sparsity inherent in the channel model. Furthermore, the framework is trained in a self-supervised manner, obviating the need for clean channel labels. Theoretical analysis validates the effectiveness of the proposed method and demonstrates that the self-supervised training strategy can match the performance of its supervised counterpart given a sufficiently large training set. Numerical results confirm the superiority of the proposed SMF-Net across various challenging scenarios, including severe nonlinear distortions, low transmission power, and limited training data.

The emergence of extremely large-scale MIMO (XLMIMO) has made target sensing in near-field environments crucial. However, the vast number of antennas and the big size of near-field dictionary matrix (DM) result in substantial pilot overhead for beam training algorithms and significant computational complexity for subspace algorithms. Moreover, there is few of work capable of accurately obtaining information beyond target location, such as radar cross-section (RCS). To this end, we propose a high-precision, low-pilot-overhead off-grid compressive sensing (CS) algorithm capable of jointly estimating target's location and RCS-the Multi-Layer Reconstruction Linear Approximation Variational Bayesian Inference (MLR-LA-VBI) algorithm. Specifically, the entire algorithm is divided into two phases. In the first phase, we propose the Multi-Layer Reconstruction (MLR) mechanism to reconstruct a surrogate DM. In the second phase, based on the surrogate DM, thus proposing the MLR-LA-VBI algorithm for joint estimation of target location and RCS. The final simulation results verify the superior performance of the proposed algorithm.

This paper addresses the compressive sensing (CS)-based frequency division duplexing (FDD) massive multiple-input multiple-output (MIMO) downlink channel estimation problem in dynamic scenarios. We propose a multipath angle of arrival (AoA) and angle of departure (AoD)-based shared dictionary learning (MASDL) algorithm, where the discriminative and shared features in the angular domain are exploited via supervised dictionary learning, enhancing the generalization ability of the model. Simulation results show that the proposed algorithm achieves better normalized mean square error (NMSE) performance and substantially reduces the pilot overhead compared with other channel estimation schemes.

The quality of channel state information (CSI) feedback is critical for maximizing the spectral efficiency of massive multiple-input multiple-output systems. With multiple antenna arrays, the overhead of direct CSI feedback in frequency division duplex mode is usually large, and many CSI compression techniques have been proposed to alleviate this problem. Deep learning (DL) has achieved tremendous strides in CSI feedback. However, most current DL-based CSI compression methods utilize fully connected layers to achieve dimensionality reduction, which may be suboptimal for network optimization and result in noteworthy information loss and reduced CSI reconstruction accuracy. In this paper, we propose a novel recursive discretization compression framework with a selective state space model for CSI feedback, namely CsiMamba-RDC. The framework employs improved residual vector quantization to recursively refine CSI representation, reducing information loss and storage overhead. Additionally, we present an encoder-decoder model leveraging a selective state space model to extract diverse channel features.

Deep learning (DL) techniques have been extensively utilized to tackle challenges in the field of wireless communication, overcoming the limitations of traditional methods. However, training DL algorithms often requires large amounts of data, which is difficult to obtain in increasingly complex communication environments. Reducing the amount of data required for DL training is therefore an urgent problem to be solved. In this work, we develop a denoising diffusion probabilistic model (DDPM)-based digital twin (DT) framework of integrated sensing and communication (ISAC) multiple-input-multiple-output (MIMO) channel to address the data scarcity issue commonly found in DL-based scenarios. By sampling a small amount of data, our framework captures and simulates the data distribution, building a virtual data repository that can continuously provide samples to assist in executing control instructions to physical entities, even as the user equipment (UE) and target positions change. Specifically, we formulate the data generation problem as a distribution approximation task guided by the Kullback-Leibler (KL) divergence criterion and optimize it by meticulously designing a DDPM network composed of U-Net structure, time-embedding modules, and attention mechanisms. Moreover, we enhance the framework by formulating a task-driven objective function for two applications: 1) sensing channel estimation and 2) target detection. Numerical results demonstrate the superiority of our proposed DDPM-based DT framework compared with other data augmentation techniques in improving the performance of data-driven DL-based tasks, showcasing its robustness across diverse scenarios.

This paper investigates the challenge of acquiring channel state information at the transmitter (CSIT) in cell-free massive multiple-input multiple-output (MIMO) integrated sensing and communication (ISAC) systems operating in time-division duplex (TDD) mode. Although channel state information at the receiver (CSIR) is readily obtainable and CSIT is typically assumed to be its transpose, imperfections in the radio frequency (RF) chains disrupt this reciprocity. Focusing on this issue, we establish the necessary and sufficient conditions characterizing RF chain imperfections and their impact on system performance in a simplified scenario, underscoring the criticality of channel calibration. To address this challenge, a distributed source coding (DSC)-based calibration framework is proposed, leveraging the multiplexing of the sensing task to eliminate any additional communication overhead. This framework comprises a distributed compression scheme at each slave access point (AP) and a joint aggregation scheme at the central process unit (CPU). To validate the proposed DSC-based calibration framework, we analytically derive the performance gap relative to the fully collaborated approach. Building on this, a novel data-driven DSC-based deep learning method is proposed to address channel calibration without requiring clean labels. Numerical results demonstrate significant improvement in calibration performance achieved by our proposed method compared to existing calibration methods, approaching the performance of the fully collaborated method.

Integrating wireless sensing capabilities into base stations (BSs) has become a widespread trend in the future beyond fifth-generation (B5G)/sixth-generation (6G) wireless networks. In this paper, we investigate intelligent reflecting surface (IRS) enabled wireless localization, in which an IRS is deployed to assist a BS in locating a target in its non-line-of-sight (NLoS) region. In particular, we consider the case where the BS-IRS channel state information (CSI) is unknown. Specifically, we first propose a separate BS-IRS channel estimation scheme in which the BS operates in full-duplex mode (FDM), i.e., a portion of the BS antennas send downlink pilot signals to the IRS, while the remaining BS antennas receive the uplink pilot signals reflected by the IRS. However, we can only obtain an incomplete BS-IRS channel matrix based on our developed iterative coordinate descent-based channel estimation algorithm due to the “sign ambiguity issue”. Then, we employ the multiple hypotheses testing framework to perform target localization based on the incomplete estimated channel, in which the probability of each hypothesis is updated using Bayesian inference at each cycle. Moreover, we formulate a joint BS transmit waveform and IRS phase shifts optimization problem to improve the target localization performance by maximizing the weighted sum distance between each two hypotheses. However, the objective function is essentially a quartic function of the IRS phase shift vector, thus motivating us to resort to the penalty-based method to tackle this challenge. Simulation results validate the effectiveness of our proposed target localization scheme and show that the scheme’s performance can be further improved by finely designing the BS transmit waveform and IRS phase shifts intending to maximize the weighted sum distance between different hypotheses.

Cell-free massive multiple-input multiple-output (MIMO) is a promising technology to address the requirements for higher spectral efficiency and energy efficiency in 6G networks. Downlink beamforming scheme, essential for mitigating multiuser interference and enhancing overall system performance, relies on the estimated uplink channel state information (CSI) in time-division duplex (TDD) mode exploiting channel reciprocity. However, hardware impairments render the bi-directional channel non-reciprocal. This paper focuses on channel calibration for cell-free massive MIMO systems, taking into account both radio frequency (RF) mismatches and nonlinear distortions. We derive the closed-form expression for downlink achievable rate within a specific calibration scheme. To address the calibration challenge, we introduce a novel conceptual model, in which the calibration vector is determined by optimizing the performance of the reference antenna. Expanding on this concept, we propose a novel digital twin (DT)-enabled approach to overcome the limitations in the conceptual model, where the DT model is established to perform calibration task by introducing DT services of virtual reference antennas. By exploiting this method, the calibration vector is computed utilizing the proposed alternating optimization algorithm within the DT model, obviating the need for deploying reference antennas in the real cell-free system, thereby reducing costs. The communication overheads and computation complexity for updating the calibration vector is proportional to the access point (AP) number. Simulation results demonstrate the significant improvement of system performance through channel calibration and verify the higher downlink throughput of our proposed DT-enabled calibration method compared to the existing calibration methods.

The deployment of extremely large-scale antenna array (ELAA) brings higher spectral efficiency and spatial degree of freedom, but triggers issues on near-field channel estimation. Inspired by the success of deep learning (DL) in far-field channel estimation, this paper proposes a novel spatial-attention-based method to reconstruct extremely large-scale MIMO (XL-MIMO) channel. Initially, the spatial antenna correlation in near-field channels is drawn as the expectation over spatial region, different from only over spatial angle in far-field channels. The spatial antenna correlation implies that the near-field channel exhibits spatial nonstationarity, that the inter-antenna correlation vary with the antenna index and spatial regions and reveals the weakness of the widely applied convolutional neural network (CNN) with fixed receptive field. Subsequently, we develop a multi-scale spatial attention network (MsSAN) with low computational cost to enhance near-field MIMO channel estimation. In MsSAN, the channel is refined to subchannels of different scales layer by layer and each subchannel is treated as a whole and the spatial attention (SA) map is calculated by the sum of dot products of inter-subchannel so that the complexity grows linearly with channel size. Simulation results are presented to validate the proposed MsSAN with low computational cost outperforms others in terms of near-field channel reconstruction.

In this paper, we consider robust joint access point (AP) clustering and beamforming design with imperfect channel state information (CSI) in cell-free systems. Specifically, we jointly optimize AP clustering and beamforming with imperfect CSI to simultaneously maximize the worst-case sum rate and minimize the number of AP clustering under power constraint and the discrete constraint of AP clustering. Through transformations, the intractable simultaneous optimization of continuous and discrete variables is reduced to optimizing only the sparsity of the continuous variables, facilitating a computationally efficient unsupervised deep learning algorithm. In addition, to further reduce the computational complexity, a computationally effective unsupervised deep learning algorithm is proposed to implement robust joint AP clustering and beamforming design with imperfect CSI in cell-free systems. Numerical results demonstrate that the proposed unsupervised deep learning algorithm achieves a higher worst-case sum rate under a smaller number of AP clustering with computational efficiency.

The deployment of extremely large-scale MIMO (XL-MIMO) and short-wavelength signaling enhances communication capabilities and improves spectrum efficiency for future sixth-generation (6G) wireless communication. However, users may potentially be located in the near-field region due to the sharp increase in antenna array aperture. In the near-field region, the signal wave is spherical wave. Thus, the consideration of spatial angle and distance requires the development of novel channel estimation algorithms to reduce codebook overhead. This paper develops a novel scheme based on a low-size adaptive codebook to reconstruct the near-field channel. Initially, it is investigated that the angle spread for one channel path component is confined to a certain angular spatial region, which demonstrates the sparsity inherent in angular domain. Exploiting the angular sparsity inherent, we propose a novel adaptive joint sparse Bayesian learning (JSBL) estimation algorithm on all subcarriers to cater to reduce the codebook size. The proposed algorithm captures all spatial angular sparse information and then refines distance information so that the measurement codebook size only depends on the spatial angular resolution. Further, the proposed adaptive JSBL approach is extended to estimate the time-varying near-field channel. Moreover, Bayesian Cramér-Rao Bounds (BCRBs) are derived for quasi-static and temporal scenarios. Numerical simulations are presented to demonstrate that our approaches with low codebook overhead outperform other algorithms based on the angular-domain and polar-domain codebooks.

The deployment of extremely large-scale arrays and high-frequency signaling holds the potential to enhance communication capabilities and improve spectrum efficiency. However, channel estimation faces challenges due to the simultaneous consideration of spatial angles and distances, leading to storage constraints and energy spread. To cope with this issue, we analyze the sparsity inherent in beamspace domain representation and introduce an adaptive codebook scheme for extremely large-scale massive MIMO (XL-MIMO) channels. In this work, we transform multi-band channel estimation to sparse matrix recovery problem. Then, a novel adaptive joint sparse Bayesian learning algorithm is proposed to capture the angular-domain information and refine distance information iteratively without increasing codebook overhead for XL-MIMO channel estimation. Simulation results demonstrate our approach outperforms other algorithms based on the sampling angular-distance domain codebook with low codebook overhead.

Image anomaly detection holds significant potential across various domains. The scarcity of anomaly samples in real-world scenarios makes unsupervised anomaly detection more practical, as acquiring a substantial number of anomaly samples is often challenging. Despite the progress made by image reconstruction-based methods in this task, their reliance on fuzzy reconstruction images and the complexity of post-processing have posed challenges to the overall performance of anomaly detection. To address this issue, this paper proposes a novel Enhanced Reverse Distillation Guided Segmentation Network(ERDS-Net). Unlike conventional approaches, this network consolidates the image reconstruction and anomaly detection into a unified process, leveraging feature maps from the intermediate layers of both the encoder and decoder for segmentation. In addition, our model fully leverages a batch-wise attention mechanism, focusing on more challenging samples. This method aims to enhance overall performance by simplifying the process and mitigating the adverse effects of blurriness and complex post-processing. Moreover, this paper utilizes a self-supervised approach for training in order to extract additional information from unlabeled data. Experimental results demonstrate the outstanding effectiveness of the proposed Enhanced Reverse Distillation Guided Segmentation Network on the MVTec dataset. In comparison to traditional image reconstruction-based methods, the new approach exhibits superior performance in anomaly detection and localization tasks, demonstrating enhanced robustness with various metrics.

Dual-functional radar-communication (DFRC) is a promising direction in the future integrated sensing and communication system. The joint radar and communication (JRC) beamforming scheme is recently developed in DFRC systems. To address the JRC beamforming challenge, conventional approaches predominantly rely on convex optimization methods, which severely depend on precise channel estimation and entail a high computational complexity. Motivated by this, a deep learning-based optimization approach is investigated for tackling the JRC beamforming problem. To enhance the overall performance, we design a deep alternating neural network architecture. Simulation results verify that our proposed method guarantees the required sensing performance and outperforms numerical algorithms in terms of the average data rate of communication users.

This paper concentrates on addressing the challenging problem of sensing channel estimation in cell-free integrated sensing and communication (ISAC) multiple-input multiple-output (MIMO) system. This challenge arises from the complex mixture of signals from both the direct sensing channel and target reflected sensing channel. To tackle this challenge, we introduce the digital twin (DT), as a powerful tool to exploit and characterize the inherent features of the target sensing channel by sampling data from the real world and interacting with it. To be specific, the DT model, designed as a generative adversarial network (GAN), is trained to be capable of generating the desired results from the coarse observations, where the distribution of the sensing channel in a particular cell-free ISAC system is implicitly learned via the adversarial process. With this basis, we propose a novel digital-twin-enabled channel estimation (DTE-CE) approach to enhance the performance of channel estimation, where the DTE-CE network is meticulously designed by utilizing the virtual channel matrix (VCM) model to facilitate the estimation process. Simulation results show the excellent performance of the proposed approach, as well as the effectiveness of our designed DTE-CE network, in terms of sensing channel estimation with different transmitting power and numbers of targets.

Extremely large-scale multiple-input multiple-output (XL-MIMO) communication systems introduce a new communication paradigm called near-field communications, which identifies users’ location within the near-field (Fresnel’s region). In the near-field, beams can be steered in the angle and distance dimensions, resulting in an enormous codebook and a prolonged two-dimensional beam alignment (BA) process. To keep a low BA overhead while achieving low BA error, in this paper, we design a novel hierarchical codebook and a BA scheme for near-field XL-MIMO systems. Specifically, we first propose a novel spatial partition where the angle-offset effect is revealed and leveraged to improve the beam gain inside the coverage area. Based on the partition, we design distance-coarse and focusing beams. Distance-coarse beams are leveraged to construct the high level of the codebook for angle dimension alignment. In contrast, focusing beams construct the last level codebook for distance dimension alignment. Corresponding to the proposed codebook structure, our BA scheme is a tree search consisting of two stages: the angle aligning stage and the distance aligning stage. Next, we formulate the desired codebook design problem as difference convex optimization problems, where three beam design guidelines are considered to minimize the BA error rate raised by the near-field angle-offset effect. After that, the proposed optimization problem is solved by the constrained concave-convex procedure. Numerical simulations verify the angle offset effect and our designed near-field beam. Furthermore, we show that our BA scheme only utilizes one percent of overhead but achieves a lower BA error rate than exhaustive searching.

Intelligent reflecting surface (IRS) is a promising new paradigm for enhancing wireless information transmission (WIT) and wireless power transfer (WPT) cost-effectively in the future. In this paper, we study an IRS-aided full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid node (HN) operating in FD mode sends information signals to multiple devices in the downlink (DL), and meanwhile receives energy signals from a power station (PS) in the uplink (UL), both of which are assisted by an IRS. Our objective is to boost the weighted sum throughput by jointly optimizing the active transmit beamformer at the PS and HN, along with the passive reflection coefficients of the IRS. To deal with the formulated non-convex optimization problem with intricately coupled design variables, most of existing works employ the alternating optimization (AO) method, whose performance, however, is closely related to parameter initialization. In contrast, we develop two novel penalty-based algorithms for the single-device and multi-device cases, respectively. In particular, our proposed rank-one constraint reformulation method of matrix proves to be efficient, especially for the case where the objective function is a higher-order function of the IRS phase shifts. Numerical results demonstrate the superiority of our proposed design over benchmark schemes, and also unveil the necessity of the joint design of passive IRS beamforming and resource allocation for achieving better WPCN performance. Moreover, we draw useful insights into the fine-tuning of IRS deployment location in the studied WPCN.

Cell-free massive multiple-input multiple-output (MIMO) is known for its potential to enhance overall system performance. Thanks to the principle of channel reciprocity, it becomes possible to implement downlink beamforming by exploiting the estimated uplink channel in time-division duplex (TDD) mode. However, the assumption of perfect hardware conditions, as made in prior studies, is not reflective of practical realities. The involvement of hardware impairments disrupts this reciprocity, resulting in performance degradation. This paper investigates the impact of hardware impairments in downlink data transmission, where a novel model is established by jointly considering the radio frequency (RF) mismatches and nonlinear distortions. We first derive closed-form achievable user rate expressions and prove that the impact of RF mismatches vanishes as the number of access points (APs)$M \to \infty $in certain distributions of RF gains. Then, we study the scenarios when the number of user equipments (UEs)$K \to \infty $, as well as various degrees of hardware impairments’ severity scaling M. Finally, we introduce a channel calibration process and theoretically derive its performance, observing that in certain scenarios, the need for calibration becomes redundant as$M \to \infty $. These findings are further validated through numerical results, confirming the scaling laws derived in our study.

Network slicing-based communication systems can dynamically and efficiently allocate resources for diversified services. However, due to the limitation of the network interface on channel access and the complexity of the resource allocation, it is challenging to achieve an acceptable solution in the practical system without precise prior knowledge of the dynamics probability model of the service requests. Existing work attempts to solve this problem using deep reinforcement learning (DRL). However, such methods usually require a lot of interaction with the real environment to achieve good results. In this paper, a framework consisting of a digital twin and reinforcement learning agents is present to handle the issue. Specifically, we propose to use the historical data and the neural networks to build a digital twin model to simulate the state variation law of the real environment. Then, we use the data generated by the network slicing environment to calibrate the digital twin so that it is in sync with the real environment. Finally, DRL for slice optimization optimizes its performance in this virtual pre-verification environment. We conducted an exhaustive verification of the proposed digital twin framework to confirm its scalability. Specifically, we propose to use loss landscapes to visualize the generalization of DRL solutions. We explore a distillation-based optimization scheme for lightweight slicing strategies. In addition, we also extend the framework to offline reinforcement learning, where solutions can be used to obtain intelligent decisions based solely on historical data. Numerical simulation experiments show that the proposed digital twin can significantly improve the performance of the slice optimization strategy.

Accurate channel estimation is an essential prerequisite for achieving significant performance gains in intelligent reflecting surface (IRS)-aided communication systems. Recent studies have shown that deep neural network-based channel estimation holds promise as a competitive alternative to conventional methods. However, existing neural network-based approaches typically involve manual design of network architectures through a trial-and-error process, demanding extensive domain knowledge and human resources. In this paper, we propose an automatic approach to construct a high-performance neural network architecture for channel estimation. Our method, called the channel estimation neural network architecture search (CENAS), utilizes a truncated back-propagation optimization search strategy to explore a neural network tailored for channel estimation. By carefully designing a search space tailored to channel estimation tasks, the automatically constructed network surpasses both conventional and deep learning-based channel estimation algorithms. The convergence of our framework’s network construction process is comprehensively analyzed, providing formal evidence of its convergence properties. Additionally, the proposed framework exhibits good generalization and applicability by allowing flexible adjustment of hyperparameters to generate networks with varying scales. Empirical results show the stability and the improved performance of CENAS framework, validating its effectiveness and desirability.

Ideally, the bi-directional channel in time division duplex (TDD) millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) systems exhibits reciprocity. However, the involvement of low-cost and non-ideal radio frequency (RF) chains disrupts this reciprocity. Consequently, prior to fully leveraging the advantage of channel reciprocity, it is essential to implement channel calibration. Despite numerous over-the-air calibration methods, such as Argos, the typical least square (LS) are proposed in the literature, none of their criteria directly focus on the calibration performance. To address this gap, we propose a novel deep learning based approach that aims to optimize the calibration performance and introduce device-level intelligence towards 6G networks. To be specific, two cascaded modules are designed in a model-assisted end-to-end manner. Firstly, we propose the double-CNN-based channel denoising module for joint bi-directional channel estimation by exploiting the characteristics of mmWave channel. Secondly, the deep calibration learning module is meticulously designed to obtain the calibration coefficients with the aid of assisted model. This traceable assisted model is established by leveraging the expert knowledge of calibration process, based on which the MetrNet and the CaliNet are designed. Numerical results demonstrate the superior performance of our proposed method compared to existing calibration methods. Particularly, additional simulations and analysis are conducted to verify the effectiveness of the two properly designed modules.

Dual-functional radar-communication (DFRC) is a promising technology in future integrated sensing and communication systems. Since communication and sensing performance need to be taken into consideration for joint radar and communication (JRC) beamforming in the DFRC system, existing approaches mainly transform JRC beamforming problems into convex optimization problems and then solve them with classical convex solvers. These traditional solutions heavily rely on precise channel estimation and entail high computational complexity. In this paper, we investigate a deep learning-based optimization approach for JRC beamforming to enhance the spectral efficiency for communication users and guarantee the probability of detecting targets. To achieve better performance, we leverage the theoretical optimal structures of JRC beamforming and design an effective deep neural network architecture. To further reduce the computational burden in the training phase of neural network, we develope an improved orthogonal beamforming technique. Simulation results verify that our proposed algorithm guarantees the required sensing performance and outperforms numerical algorithms in terms of communication performance. The orthogonal beamforming technique achieves satisfactory performance with low computational complexity.

Channel estimation stands as a pivotal and challenging task for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) communication system, especially in a time-varying scenario, where exists a massive number of channel coefficients and severe propagation loss due to the Doppler shifts. Conventional estimation schemes may fail to track the fast varying channels and not be able to fully exploit the unique characteristics of mmWave channels in their model designs. In this work, we leverage the Generative Adversarial Networks (GANs) and meticulously design a novel framework named Homogeneous Denoising Generative Adversarial Network (HDnGAN) to tackle the challenge of time-varying channel estimation for mmWave MIMO system. Our framework incorporates the distinctive traits of mmWave channels, such as temporal and spatial correlations, as well as angular sparsity, into the network architecture design. Theoretically, a special case of our proposed HDnGAN with a linear structure is demonstrated to be not inferior to the linear minimum mean squared error (LMMSE) estimator. Numerical simulations underscore the superiority of HDnGAN over existing channel estimation methods, particularly in low signal-to-noise ratio (SNR) regions. Furthermore, it exhibits robustness across varying scenarios. Notably, it remains applicable in out-of-distribution situations and in the absence of ground truth.

Acquiring the wireless channel state information (CSI) is an essential task to reap the wireless system performance gain brought by intelligent reflecting surface (IRS). In this paper, we study an IRS-assisted wireless energy transfer (WET) network, where an energy receiver (ER) harvests the wireless energy transmitted from an energy transmitter (ET) with the help of an IRS. Different from the commonly adopted wireless CSI acquisition approaches such as pilot or codebook based methods, we propose a novel channel learning method that requires only one-bit feedback information from the ER. Specifically, each feedback bit indicates whether the increase or decrease of the harvested energy amount at the ER within the present interval as compared to the previous one. Based on the feedback information, the ET continually adjusts its transmit beamforming in subsequent channel learning intervals to help infer the cascaded ET-IRS-ER CSI. It is worth noting that an optimization technique named analytic center cutting plane method (ACCPM) is applied in the channel learning phase. Numerical results unveil that our proposed one-bit feedback based channel estimation method is able to effectively estimate the cascaded ET-IRS-ER channel, and greatly reduce the requirement on the hardware complexity of the ER simultaneously.

From practical considerations in massive multiple-input multiple-output (MIMO) systems, with the involvement of radio frequency (RF) chains, the channel reciprocity no longer holds even under time division duplex (TDD) operation. To fully leverage the advantage brought by TDD systems, channel reciprocity calibration needs to be necessarily investigated. In this paper, we propose the CNN-enhanced calibration method, which is composed of the channel estimation task and the calibration coefficient calculation task. Different from previous works, our method is based on our proposed double-CNN-based bi-directional channel estimator, which is designed specifically for the calibration problem to exploit the bi-directional channel correlation, the spatial correlation, and the angular correlation in millimeter wave (mmWave) channel. Based on this, a formulated LS calibration problem is solved. Numerical results manifest that our proposed method outperforms the existing calibration methods in the literatures.

In this paper, we consider an intelligent reflecting surface (IRS)-aided full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid access point (HAP) operating in FD mode sends information signals to a device in the downlink (DL) and meanwhile receives energy signals from a power station (PS) in the uplink (UL) with the help of an IRS. Our objective is to maximize the achievable data rate from the HAP to the device by jointly optimizing the transmit covariance matrix at the PS, the transmit beamforming vector at the HAP, and the phase shift vector at the IRS. The optimal transmit beamformer at the HAP is derived in closed from, and the joint optimization of the transmit covariance matrix at the PS and the phase shift vector at the IRS results in an intractable non-convex problem. To tackle this challenge, we propose an efficient penalty-based algorithm consisting of two layers. In the inner layer, we iteratively increase the device's signal-to-interference-plus-noise ratio (SINR) by applying the Dinkelbach's transform. While in the outer layer, we gradually decrease the penalty parameter. Numerical results demonstrate the superiority of our proposed design over benchmark schemes, and also unveil the necessity of the joint design of passive IRS beamforming and active beamforming for achieving better WPCN performance.

Accurate channel estimation is an indispensable prerequisite for intelligent reflecting surface (IRS) aided communication systems to achieve huge system performance gains. Current works show that deep neural network-based channel estimation is a promising solution to achieve competitive performance compared with the conventional methods. However, neural network-based approaches generally realize the channel estimation by manually designing network architectures in a trial-and-error manner which need complex neural network domain knowledge and tremendous computation resource. This paper automatically constructs a high-performance neural network architecture to obtain dedicated channel estimation schemes intelligently. Specifically, we propose a channel estimation neural network architecture search (CENAS) method based on gradient alternatively search strategy to search a channel estimation neural network. With the search space designed meticulously for the channel estimation task, the network searched by the proposed method outperforms the conventional and deep learning-based channel estimation algorithms.

In this paper, a cross-layer optimization problem of access point selection (APS) and beamforming (BF) in cell free network (CFN) has been studied, where constraints of per access point (AP) power and per user receiving data streams are considered. Such a cross-layer design of APS&BF problem is modeled as a mixed-integer nonlinear programming (MINP) program. Then, by adopting the weighted l1-norm approximation, the MINP problem is transformed into the sum logarithmic multiple-ratio form. To be specific, a novel and low-complexity mix-integer fractional programming (MIFP) algorithm is proposed to solve the transformed problem effectively. Convergence analysis validates that the proposed MIFP converges to a local optimal solution. Finally, numerical results show that cross-layer design of APS&BF scheme is superior to separate design of APS&BF schemes. In addition, the proposed MIFP has the approximate performance as partial exhaustive search algorithm.

Joint access point (AP) clustering and beamforming design is an effective way to improve system performance and reduce signaling overhead for cell-free networks. However, conventional optimization methods usually solved the joint AP clustering and beamforming design by separately handling them, at the cost of high computing resources, especially when quality of service (QoS) constraint is also considered. To this end, this paper proposes a low-complexity unsupervised deep learning method to jointly optimize AP clustering and beamforming design, called as joint clustering and beamforming network (JcbNet). The JcbNet also designs a neural network to handle the QoS constraint to reduce the hyperparameters of loss function, and it introduces a learnable safety distance parameter in the loss function to reduce the violation rate of QoS constraint. In addition, the JcbNet is scalable since the dimensions of parameters and output beamforming vary with the dimension of input channel state information (CSI). The experimental results show that the JcbNet is low-complexity, and achieves a higher sum rate under a smaller number of AP clustering compared to traditional and deep learning algorithms such as weighted minimum mean square error (WMMSE), sparse WMMSE (S-WMMSE) and convolutional neural network (CNN).

In this paper, we propose a robust max-min fairness transmission design for intelligent reflecting surface (IRS)-aided wireless network in the presence of user location uncertainty. In particular, the non-isotropic reflection property for the IRS element is considered. We investigate the joint design of the active transmit beamformer at the base station (BS) and the passive phase shift matrix along with the deployment orientation (facing/pointing direction) of the IRS for maximizing the worst-case minimum signal-to-interference-plus-noise ratio (SINR) received by the users. In order to show the potential gains obtained by adjusting the deployment orientation of the IRS, a single-input-single-output (SISO) system is studied where a closed-form signal-to-noise ratio (SNR) of the user is obtained. For the multi-user case, to solve the resulting non-convex problem, an inexact-alternating-optimization algorithm consisting of a double-loop iteration is proposed. Specifically, in the inner loop, an optimization problem with semi-infinite constraints needs to be solved to increase the worst-case min-SINR compared to the given SINR reference value. We first transform the semi-infinite constraints into linear matrix inequality (LMI) constraints with finite form by applying the Taylor expansion approximation method, the general S-procedure, and the general sign-definiteness lemma. Then an efficient alternating optimization (AO) algorithm based on the two-dimensional search method, negative square penalty (NSP) method, and successive convex approximation (SCA) technique is proposed. While in the outer loop, we update the given SINR reference value as the worst-case minimum SINR obtained after each inner loop iteration. The whole algorithm terminates when the updated SINR reference values converge. Simulation results demonstrate the effectiveness of the proposed algorithm, and also show the additional system performance gain brought by the optimization of the IRS deployment orientation compared to its counterpart with fixed IRS deployment orientation, especially for a smaller IRS element number and a more prominent non-isotropic reflection property of the IRS element.

Large antenna arrays and beamforming are necessary for the mmWave communication system, resulting in heavy time and energy consumption in the beam training stage. Therefore, dual-band operations are expected to be deployed in future communication systems, where low-frequency channels are used to meet basic communication needs, and millimeter wave (mmWave) channels are exploited when the high-rate transmission is required. Existing works utilize deep learning methods to extract low-frequency channel state information (CSI) to reduce the mmWave beam training overheads. However, an important limitation of deep learning approaches is that the model is usually trained in a given environment. When employed in an unseen environment, it usually requires a large amount of data to retrain. In this paper, a model-agnostic optimization algorithm based on meta-learning is proposed to provide a general mmWave beam prediction model. This model can be deployed to edge base stations and effectively adapted to the environment without the need for a heavy collection of data. Simulation results demonstrate that the proposed approach could reduce the model adaptation overheads. The meta-learning-based beam prediction model is robust and achieves high prediction accuracy and spectral efficiency in different signal-to-noise ratio (SNR) regimes.

Deep neural network-based learning methods have been considered promising techniques used in beam selection problems. However, existing research ignores the peculiar vulnerabilities of neural networks. The adversaries can use data poisoning to embed predefined triggers into a model during training time such that the neural network-based beam model may make an incorrect output decision of a test example when patched with the trigger. Data poisoning offers attackers the possibility to build backdoors. The goal of backdoors is often unethical, such as giving users a poor experience by manipulating infected models to output inappropriate beams. In this paper, first, we introduce a simple backdoor attack method by using data poisoning in a mmWave beam selection system. By numerical simulations, we verify that this poisoning attack is effective for neural networks with different structures. In addition, we explore the effect of poisoned data volume on the effect of backdoor attacks. The results show that the backdoor can be successfully implanted into the beam selection neural network. Besides, we fine-tune the trained model for a new wireless communication environment, and the results show that backdoors still exist even when the model is tuned with data from new scenarios. Then, we propose a machine unlearning solution to mitigate the backdoor of the trained beam selection model. The problem of eliminating backdoors is modeled as a minimax optimization problem. We propose a novel adversarial unlearning method along with label smoothing to solve the backdoor removal problem. We compared the proposed backdoor elimination method with the classical fine-tuning elimination method and the neural network pruning method through numerical simulations. The results show that the fine-tuning and the pruning methods cannot effectively remove the backdoor. The proposed machine unlearning method can make the trained model forget about the backdoor under the condition that the performance of the benign task (beam selection tasks when the trigger does not appear) is guaranteed to be slightly degraded. In summary, our work illustrates that data poisoning-based backdoor attacks may exist in wireless networks, and we propose a scheme to eliminate backdoors.

Cell-free massive multiple-input multiple-output (MIMO) is an attractive network in 6G communications that significantly increases the spectral efficiency. Operating in time-division duplex (TDD) mode, the downlink beamforming is achieved by the estimated uplink channel, which is equal to the downlink channel due to the property of channel reciprocity. However, the involvement of different radio frequency (RF) gains in transceiver antennas renders the whole channel non-reciprocal. Therefore, it is of great necessity to calibrate the bi-directional channel. In this paper, we focus on the issue of over-the-air channel calibration in cell-free system. Taking a toy scenario as an example, we examine the performance differences between the calibration methods of ‘Direct Process’ and ‘Indirect Process’. A novel low-cost calibration method based on spanning tree model is proposed specifically for this distributed AP scenario, where a calibration tree is established to calculate calibration coefficients. Numerical results manifest that higher accuracy of our method is achieved compared to the existing calibration methods in the literatures. Our method is less sensitive to the location of master AP compared to Argos, and practical applications under the impact of phase noise show the priority of our method compared to LS method.

Deep learning (DL) is an emerging paradigm for accurate channel estimation for intelligent reflecting surface (IRS)-aided wireless communication systems. It has been proven to be a promising way to achieve better channel estimation performance for the IRS-aided wireless communication system than traditional methods (e.g., least-square algorithm). However, existing DL-based methods rely on ground truth (labels of the true channels) which is difficult to obtain in real networks. In this paper, we propose a self-supervised learning (SSL) method for the IRS channel estimation problem. No ground truth channel is needed in the training, while a simple and novel self-supervised denoising formula without a clean reference signal is presented. Particularly, in the training phase, the self-supervised signal and the input are the received signal vector and its noisy version, respectively. While in the inference phase the input is the estimated channel by using the least-square method and the output is the refined channel estimation. That is, our neural network-based channel estimation algorithm is not reciprocal for training and testing. We demonstrate that the proposed SSL solution has good convergence performance and generalization ability through numerical simulations. Interestingly, we find a “double descent” phenomenon in the learning curve during the test phase, i.e., when we gradually increase the number of training epochs, the performance first gets better, then becomes worse, and further gets better again. Besides, we propose to analyze SSL using the loss landscape and centered kernel alignment method. The results show that the self-supervised model has a similar loss landscape and representational similarity to the supervised model. We explored the effects of different signal-to-noise ratios (SNRs), different neural network sizes, and different training data volumes on our algorithm through numerical simulations. Extensive numerical simulation results show that our SSL algorithm is still competitive without ground truth. We also show that the developed scheme exhibits robustness to SNR ratio mismatch.

This paper studies the performance of multi-antenna proactive eavesdropping in 5G uplink systems with spatially correlated Rayleigh fadings, where the base station (BS) serves an illegal user and a multi-antenna legitimate monitor eavesdrops the suspicious link with the help of jamming attack. Based on a practical assumption of channel state information (CSI) in 5G uplink, i.e., imperfect instantaneous CSI of the suspicious link at the BS and that of eavesdropping link at the monitor, and only jamming channel statistics at the monitor, we first give a statistical jamming beamforming design. Then, semi-closed form expressions of eavesdropping non-outage probability and relative average eavesdropping rate are, respectively, derived for delay-sensitive and delay-tolerant scenarios. Via reasonable approximations and asymptotic analysis, we gain many insights on the effect of key system parameters, e.g., location-dependent channel path loss and angular spread, jamming energy and the number of antennas. Further, we provide the optimal energy allocation between pilot and data jamming and the optimal antenna allocation between jamming and eavesdropping under total energy constraint and total antenna number, respectively, which are both explicit functions of system parameters. Finally, simulation results validate our analytical results.

Abstract This paper investigates a novel wireless information surveillance scheme assisted by reconfigurable intelligent surface (RIS) beamforming and artificial noise jamming cooperation, aiming at monitoring the information sent by an access point (AP) to a suspicious illegal user (SIU). It is assumed that the AP adopt the fixed maximum ratio transmission (MRT) precoding scheme, which is not affected by the information monitoring party. The goal of this paper is to maximize the effective information monitoring rate by jointly optimizing the RIS phase shifts, the receive beamforming vector of the legitimate receiver (LR), and the transmit beamforming vector along with jamming power of the jamming antenna (JA). The resultant optimization problem is non‐convex, and its optimization variables are highly coupled in the objective function and constraints. To tackle this difficulty, the optimization variables are optimized under the alternate optimization (AO) framework. Especially, the intractable RIS phase shifts are optimized by using Riemannian manifold optimization (RMO) algorithm under the penalty dual decomposition (PDD) framework and the semidefinite relaxation (SDR) technique, respectively. Numerical results verify the effectiveness of the proposed algorithms, and also demonstrate the superiority of the designed wireless information surveillance scheme over other benchmark schemes.

Learning-based resource allocation (LRA) is envisioned as an integral element of 6G. This article proposes a novel learning-based paradigm to address resource allocation problems in heterogeneous ultradense networks (HUDNs). Our paradigm is a highly efficient realization for utilizing the inherence properties in HUDN, which comprise the local validity and correlation attenuation. Concretely, we formulate the HUDNs as a heterogeneous bipartite graph model and propose the corresponding heterogeneous bipartite graph neural network (HBGNN). The local sampling characteristic of HBGNN matches the inherence properties. Meanwhile, our paradigm combines data-driven and model-driven learnings and employs online and offline trainings. Hence, two of LRA’s obstacles: 1) the overreliance on the perfect data set and 2) the low calculation efficiency are mitigated, and the realizability of our paradigm is improved. Besides, entropy regularization is utilized to guarantee the effectiveness of exploration in the configuration space. We apply our approach to a representative resource allocation problem, the jointly user association (UA) and power allocation (JUAPA) problem. We formulate JUAPA as a combination classification and regression problem and adopt a dynamical hyperparameter output layer to address the discrete variable of UA. Simulation results demonstrate that the proposed method has better performance and higher computational efficiency than traditional optimization algorithms.

Nowadays, wireless communication is rapidly reshaping entire industry sectors. In particular, mobile-edge computing (MEC) as an enabling technology for the Industrial Internet of Things (IIoT) brings a powerful computing/storage infrastructure closer to the mobile terminals and, thereby, significantly lowers the response latency. To reap the benefit of proactive caching at the network edge, precise knowledge on the popularity pattern among the end devices is essential. However: 1) the spatiotemporal variability of content popularity; 2) the data deficiency in privacy-preserving system; 3) the costly manual labels in supervised learning; as well as 4) the not independent and identically distributed (non-i.i.d.) user behaviors pose tough challenges to the acquisition and prediction of content popularities. In this article, we propose an unsupervised and privacy-preserving popularity prediction framework for MEC-enabled IIoT to achieve a high popularity prediction accuracy while addressing the challenges. Specifically, the concepts of local and global popularities are introduced and the time-varying popularity of each user is modeled as a model-free Markov chain. On this basis, we derive and validate the essential relationship between the local and global popularities and then propose an unsupervised recurrent federated learning (URFL) algorithm to predict the distributed popularity while achieving privacy preservation and unsupervised training. Moreover, a federated loss-weighted averaging (FedLWA) scheme for the parameter aggregation is further designed to alleviate the problem of non-i.i.d. user behaviors. Simulations indicate that the proposed framework can enhance the prediction accuracy in terms of a reduced root-mean-squared error by up to 60.5%–68.7% compared to other baseline methods, i.e., recommendation algorithms, centralized learning algorithms, and other distributed learning algorithms. Additionally, manual labeling and violation of users’ data privacy are both avoided.

For the estimation of real-valued Gaussian signals, the unscented Kalman filter (UKF) can provide a state estimate with second-order accuracy. However, when a general complex-valued system is considered, a direct extension of UKF from the real domain to the complex domain is inadequate, since the complementary covariance information associated with general improper complex-valued signals has been systematically ignored. To this end, in this work, we propose a general complex-valued unscented Kalman filter (GCUKF) algorithm which can be applied for both proper and improper signals. This is achieved by first proposing a novel sigma points selection scheme for the general complex-valued case, followed by a modified state update method to fully utilize both the innovation and its conjugate. A rigorous MSE analysis illustrates the superiority of the proposed state update method, and simulations support the analysis.

Hybrid heterogeneous cellular networks (HCNets) with sub-6G and millimeter-wave (mmWave) base stations (BSs) achieves good performance-and-cost tradeoffs. Via noticing the negligible retrieving latency and the potential joint transmission (JT) gain of sub-6G BSs, we propose a novel cache-enabled user association scheme for hybrid HCNets with limited local storage, in which partial sub-6G local storage caches contents with relatively low popularity for higher overall content diversity. To sufficiently exploit the large bandwidth of mmWave BSs, they are endowed with higher association priority. Then, the success probability and meta distribution of achievable rate are studied for the proposed scheme, respectively. We further provide the optimization of caching parameters and the condition for superior performance over the MPC-based scheme. Analytical and numerical results show that the network performance can be improved for larger sub-6G BS cooperation size and the array size at mmWave BSs, while the mmWave BS density has two adverse effect for low-to-medium and high rate threshold. For the proposed scheme, the content diversity in combination with JT gain benefits the success probability. And its performance advantage increases for larger local storage and/or higher association probability with mmWave BSs.

Federated learning (FL) is an emerging paradigm for distributed machine learning that uses the data and the computational power of user devices while maintaining user privacy (e.g., position and motion track). It has been proved a promising way to help the learning-based millimeter wave (mmWave) system achieve efficient link configuration. However, FL systems have an inherent vulnerability to backdoor attacks during training, and this has not received attention in current FL-based beam selection research. The goal of a backdoor attacker is to implant a backdoor in the model such that at test time, the model will mispredict a certain family of inputs, and corrupt the performance of the trained model on specific sub-tasks. We study backdoor attacks in an FL-based beam selection system based on a deep neural network that utilizes user location information. Specifically, we propose a backdoor attack scheme that can be configured in the real world. The attacker’s trigger is an obstacle placed in certain locations. When the model encounters an input with these obstacles, the backdoor will be triggered, and the model will output the beam specified by the attacker. Through experiments, we show that the proposed attack can achieve a high attack success rate in a system without a defense mechanism. Moreover, we show that the traditional norm-clipping defense method cannot effectively defend against our attack. Furthermore, we propose a new backdoor attack defense method and verify the effectiveness of this scheme through experiments. In addition, we propose a backdoor detection method: the federated noise titration method, which can diagnose whether the model has a backdoor. Overall, our work explored backdoor attacks, defenses, and detection of the FL-based mmWave beam selection system.

Non-orthogonal multiple access (NOMA) exhibits superiority in spectrum efficiency which is particularly essential in the Internet of Things (IoT) system involving massive number of device connections. This paper addresses the achievable rate improvement for the downlink NOMA system, in the context of imperfect successive interference cancellation (SIC), by means of the improper Gaussian signaling (IGS) technique. We investigate a basic scenario where the strong user transmits the conventional proper data, while the weak user adopts an improper signaling scheme. The users’ data rates are first formulated in terms of the impropriety degree of the IGS, under residual interference introduced by the imperfect SIC. In this way, analytical expressions for the best improper transmission can be characterized by jointly optimizing the user’s power and the impropriety degree, where their sufficient and necessary conditions are provided. When the strong user transmits with its maximum power, the IGS scheme always increases the achievable rate of the strong user while the weak user may also benefit. When the weak user transmits with its maximum power, such a scheme enables us optimize the achievable rate of the strong user under various levels of channel-to-noise ratios (CNR) and imperfect SIC. Finally, when both the users are imposed by quality of service (QoS) constraints, a Q-learning based solution is proposed to maximize their sum rate. Simulations on the downlink NOMA system support the analysis.

This paper considers an adversarial scenario between a legitimate eavesdropper and a suspicious communication pair. All three nodes are equipped with multiple antennas. The eavesdropper, which operates in a full-duplex model, aims to wiretap the dubious communication pair via proactive jamming. On the other hand, the suspicious transmitter, which can send artificial noise (AN) to disturb the wiretap channel, aims to guarantee secrecy. More specifically, the eavesdropper adjusts jamming power to enhance the wiretap rate, while the suspicious transmitter jointly adapts the transmit power and noise power against the eavesdropping. Considering the partial observation and complicated interactions between the eavesdropper and the suspicious pair in unknown system dynamics, we model the problem as an imperfect-information stochastic game. To approach the Nash equilibrium solution of the eavesdropping game, we develop a multi-agent reinforcement learning (MARL) algorithm, termed neural fictitious self-play with soft actor-critic (NFSP-SAC), by combining the fictitious self-play (FSP) with a deep reinforcement learning algorithm, SAC. The introduction of SAC enables FSP to handle the problems with continuous and high dimension observation and action space. The simulation results demonstrate that the power allocation policies learned by our method empirically converge to a Nash equilibrium, while the compared reinforcement learning algorithms suffer from severe fluctuations during the learning process.

In this paper, we investigate the navigation for unmanned aerial vehicle (UAV)s in the secure communication system, where we design the UAV's navigation/trajectory to ensure the Quality of Service (QoS) with the Base Station (BS) in the existence of multiple unknown-location dynamical eavesdroppers and jammers. To this end, we formulate a UAV trajectory optimization problem to minimize its mission completion time with QoS and security constraints. The imperfect information, dynamic communication environment, and non-convexity make the problem intractable. For these reasons, we propose a novel solution approach, namely Model-Assisted Reinforcement Learning (MARL) algorithm, where the communication system model is embedded into Deep Reinforcement Learning (DRL) framework to ensure secure communication and shorten the learning process. Numerical results show that our proposed methodology can safeguard security and find the shortest way to finish the mission.

This paper focuses on the outage performance of a downlink integrated satellite-terrestrial relay network (ISTRN), which includes a satellite (S) transmitting messages to a user (D) with the help of K relays ({Rk, k =1,⋯,K}) using a threshold-based decode-and-forward (DF) transmission protocol. In addition, we consider the case of relay selection based on out-dated channel state information (CSI) to better reflect the actual scenario. The shadowed-Rician (SR) fading and Nakagami-m fading are considered for the channel model of the S-Rklinks and Rk-D links, respectively. In order to reveal the impact of the parameters on the performance of the considered network, the outage probability is adopted as a performance criterion and the corresponding exact closed-form expressions are derived. Further, in order to investigate the influence of system parameters more intuitively, asymptotic outage probabilities are considered for the two cases: 1) high average SNR for S-Rklink and Rk-D link; 2) high average SNR for Rk-D link. The asymptotic analysis results exactly reveal the influence of the relevant system parameters on the decoding gain and the diversity gain. Finally, simulation and numerical results verify the correctness of the analysis.

Ultra-Dense Network (UDN) has become a key technology in 5G communication systems. By deploying low power micro base stations (BSs) densely and flexibly to reduce the distance between access nodes and user equipments (UEs), the spectrum efficiency and energy efficiency of the network can be improved effectively. But at the same time, it also poses new challenges for power control and user association. In this paper, the joint optimization problem of user association and power control of the downlink in a UDN scenario is considered. To make full use of channel information, we build a graph model with UEs as nodes and leverage the Spectral Clustering algorithm for user association. Then we build a graph model with BSs as nodes for the UDN scenario and train an unsupervised graph neural network to achieve power allocation. The analysis of the simulation results verifies the convergence of the proposed scheme which is effective in achieving user association and power control in UDN.

Abstract The dominant video captioning methods employ the attentional encoder–decoder architecture, where the decoder is an autoregressive structure that generates sentences from left‐to‐right. However, these methods generally suffer from the exposure bias issue and neglect the guidance of future output contexts obtained from the right‐to‐left decoding. Here, the authors propose a new symmetric bidirectional decoder for video captioning. The authors first integrate the self‐attentive multi‐head attention and bidirectional gated recurrent unit for capturing the long‐term semantic dependencies in videos. The authors then apply one single decoder to generate accurate descriptions from left‐to‐right and right‐to‐left simultaneously. The decoder in each decoding direction performs two cross‐attentive multi‐head attention modules to consider both the past hidden states from the same decoding direction and the future hidden states from the reverse decoding direction at each time step. A symmetric semantic‐guided gated attention module is specially devised to adaptively suppress the irrelevant or misleading contents in the past or future output contexts and retain the useful ones for avoiding under‐description. Experimental evaluations on two widely applied benchmark datasets: Microsoft research video to text and Microsoft video description corpus, demonstrate that the authors' proposed method obtains substantially state‐of‐the‐art performance, which validates the superiority of the bidirectional decoder.

Bistatic backscatter communication is emerged as a promising technique to significantly enlarge the lifetime of Internet of Things (IoT) network due to its inherently low-power passive component. However, the effective communication range is limited to only several meters. This article studies the tag circuit shunt network, and propose three modes, namely series mode, parallel mode, and mixed mode, to adjust circuit load impedance of the tag to extend the communication range as well as address the integrated circuit (IC) power supply problem. Specifically, we formulate the bit error rate (BER) minimization problems for the three modes by changing the reflection coefficients, subject to power supply constraint. The resulting problems are shown to be nonconvex fractional optimization problems, which are hard to be solved optimally in general. We first obtain a globally optimal solution to the series mode problem by exploiting the hidden monotonic structure based on monotonic optimization theory. Subsequently, we propose a low-complexity iterative suboptimal algorithm for the three modes based on the successive convex approximation (SCA) techniques. Numerical results show that when the direct link is available, the mixed mode outperforms the parallel mode and series mode, and can adaptively adjust the reflection coefficient to satisfy the requirement of IC power supply. In contrast, when the direct link is unavailable, the series mode is the best choice in terms of IC power supply. In addition, traditional on-off keying modulation is shown to be suitable for a low IC power supply, whereas a shunt network is necessary for high of power supply. Furthermore, the performance of SCA-based method closely approaches the optimal solution while with much lower complexity.

This article investigates intelligent reflecting surface (IRS)-aided multicell wireless networks, where an IRS is deployed to assist the joint processing coordinated multipoint (JP-CoMP) transmission from multiple base stations (BSs) to multiple cell-edge users. By taking into account the fairness among cell-edge users, we aim at maximizing the minimum achievable rate of cell-edge users by jointly optimizing the transmit beamforming at the BSs and the phase shifts at the IRS. As a compromise approach, we transform the non-convex max-min problem into an equivalent form based on the mean-square error method, which facilities the design of an efficient suboptimal iterative algorithm. In addition, we investigate two scenarios, namely the single-user system and the multiuser system. For the former scenario, the optimal transmit beamforming is obtained based on the dual subgradient method, while the phase shift matrix is optimized based on the Majorization-Minimization method. For the latter scenario, the transmit beamforming matrix and phase shift matrix are obtained by the second-order cone programming and semidefinite relaxation techniques, respectively. Numerical results demonstrate the significant performance improvement achieved by deploying an IRS. Furthermore, the proposed JP-CoMP design significantly outperforms the conventional coordinated scheduling/coordinated beamforming coordinated multipoint (CS/CB-CoMP) design in terms of max-min rate.

This paper investigates a symbiotic unmanned aerial vehicle (UAV)-assisted intelligent reflecting surface (IRS) radio system, where the UAV is leveraged to help the IRS reflect its own signals to the base station, and meanwhile enhance the UAV transmission by passive beamforming at the IRS. First, we consider the weighted sum bit error rate (BER) minimization problem among all IRSs by jointly optimizing the UAV trajectory, IRS phase shift matrix, and IRS scheduling, subject to the minimum primary rate requirements. To tackle this complicated problem, a relaxation-based algorithm is proposed. We prove that the converged relaxation scheduling variables are binary, which means that no reconstruct strategy is needed, and thus the UAV rate constraints are automatically satisfied. Second, we consider the fairness BER optimization problem. We find that the relaxation-based method cannot solve this fairness BER problem since the minimum primary rate requirements may not be satisfied by the binary reconstruction operation. To address this issue, we first transform the binary constraints into a series of equivalent equality constraints. Then, a penalty-based algorithm is proposed to obtain a suboptimal solution. Numerical results are provided to evaluate the performance of the proposed designs under different setups, as compared with benchmarks.

Adverse impacts of in-phase and quadrature-phase (I/Q) imbalance in both the transmitter (Tx) and receiver (Rx) are quantified for the generalized frequency division multiplexing (GFDM) based transmission over frequency selective fading channels. To this end, we first equip the standard signal-to-interference-plus-noise (SINR) performance evaluation with the ability to consider second-order noncircular (improper) signals, and thus precisely evaluate performance deterioration caused by I/Q distortions over the in-phase (I) and quadrature-phase (Q) channels of a transmission system. Next, we propose a novel means to evaluate the individual SINR contributions from both the channels of GFDM, and hence, provide more meaningful insights into the underlying wireless transmission in the presence of complex non-circularity. This is accompanied by an account of complete augmented second-order statistics of I/Q imbalanced GFDM waveforms which caters for various sources of complex improperness. Simulations in the GFDM system setting support our analysis.

Mobile edge computing (MEC) has received broad attention as an effective network architecture and a key enabler of the wireless virtual reality (VR) video service which is expected to take a huge share of communication traffic. In this work, we investigate the scenario of multi-tiles-based wireless VR video service with the aid of MEC network, where the primary objective is to minimize the system energy consumption and the latency as well as to arrive at a tradeoff between these two metrics. To this end, we first cast the time-varying view popularity as a model-free Markov chain and use a long short-term memory autoencoder network to predict its dynamics. Then, a mixed strategy, which jointly considers the dynamic caching replacement and the deterministic offloading, is designed to fully utilize the caching and computing resource in the system. The underlying multiobjective optimization problem is reformulated as a partially observable Markov decision process and solved by using a deep deterministic policy gradient algorithm. The effectiveness of the proposed scheme is confirmed by numerical simulations.

This paper investigates unmanned aerial vehicle (UAV)-aided backscatter communication (BackCom) networks, where the UAV is leveraged to help the backscatter device (BD) forward signals to the receiver. Based on the presence or absence of a direct link between BD and receiver, two protocols, namely transmit-backscatter (TB) protocol and transmit-backscatter-relay (TBR) protocol, are proposed to utilize the UAV to assist the BD. In particular, we formulate the system throughput maximization problems for the two protocols by jointly optimizing the time allocation, reflection coefficient and UAV trajectory. Different static/dynamic circuit power consumption models for the two protocols are analyzed. The resulting optimization problems are shown to be non-convex, which are challenging to solve. We first consider the dynamic circuit power consumption model, and decompose the original problems into three sub-problems, namely time allocation optimization with fixed UAV trajectory and reflection coefficient, reflection coefficient optimization with fixed UAV trajectory and time allocation, and UAV trajectory optimization with fixed reflection coefficient and time allocation. Then, an efficient iterative algorithm is proposed for both protocols by leveraging the block coordinate descent method and successive convex approximation (SCA) techniques. In addition, for the static circuit power consumption model, we obtain the optimal time allocation with a given reflection coefficient and UAV trajectory and the optimal reflection coefficient with low computational complexity by using the Lagrangian dual method. Simulation results show that the proposed protocols are able to achieve significant throughput gains over the compared benchmarks.

In this paper, we investigate the unmanned aerial vehicle (UAV)-aided simultaneous uplink and downlink transmission networks, where one UAV acting as a disseminator is connected to multiple access points (AP), and the other UAV acting as a base station (BS) collects data from numerous sensor nodes (SNs). The goal of this paper is to maximize the system throughput by jointly optimizing the 3D UAV trajectory, communication scheduling, and UAV-AP/SN transmit power. We first consider a special case where the UAV-BS and UAV-AP trajectories are pre-determined. Although the resulting problem is an integer and non-convex optimization problem, a globally optimal solution is obtained by applying the polyblock outer approximation (POA) method based on the problem's hidden monotonic structure. Subsequently, for the general case considering the 3D UAV trajectory optimization, an efficient iterative algorithm is proposed to alternately optimize the divided sub-problems based on the successive convex approximation (SCA) technique. Numerical results demonstrate that the proposed design is able to achieve significant system throughput gain over the benchmarks. In addition, the SCA-based method can achieve nearly the same performance as the POA-based method with much lower computational complexity.

Proposed by Maddah-Ali and Niesen, a coded caching scheme has been verified to alleviate the load of networks efficiently. Recently, a new technique called placement delivery array (PDA) was proposed to characterize the coded caching scheme. In this paper, we consider a caching system in the scope of ultra dense networks (UDNs). Each base station (BS) has a finite cache and stores some contents. We propose an efficient coded content caching scheme called double coded caching to make the transmission robust to in-and-out wireless network quality. Then the dynamic caching and multicast scheduling are considered to jointly minimize the average delay and power of the content-centric wireless networks. This stochastic optimization problem can be formulated as a Markov decision process (MDP) with unknown transition probabilities and large state space. We propose a deep reinforcement learning approach to deal with the decision problem. Our algorithm uses a variational auto-encoder (VAE) neural network to approximate the state sufficiently, and uses a weighted double Q-learning scheme to reduce variance and overestimation of the Q function. Numerical results demonstrate that the proposed double coded caching scheme increases the probability of the successful transmission, and the caching and scheduling policy can effectively reduce the delay and the power consumption.

The use of the millimeter wave (mmwave) spectrum for next generation mobile communication systems has gained significant attention recently. Large antenna arrays along with beamforming techniques are required to combat the large path-loss at mmwave frequencies. However, the existing beam designs often cause a large peak to average power ratio, and thus require power-inefficient power amplifiers (PAs). In this paper, we propose power-efficient beam design methods that facilitate the use of power-efficient PAs. Specifically, we design digital and hybrid analog-digital mmwave beams that possess a per-antenna constant envelope (PACE) and thus are highly power-efficient. Meanwhile, we also minimize the ripples in the mainlobe and sidelobe of the beams and consider both infinite and finite resolution phase shifters. To this end, we first propose an efficient feasible point search method to provide a feasible solution for the considered difficult beam design problem. Then, a novel hybrid analog-digital mapping algorithm is developed to map a designed digital beam to a hybrid analog-digital beam. To achieve better performance, we propose an improved hybrid analog-digital beam design method employing further optimization based on the feasible point. The proposed method is applicable to both infinite-resolution and finite-resolution phase shifters. Comprehensive simulation results are provided to demonstrate the effectiveness and superiority of the proposed beam designs.

Direct-conversion receivers (DCRs) have been adopted in wideband communication systems owing to their simple structure and low cost, however, their operation is affected by amplitude and phase mismatches between their analog inphase (I) and quadrature (Q) branches, as well as the discrepancy of low-pass filter coefficients between these two channels. In this paper, a blind adaptive frequency-dependent I/Q imbalance compensator is proposed, which exploits the complex properness (second-order circularity) of ideal constellation mappings to provide more enhanced insight into the problem setting within the proposed compensator. This serves as a basis for a novel full second-order performance assessment framework, which is established through a joint consideration of the weight error covariance and complementary covariance in both the transient and steady-state stages. This conjoint analysis is further shown to facilitate accurate quantification of the overall mirror-frequency interference attenuation capability of the proposed compensator. Simulation results in an orthogonal frequency division multiplexing (OFDM) transmission system demonstrate the excellent performance of the proposed compensator.

This paper investigates unmanned aerial vehicle (UAV)- aided backscatter communication (BackCom) networks, where the UAV is leveraged to help the backscatter device (BD) forward signals to the receiver using transmit- backscatter (TB) protocol. Our goal is to maximize the system ergodic capacity by jointly optimizing the time allocation, reflection coefficient and UAV trajectory. The resulting optimization problem is shown to be non-convex, which is challenging to solve. We consider two different circuit power consumption models, namely dynamic and static models. We first consider the dynamic model, and decompose the original problem into three sub- problems, and an iterative algorithm is proposed to optimize three subproblems alternately by leveraging the block coordinate descent method and successive convex approximation (SCA) techniques. In addition, for the static model, we obtain the optimal time allocation with a given reflection coefficient and UAV trajectory and the optimal reflection coefficient with low computational complexity using the Lagrangian dual method. Simulation results show that the proposed scheme is able to achieve significant throughput gains over the compared benchmarks.

Coded caching is a promising approache to support low latency transmission over broadcast wireless networks. The process of selecting the nodes that forward coded messages can be considered as a set cover problem. However, existing research efforts don't focuse on solving the set cover problem. This paper investigates the problem of the cover problem for coded caching in wireless networks. First, we propose a novel coded caching method using deep neural networks. Then, we establish a mathematical model for cover problem of the coded caching system. Then, we propose a deep learning approach to solve it. Different from previous works, our proposed deep neural architecture uses sequence-to- sequence model to learn the solutions. Finally, numerical results are given to demonstrate the proposed coded caching method have lower load than traditional coded caching method, and that proposed method for solving the cover problem can effectively implement coded caching with lower computational complexity.

Complex least mean square (CLMS) based adaptive computation of discrete orthogonal transforms has been extensively investigated in the literature. However, all of these results provide only a means for the calculation of either forward orthogonal transforms or their inverse orthogonal transforms, separately. In this work, a way to simultaneously calculate the discrete Fourier transform (DFT) and the inverse DFT (IDFT) is established via the widely linear (WL) signal processing framework. We show that by appropriately selecting the input vector and adaptation speed of the widely linear complex least mean square (WL-CLMS), the resulting spectrum analyzer is capable of simultaneously performing DFT and IDFT of the signal to be Fourier analyzed in both the block-based and online manners.

This paper investigates the optimal design of multiple panel arrays (MPAs) for line-of-sight (LoS) multiple-input multiple-output (MIMO) communication systems. We use the spherical wave channel model and give a geometric model to model the LoS channel, which allows the receive antenna arrays to have azimuth rotation, elevation angle rotation, up-down offset and left-right offset distance. Based on the geometric model, we derive the optimal antenna design conditions for achieving the maximum channel capacity and spatial multiplexing gain according to the effective degrees of freedom. The results show that the proposed antenna design can achieve high channel space freedom when the receive antennas have angle rotation and offset, and is suitable for the case where the receive antennas have a large left-right offset distance.

The energy reduction for wireless systems becomes more and more important due to its impact on the operation cost and global carbon footprint. In this paper, we design two kinds of energy-efficient association schemes under an open loop power control for uplink heterogeneous cellular networks (HCNs), which are formulated as problems with maximizing sum energy efficiency (EE) and EE utility respectively. In them, the second scheme integrates with the load balancing level and user fairness. Since the first problem is in a simple form, we can easily solve it without any iteration. As for the second problem, we first introduce a dual variable to decouple the constraint and then develop a distributed algorithm using dual decomposition. In addition, we also give some convergence proofs for the proposed algorithms. In the simulation, we investigate the influences of different parameters on the association performance of designed association schemes.

Different from the conventional receive scheme for millimetre wave (mmWave) communication, this study proposes a multi‐beam receive scheme to improve the quality of the received signal and enhance the robustness of the system. The authors proposal is firstly formulated as an optimisation problem, where each signal received by different beams is combined through phase compensation to harvest more transmission energy. Then the original problem is divided into a series of sub‐problems and an analytical solution is further obtained for each sub‐problem. Furthermore, considering the spatial sparsity of the mmWave channel, they propose further a low‐computational complexity algorithm by choosing a few candidate codewords with non‐negligible receive signal power. Numerical results show that their proposal achieves remarkable performance improvements even with a small size codebook and is more robust for different scenarios, especially for a non‐line of sight scenario. Compared with doubling receive antennas to obtain diversity gain, their proposal obtains larger signal‐to‐noise ratio gain while using fewer hardware resources.

This study investigates a novel unmanned aerial vehicle (UAV)‐based wireless sensor network, where the UAV acts as a flying base station to serve multiple wireless sensor nodes (SNs). The authors goal is to maximise the system energy efficiency of the UAV while satisfying the fairness among SNs by jointly optimising the UAV trajectory and UAV time allocation. The formulated problem is shown to be a non‐convex fractional optimisation problem, which is hard to tackle. To this end, they decompose the original problem into two sub‐problems, and the block coordinate descent method and successive convex optimisation technique are employed to solve these two sub‐problems iteratively. Specifically, in the first sub‐problem, the optimal UAV time allocation is obtained by maximising the minimum achievable rate of SNs with given UAV trajectory constraints. In the second sub‐problem, the UAV trajectory is achieved by minimising the energy consumption of the UAV with the given UAV time allocation. Subsequently, an iterative algorithm is proposed to optimise the time allocation and UAV trajectory alternately. Furthermore, the convergence and complexity of their proposed algorithm are provided. Numerical results show that the proposed scheme outperforms the existing benchmark strategies in terms of energy efficiency.

Caching popular contents in the storage of base stations (BSs) has emerged as a promising solution for reducing the transmission latency and providing extra‐high throughput. This study tackles the optimal trade‐off problem between the sum of effective rates and backhaul saving through joint service improvement and content placement in cache‐enabled heterogeneous cellular networks while guaranteeing the quality‐of‐service requirements of all user terminals (UTs) and backhaul traffic constraints of all BSs. However, there exists an intractable issue of mixing the integer nature into the feasible region in the nonlinear optimisation problem. To this end, the authors decompose the optimisation problem into three subproblems by alternately fixing two of three classes of variables (i.e. UT association, power control, and content placement). Aiming at these subproblems, they, respectively, convert them into the tractable forms and propose the corresponding algorithms. By combining them, they propose a three‐tier iterative algorithm for jointly optimising UT association and cache placement. Finally, numerical results have verified the effectiveness of proposed schemes.

This letter investigates the robust beamforming design for multigroup multicast in a backhaul-limited cloud radio access network. Users requesting the same content form a multicast group, served by remote radio heads (RRHs) cooperatively. Each RRH acquires the requested contents from baseband unit via backhaul links. We first formulate the robust beamforming design as maximizing the sum of the minimum rate of users in each multicast group under the transmission power and backhaul constraints. Due to the introduction of the channel estimation error and inter-user interference, the considered problem becomes more complex and difficult to address directly. To overcome these difficulties, convex approximation methods are adopted to transform the original problem into convex one. Then, an effective optimization algorithm is developed to address the resulting problem. Numerical results demonstrate the effectiveness of the proposed robust beamforming design of multigroup multicast transmission.

Generalized frequency division multiplexing (GFDM) has become one of the most important waveform candidates for beyond 5G (B5G) communications. However, physical distortions, such as in-phase and quadrature (I/Q) imbalance caused by the imperfections of radio frequency (RF) components within direct-conversion transceivers (DCTs), may cause severe performance degradation in GFDM-based wireless systems. To this end, we first conduct a rigorous sum rate analysis to quantify the impact of I/Q imbalance in both the transmitter and the receiver on the GFDM wireless transmission. An efficient I/Q imbalance compensation scheme is next proposed based on pilots; this is achieved through a nonlinear least squares analysis of the joint channel and I/Q imbalance estimation, and a simple symbol detection procedure. For rigor, the Cramer-Rao lower bounds for both the I/Q imbalance parameters and the channel coefficients are also derived. The simulation results illustrate that the mean square error performance of the proposed estimator closely approaches the corresponding CRLB over static frequency selective channels, thus significantly reducing the sensitivity of GFDM DCTs to physical I/Q impairments.

This paper investigates the problem of proactive caching for multi-view 3D videos in the fifth generation (5G) networks. We establish a mathematical model for this problem, and point out that it is difficult to solve the problem with traditional dynamic programming, then we propose a deep reinforcement learning approach to solve it. First, we model the proactive caching system for multi-view 3D videos as a Markov decision process jointing views selection and local memory allocation. Then, we present an actor-critic, model-free algorithm based on the deep deterministic policy gradient to find effective proactive caching policy. Since the action space is affected by the system state, we embed dynamic k-Nearest Neighbor algorithm into actor-critic algorithm to implement the deep reinforcement learning algorithm working in an action space of variable size. Finally, the numerical results are given to demonstrate that the proposed solution can effectively maintain high-quality user experience for high-mobility 5G users moving among small cells. We also investigate the impact of configuration of critical parameters on the performance of the algorithm.

Millimeter wave (mmwave) communication operating in the band of 30-300 GHz is promising to provide Gbps data rates owing to its abundant spectrum resource, and has attracted increasing attention. Cooperative transmission, by converting undesired interferences into useful signals, is able to further improve performance of mmwave systems. In this paper, we propose a novel cooperative transmission scheme for mmwave communication networks, where each mobile user is cooperatively served by multiple access points (APs) that use hybrid precoders. Our goal is to maximize the system energy efficiency, which leverages on a joint design of the hybrid precoders of all APs. The formulated problem is a difficult nonlinear fractional programming subject to unit modulus constraints. We propose an efficient algorithm by incorporating penalty decomposition and block coordinate descent methods. Numerical results are provided to confirm the effectiveness of the proposed algorithm and reveal some important insights.

In this paper, we study the beam-based training design for the single-user (SU) hybrid massive antenna system based on outage probability performance. First, an interleaved training design is proposed where the feedback is concatenated with the training procedure to monitor the training status and to have the training length adaptive to the channel realization. Then, the average training length and outage probability are derived for the proposed interleaved training and SU transmission. Analytical results and simulations show that the proposed interleaved scheme achieves the same outage performance as the traditional full-training scheme but with significant saving in the training overhead.

Zero-forcing (ZF) precoding plays an important role for massive MIMO downlink due to its near optimal performance in high signal-to- noise (SNR) region. However, the high computation cost of the involved matrix inversion hinders its application in practical large-scale systems. In this paper, we adopt the first order Neumann series (NS) expansion for a low-complexity approximation of matrix inversion. Compared to existing NS based schemes, we introduce a relaxation parameter jointly with one user's channel interference to others into the precondition matrix and propose the identity-plus- column NS (ICNS) method. By further exploiting the multi-user diversity gain via choosing the user with largest interference to others, the ordered ICNS method is also proposed. Moreover, the closed-form sum-rate approximation of the ICNS method is derived. Simulations verify our analytical results and the advantage of the proposed schemes over other existing low-complexity ZF precodings for massive MIMO systems with correlated channels and not-so-small loading factor.

In this paper, we employ the unmanned aerial vehicle (UAV) as a flying base station (BS) to offload the data computing tasks from mobile terminal (MT) for saving mobile energy consumption. Our goal is to minimize consumption of the computational tasks at MT by jointly designing the resource partitioning scheme and bit allocation strategy. Specifically, the portion of total bits for local computation at MT is optimized, and the other portion of bits is computed by jointly optimizing the number of bits transmitted in the uplink, the number of bits computed locally at UAV and the number of bits transmitted in the downlink. The formulated problem has been shown in a convex form, which has optimal solutions. Instead of solving original problem using standard convex optimization techniques, we propose a resource partitioning scheme and bit allocation strategy based on dual decomposition, which has been shown in a low computational complexity. Furthermore, the numerical results are provided to demonstrate the superiority of our proposed scheme over the compared benchmarks.

Traveling by bicycle has become a rising trend recently for its convenience and flexibility, which calls for considerate bicycle trip planning schemes. While research for traditional trip planning has focused on quantized quality of point-of-interest (POI) or correlations among POIs, problems appear for distinct influential factors in bicycle trips and being unable to plan in a foreseeable stage with satisfying various demands of cyclists. In this paper, to alleviate the deficiencies of conventional approaches that merely concentrating on temporary interests and fully depending on greedy algorithm, the active Q-learning algorithm derived from reinforcement learning (RL) is adopted for Q-value iteration for planning overall optimal bicycle trips. To further meet personal improvised demands such as containing some specific places in the trip, Tailored Trip is provided and a dynamic and flexible place inserting algorithm is proposed to automatically tweak the trip and keep the planning optimum status. Experiments have been conducted to intuitively evaluate the performance of our schemes on two real-world datasets. The planning results clearly illustrate that the optimal node choosing policy is continuously reinforced in our schemes and the result for Tailored Trip highlights the guarantee of overall superiority after trip tweaking.

With an unprecedented amount of sensitive private data generated by mobile user equipment (UE), securing the emerging ultra-dense networks (UDNs) becomes critical. Although involving more access points (APs) is potentially capable of enhancing both the UE's throughput and security, the energy consumption becomes significant. In this paper, we investigate secure UDNs in the context of the user-centric clustering of UDNs from a secrecy energy efficiency perspective, while satisfying both the throughput and the security of each UE. We first propose a secure user-centric clustering architecture by introducing both a dedicated jamming strategy and an embedded jamming strategy, both of which degrade the overheard signals of the eavesdroppers and guarantee secure transmission relying on the different APs' involvement status. We formulate the secure user-centric clustering design for both known and unknown eavesdropper channel state information (CSI), whilst maximizing the secrecy energy efficiency with the aid of various secure transmission schemes. Since the problem formulated is a non-convex mixed integer non-linear programming problem, we develop a set of heuristic greedy secure user-centric clustering algorithms for diverse operating scenarios. Finally, our numerical results reveal the quantitative benefits of the proposed secure user-centric clustering architectures as a function of the network densities (i.e., AP, UE, and eavesdropper) and of both the throughput and the security constraints on the secrecy energy efficiency trade-off in different scenarios.

Zero-forcing (ZF) precoding plays an important role for massive MIMO downlink due to its near optimal performance. However, the high computation cost of the involved matrix inversion hinders its application. In this paper, we adopt the first order Neumann series (NS) for a low-complexity approximation. By introducing a relaxation parameter jointly with the channel non-orthogonality between one selected user and others into the precondition matrix, we propose the identity-plus-column NS (ICNS) method. By further choosing the user with the least channel orthogonality with others, the ordered ICNS method is also proposed. Moreover, the sum-rate approximations of the proposed ICNS method and the competitive existing identity matrix based NS (INS) method are derived in closed-form, based on which the performance loss of ICNS due to inversion approximation compared with ideal ZF and its performance gain over INS are explicitly analyzed for three typical massive MIMO scenarios. Finally, simulations verify our analytical results and also show that the proposed two designs achieve better performance-complexity tradeoff than ideal ZF and existing low-complexity ZF precodings for practical large antenna number, correlated channels, and not-so-small loading factor.

This paper investigates secure cooperative transmissions in a dual-hop MIMO relay system using a combined transmit antenna selection (TAS) and maximal-ratio combining (MRC) scheme over the Nakagami-m fading channels, where an adaptive decode-and-forward relaying protocol and an multi-antenna eavesdropper are considered. Due to the feedback delay, channel state information (CSI) for TAS might be outdated at both the source and the relay. To evaluate the secrecy performance of the TAS/MRC scheme and the impacts of outdated CSI, the closed-form expressions for the metrics of exact ergodic secrecy rate and exact secrecy outage probability are derived under both perfect and outdated CSI conditions in a channel feedback error model. In order to explicitly reveal the behaviors of the secrecy performance in high signal-to-noise ratio regime, asymptotic expressions for both the metrics are further derived. As validated by simulation results, analytically numerical results demonstrate that outdated the CSI always results in a loss in the secrecy performance, but the loss can be recovered by increasing the number of antennas at legitimate receivers. Furthermore, the outdated CSI yields a reduced secrecy diversity order, whereas only the perfect CSI leads to the full secrecy diversity order.

For millimeter wave (mm-wave) communication systems, a lens antenna array with single-carrier transmission and path delay compensation is a promising technique for realizing cost-effective large multiple-input multiple-output communications with limited number of radio frequency chains. In this paper, we study the multi-user mm-wave downlink lens antenna array system for the general frequency-selective channels. By leveraging the angle-dependent energy focusing property of the lens antenna array and the angular sparsity of mm-wave channels, we investigate the low-complexity single-carrier transmission scheme with path delay pre-compensation applied at the base station (BS). The resulting signal-to-interference-plus-noise ratio (SINR) is derived by taking into account both the residual inter-symbol interference and inter-user interference. Based on the derived SINR expression, we propose an effective joint antenna selection and beamforming scheme by utilizing the group sparse optimization to accommodate for the limited number of RF chains at the BS. Thus, the proposed scheme can obtain the approximate performance with the fully digital case and has a better performance than the conventional orthogonal frequency-division multiplexing mode for the frequency-selectivity channels. Numerical results are provided to verify the effectiveness of the proposed schemes.

Performance analysis is studied in this paper for the wireless transmissions in Internet of Things (IoT) system, where both the direct link and the multihop relaying caching wireless transmission from the source node to the destination node are taken into the consideration. The key feature is the Nakagami channels of the wireless channel from the source node to the destination node, which results in the difficulty of the theoretical analysis over the system performance. To tackle this difficulty, the probability distribution function (PDF) of the received signal‐to‐noise ratio (SNR) at the destination node is derived by exploiting the function and integral properties. Then, the outage probability and bit error rate (BER) of the whole wireless IoT system are derived in the analytical expression without any approximation. Numerical simulations demonstrate the accuracy of the derived theoretical analysis for this system.

This paper studies beam training design for a codebook- based beamforming millimeter wave (mmwave) system where multiple antenna arrays are employed and each array is capable of beamforming independently. To reduce the training overhead and the complexity of subsequent beam direction search, we propose a cooperative multi- subarray beam training method. Specifically, from the perspective of excluding noneffective beam direction combinations and thus reducing search space, method and criterion of beam superposition are proposed to construct a wide beam from multiple narrow beams corresponding to multiple subarrays. Then, a cooperative multisubarray beam training scheme is proposed based on the proposed criterion. Finally, simulation results show that the proposed scheme achieves a spectral efficiency close to that of the optimal exhaustive search scheme, while has greatly reduced training overhead and computational complexity.

This paper exploits the potential of large antenna arrays to develop a secure millimeter wave (mmwave) transmission scheme. To reduce the peak-to-average power ratio (PAPR), the idea of constant envelope precoding (CEP) is introduced to improve the power efficiency of power amplifiers. In the CEP scheme, only phase variation of each antenna is used to form the desired signal at the target receiver, while the sum power of noise-free signals received by all eavesdroppers is minimized for secure transmission. A nonconvex optimization problem is formulated with equality and unit modulus constraints. To tackle the nonconvex constraints, the augmented Lagrangian penalty method is employed to address the challenging problem. An efficient iterative algorithm is further proposed to tackle the problem of precoder design. Simulation results confirm the effectiveness and superiority of the proposed CEP secure transmission scheme.

Driver distraction behaviors are usually blind to autonomous vehicles (AVs), leading to probable late preparation for AVs to take emergency measures. Hence, this paper aims to build a bridge between AV control and driver behavior detection, to assist AVs to predict the potential risk and avoid abnormal drivers carefully like experienced drivers. Our main contributions of this paper consist: i) put forward a practicable system framework integrating driver distraction monitoring, vehicle-to-vehicle communication and AV velocity control; ii) provide a real-time driver distraction monitoring implementation building on convolutional neural network trained offline; iii) propose a method of longitude velocity control of AV considering the risk of driver distraction behavior based on model predictive control strategy. Simulation results validate the effectiveness of our work.

In this study, the authors address the downlink resource (subchannels and power) allocation problem for device‐to‐device communication with wireless power transfer technique in a cellular network to improve the energy efficiency (EE). The considered problem is formulated as maximising the weighted EE and is solved by leveraging a game‐theoretic learning approach. Specifically, they first prove that an exact potential game applies to the resource allocation problem and there exists the best Nash equilibrium (NE) which is the optimal solution of the optimisation problem. Then, aiming to this optimisation problem with imperfect information, a robust and distributed learning algorithm is proposed and is proved that it can converge to the best NE. Finally, numerical results verify the effectiveness of the proposed scheme.

In cloud radio access network, a baseband unit (BBU) performs the baseband processing for a cluster of low‐power low‐cost remote radio heads (RRHs) that are connected to the BBU through low‐latency fronthaul links. In this study, the authors study the optimisation of two energy‐efficient compression and precoding strategies which take transmit power constraint, fronthaul capacity constraint and user specific rate constraint into account. To overcome the non‐convexity nature of the original problem, they first transform the objective of the original problem into a parameterised subtractive form and obtain an approximate convex problem via the successive convex approximation. Then, an effective optimisation algorithm with provable convergence is designed to solve the effective problem. Numerical results reveal that the proposed scheme outperforms the conventional maximum sum rate and minimum total power consumption schemes in terms of the energy‐efficiency criterion. In particular, compression after precoding strategy outperforms compression before precoding strategy when both of their RRHs perform the same user scheduling, while the opposite conclusion can be drawn otherwise.

The computational complexity required in the channel estimation plays an important role in underwater acoustic communications (UAC) with orthogonal frequency duplex access (OFDM), especially when the channel is sparse. The authors develop an algorithm to carry out the orthogonal matching pursuit (OMP) for the sparse channel estimation based on the compressive sensing, where the goal is to obtain the minimum computational complexity. It is discovered that the inter‐carrier interference (ICI) mainly depends on the adjacent subcarriers since the ICI interferences become more and more marginable with the increase of the distance from the other subcarriers to the current desired subcarrier in the frequency domain, which can be utilised to reduce the complexity of the design over the sparse channel estimator. By exploiting this property, the authors propose that the diagonal band of the ICI channel matrix is employed in the calculation of the objective function to minimise the required computational complexity, which develops an adaptive algorithm that is theoretically proved to be a faster algorithm. Numerical simulations are demonstrated for the typical UAC system that the proposed algorithm achieves the remarkable gain of the computational complexity compared to the existing algorithm.

In massive multiple‐input multiple‐output (MIMO) high‐speed train (HST) wireless communication systems (WCS), due to the large‐dimension and rapidly time‐varying property, channel tracking rather than conventional channel estimation is more feasible. Due to the non‐linear channel variation, the channel is first decomposed into sub‐channels with different angle of departure. By exploiting the property of near line of sight (LoS) and location information, Kalman filtering is used to track the channel by predicting and modifying the channel gain of the LoS sub‐channel. To further improve the tracking performance, a location‐based sequentially optimal beam pattern design is proposed. Since placing pilot beams for many receive antennas with different locations in time or frequency division manner costs much system resource, the authors further propose a low‐complexity grouping algorithm based on location. Finally, two transmission designs based on the proposed channel tracking scheme and the location only, respectively, are introduced. Simulations validate the efficiency of the authors' proposed tracking scheme and the corresponding transmission design, which shows the importance of location information and channel tracking in massive MIMO HST‐WCS.

Non-orthogonal multiple access (NOMA) enables power-domain multiplexing via successive interference cancellation (SIC) and has been viewed as a promising technology for 5G communication. The full benefit of NOMA depends on resource allocation, including power allocation and channel assignment, for all users, which, however, leads to mixed integer programs. In the literature, the optimal power allocation has only been found in some special cases, while the joint optimization of power allocation and channel assignment generally requires exhaustive search. In this paper, we investigate resource allocation in downlink NOMA systems. As the main contribution, we analytically characterize the optimal power allocation with given channel assignment over multiple channels under different performance criteria. Specifically, we consider the maximin fairness, weighted sum rate maximization, sum rate maximization with quality of service (QoS) constraints, and energy efficiency maximization with weights or QoS constraints in NOMA systems. We also take explicitly into account the order constraints on the powers of the users on each channel, which are often ignored in the existing works, and show that they have a significant impact on SIC in NOMA systems. Then, we provide the optimal power allocation for the considered criteria in closed or semi-closed form. We also propose a low-complexity efficient method to jointly optimize channel assignment and power allocation in NOMA systems by incorporating the matching algorithm with the optimal power allocation. Simulation results show that the joint resource optimization using our optimal power allocation yields better performance than the existing schemes.

This letter studies the cooperative precoding design for a coexisting wireless energy transfer (WET) and cognitive radio (CR) system, where the WET system share the same spectrum with the CR system. Different from the traditional wireless networks, interference here is regarded as a useful rather than harmful resource. Specifically, we address the transmit covariance design to minimize the total transmit power at the energy transmitter and the secondary transmitter while satisfying secrecy rate, energy harvesting, and interference temperature constraints. We propose an iterative algorithm to tackle the formulated nonconvex optimization problem, and prove that it could converge to a Karush-Kuhn-Tucker point of the original problem. Simulation results are finally provided to illustrate the effectiveness of our proposed algorithm.

Owing to abundant spectrum resources, millimeter wave (mmwave) communication promises to provide Gbps data rates, which, however, may be restricted by large path-loss. Thus, antenna arrays are commonly used along with beam alignment (BA) as an important step to achieve the array gain. Efficient BA relies on the beam training codebook design. In this paper, we propose a new hierarchical codebook to achieve uniform BA performance with low overhead. To better elaborate on the design principle, a single-path channel model is considered first to frame the proposal. The codebook design is formulated as an optimization problem, where the ripple in the main/side lobes is constrained such that each training beam is close to the ideal one with a flat magnitude response and a narrow transition band. Then, we propose an efficient algorithm to find such a beam training codebook. Furthermore, we derive closed-form expressions of the BA misalignment probability or error rate of the proposed beam training codebook. Our results reveal that using the proposed codebook, the error rate of tree-search-based BA exponentially decreases with the SNR for a given channel, and linearly decreases in the log-log coordinate axis for a fading channel. We further propose a power allocation scheme used in different training stages to further improve the BA performance. Finally, the proposed framework is extended to the more complex case of multi-path channels. Numerical results confirm the effectiveness of the proposed training codebook and power allocation scheme as well as the accuracy of the performance analysis.

Statistical beamforming is an important technique for multi-user massive MIMO downlink, since it depends on the downlink channel covariance only. In this paper, we first derive an explicit analytical sum-rate expression for generic channel covariance-based beamforming scheme. Then, a low-complexity joint statistical beamforming and user scheduling algorithm via greedy search is proposed, where the beamforming is based on the signal-to-leakage-and-noise-ratio (SLNR) for closed-form design and tractable analysis, while the user scheduling is based on the derived sum-rate expression. Further, with the help of large-scale asymptotic simplifications and the introduction of the interference user number parameter, a simple analytical sum-rate expression of the joint algorithm is derived for channels with flat power beam spectrum. The expression explicitly exhibits the sum-rate behavior with respect to different network parameters and captures the effect of sum-rate-based user scheduling. Finally, simulation results are provided to verify our analytical results and to show the advantage of the proposed joint design compared with existing schemes.

Hybrid multiple input multiple output (MIMO) beamforming can be divided into shared and split MIMO beamforming architectures, according to different concatenations of radio frequency (RF) chains and antennas. This paper considers split MIMO beamforming for millimeter wave system, i.e., each antenna subarray is only connected with one RF chain. To obtain analog precoding matrix and combining matrix, an algorithm based on signal to leakage plus noise ratio (SLNR) is proposed to align the transmitter's and receiver's antenna subarrays in one- to-one way. The effectiveness of our proposed subarray alignment algorithm is validated by simulation, and the hybrid and purely digital beamforming are compared in terms of channel capacity. Numerical results show that for the number of transmit and receive antennas, the performance gap between purely digital and hybrid beamforming decreases by increasing the number of RF chains. Moreover, effective degree of freedom (EDOF) is introduced to analyze the channel characteristic.

When massive MIMO technology is combined with dense heterogeneous networks (HetNets), the user association and power allocation problems are fundamentally different although the energy- efficiency benefits can be intensified. This paper aims to investigate the energy efficient joint user association and power allocation problem in downlink massive MIMO empowered dense HetNets under proportional fairness criterion. The joint optimization problem is a non-convex mixed-integer nonlinear program (MINLP) which is NP-hard, and hence it is difficult to efficiently obtain exact solution. In order to obtain the highquality suboptimal solution, the joint optimization problem is first decomposed into two subproblems with alternating iterative method. Then a two-layer iterative suboptimal algorithm is proposed to solve the joint optimization problem with guaranteed convergence. The involved association subproblem adopts dual decomposition to achieve the optimal association index, whilst the power allocation subproblem allocates the transmit power of each BS with Newton's method. Numerical results verify the effectiveness of our proposed algorithm and show that our proposed algorithm outperforms conventional association schemes in the enhancement of energy efficiency performance. Furthermore, it can be seen that the energy efficiency performance is enhanced by increasing the number of antennas at macro base station (MBS).

To combat bursty errors caused by wireless channels, interleaving is usually employed to randomize these errors with an aim to make error correction codes more effective. Subsequently, the design of efficient interleaving strategies becomes an attractive topic. Our main contributions of this paper consist: i) put forward equivalent distance sum from the physical scenarios as the metric of an interleaving sequence, which can give an overall but meticulous characterization of interleaving; ii) combine unequal grouping strategy with group interleaving to exploit the potential of interleaving which mostly outperforms classical block interleaving; iii) develop a practical algorithm to generate the near-optimal interleaving sequence with arbitrary length based on underlying insights. Numerical results under IEEE 802.11aj (45 GHz) millimeter-wave system in single carrier mode validate the effectiveness of the algorithm.

This paper investigates the joint power control and subchannel allocation problem for device-to-device (D2D) and small cell uplink communications in a cellular network to improve the cellular throughput. For this considered throughput maximization problem, we propose to solve it leveraging a game-theoretic learning approach. However, there is an intractable issue for obtaining the optimal power allocation profile in the continuous space. To this end, we first deduce the optimal power expressions under any given subchannel allocations. Based on the optimal power profile, we then formulate the subchannel allocation problem into a game framework. Next, aiming to this optimization problem, a cloud-assisted learning algorithm with conditioned strategies is proposed to converge to an equilibrium point which maximizes the optimization objective. Finally, numerical results verify the effectiveness of the proposed scheme.

To fully exploit the spatial multiplexing gains and array gains of massive multiple-input-multiple-output (MIMO), the channel state information must be obtained accurately at the transmitter side (CSIT). However, conventional channel estimation solutions are not suitable for Frequency-Division Duplexing (FDD) multi-user massive MIMO systems, due to overwhelming pilot and feedback overhead. In this paper, We find that part of the user channels tend to exhibit an approximate beam-blocked sparsity. To exploit this property, we propose a novel blocked compressive channel estimation scheme based on user grouping to reduce the pilot and feedback overhead. More specifically, we adopt user grouping by making the users in one group have similar channel covariance, which makes the channels in one group exhibit beam block sparsity. Then users feed the compressed measurements back to BS and the BS performs the CSIT recovery. Using the beam block sparsity, an optimal block orthogonal matching pursuit algorithm (OBOMP) is developed which effectively recovers the channel parameters. Numerous simulation results demonstrate our proposed scheme outperforms conventional solutions.

Delayed channel state information (CSI) degrades the system performance and predictor can mitigate the effects of outdate CSI. In massive multiple input multiple output (MIMO) systems with large dimensional channel vectors, low‐complexity prediction can reduce operation time and process latency. This study adopts a low‐complexity channel predictor based on polynomial fitting for the massive MIMO system. Compared with the conventional Wiener predictor, it does not need statistical channel estimation and avoids matrix inversion. The authors derive the approximate signal‐to‐interference‐plus‐noise ratio (SINR) with predicted channel information and the approximate gaps of the average rate per user between using perfect CSI, the predicted CSI provided by Wiener predictor and polynomial fitting, respectively, in the uplink massive MIMO system. The authors also analyse the normalised mean square error of prediction. The performance is investigated in a more practical and general angle of departure spectrum model with a concentration direction and a spreading factor. Simulations validate that the SINR approximations are tight, and show that the polynomial fitting with a proper prediction order can achieve a satisfying performance, when the concentration direction and the spreading factor are small.

This paper studies joint beamforming and power allocation for multicell multiuser multi‐antenna systems with the objective of maximising the minimum signal‐to‐interference‐plus‐noise ratio (max–min SINR). The authors first consider developing an iterative algorithm to achieve the optimal performance by extending the uplink–downlink duality for finite‐scale wireless communication systems. The solution is then generalised to achieve the asymptotically optimal multicell beamforming with the aim to reduce the overhead of signalling exchange between coordinated base stations based on large dimension random matrix theory. Based on that, an efficient multicell beamforming algorithm is proposed to asymptotically achieve the max–min SINR. To further solve the complexity issue of large dimensional matrix inversion involved in the calculation of beamforming vectors, they propose a low‐complexity beamforming calculator based on truncated polynomial expansion approach. Numerical results validate the effectiveness of the authors’ proposed algorithms and show that they can achieve the optimal or asymptotically optimal performance in a massive multi‐input multi‐output system with low complexity and small backhaul overhead.

In this study, the authors propose an energy‐efficient user association scheme to maximise the overall energy efficiency for downlink heterogeneous cellular networks, and formulate it as a non‐linear and mixed‐integer optimisation problem. Such a problem includes user association problem and power control problem. Since the formulated problem is in a fractional and mixed‐integer form, it is challenging for designers to achieve the optimal solutions of this problem. To this end, they design an effective three‐layer iterative algorithm. In the first layer, the energy efficiency parameter is found via bisection method. In the second layer, association index and transmit power are optimised alternately. In the third layer, the user association problem is solved via dual decomposition method and the transmit power is updated by employing a power update function. In addition, they further give some convergence analyses for some parts (user association algorithm and power control algorithm) of the proposed algorithm, and also give some complexity analyses for the whole algorithm. Numerical results show that, compared with non‐energy‐efficient association, the energy‐efficient association has significant superiorities on load balancing level, system throughput and energy efficiency.

A hierarchy precoding approach is proposed in this study for multi‐cell multiuser systems with any number of base stations and that of users, which is suitable for any number of data streams. The key feature of this approach is aligning the inter‐user interferences within the same cell to the room spanned by the inter‐cell interferences, by which both the inter‐cell and inter‐user interferences are cancelled simultaneously. Then, the inter‐stream interference for each user can be easily tackled. It is found that the interference alignment‐based hierarchy precoder achieves to the full freedom of degree. With interference‐free transmissions achieved by the proposed precoder, the transmit power is optimised in an analytical expression by maximising the sum rate and minimising the sum weighted mean square error. Extensive simulations demonstrate the effectiveness of the proposed method.

Wireless networks face the challenge of increasing energy consumption while satisfying the unprecedented demand for higher data rates. Energy-efficient transmission has been regarded as a key technology for the next-generation wireless system. Meanwhile, to reduce the cost, in practice, a base station usually has less radio chains than the antennas, which makes antenna selection an appealing transmission strategy. This letter addresses the problem of joint optimization of energy-efficient beamforming and antenna selection for downlink multiuser systems. The nonconvexity arising from both the nonlinear fractional programming and the ℓ0-(quasi)norm presents the main difficulty in solving the joint optimization problem. Nevertheless, we develop an effective algorithm to address this problem. Numerical results are given to validate the effectiveness and the performance of the developed algorithm.

An adaptive overhearing protocol is proposed for the two-way multi-antenna-relay network composed of a base station (BS), relay, and two user equipments (UEs), where one UE is in the uplink (UL) transmission mode (UE-Tx) while the other is in the downlink (DL) reception mode (UE-Rx). Specifically, UE-Rx not only receives the DL signal transmitted by BS but also overhears the signal transmitted by UE-Tx, and exploits the overheard signal to improve the detection performance. The transmit adaptive weights of UE-Tx over the two times slots and the precoding matrix at the relay in the second time slot are jointly optimized via the proposed iterative algorithm in the sense of maximizing the minimum signal-to-interference-plus-noise-ratio. Numerical results show that the proposed joint design provides significant sum-rate gain over the existing overhearing scheme.

This paper studies the secure beamforming design for simultaneous wireless information and power transfer in a multiple-input single-output broadcast channel with confidential messages and external eavesdroppers, where each receiver adopts the power splitting (PS) scheme to decode information and harvest energy concurrently, and it is also seen as a potential eavesdropper for messages not intended for it. Our objective is to minimize the total transmit power while guaranteeing the individual secrecy rate and energy harvesting constraints at each receiver by jointly optimizing transmit beamforming vectors, artificial noise covariance, and receive PS ratios. Both scenarios of perfect and imperfect channel state information (CSI) at the transmitter are considered. For the perfect CSI case, we propose a two-stage optimization approach to solve the original non-convex problem global optimality, and also provide a low-complexity suboptimal solution based on the particle swarm optimization algorithm. Furthermore, we also extend the above result to the colluding eavesdroppers scenario. For the imperfect CSI case, we propose a worst-case-based robust formulation, where the CSI errors are norm-bounded. With the aid of S-Procedure, we derive the equivalent forms for constraints and then transform the non-convex robust design into a convex optimization problem. Simulation results are finally presented to demonstrate the performance of our proposed schemes.

In this paper, we propose a secure transmission scheme for simultaneous wireless information and power transfer (SWIPT) in a multiple-input single-output (MISO) broadcast channel with confidential messages, where each receiver utilizes the power splitting approach to decode information and harvest energy simultaneously, and it also acts as a potential eavesdropper for the independent message sent to the others. By jointly optimizing the transmit beamforming vectors, covariance of artificial noise, and receive power splitting (PS) ratios for all receivers, we aim to maximize the total harvested energy while guaranteeing the secrecy rate constraint at each receiver and the total transmit power constraint at the transmitter, which is a non-convex optimization and hard to solve. In this paper, we propose a two-stage optimization approach based iterative algorithm to tackle such a challenging problem. Moreover, we prove that the proposed algorithm can achieve convergence, and also analyze its computational complexity. Finally, simulation results are provided to demonstrate the performance of our proposed algorithm.

This paper considers a downlink massive MIMO frequency division duplexing (FDD) system. Due to the large number of antennas, the required length of training sequence for downlink training significantly increases in FDD mode, which leads to prohibitive overhead in real system. Thus, in this work we investigate how the length of training sequence affects the system performance. For this purpose, we derive an analytical expression of the ergodic achievable rate from a worst case viewpoint with the the training sequence length as a parameter in it. It is revealed from the analytical results that i.) the length of training sequence divided by the number of base station antennas approaches to zero yet the achievable rate can increase to infinity as long as the antenna number is sufficient large; ii.) there is a ceiling effect on the achievable rate if the antenna number grows large with any fixed training length. Furthermore, we propose a guideline for the selection of the training length. Numerical results validate the derivations and analysis.

To make full utilize the limited resources in heterogeneous cellular networks (HCNs), a proper offloading scheme is widely advocated. However, such scheme often lead to a bad result that the offloaded users achieves lower signal-to-interference-plus-noise-ratios (SINRs) than these users in macro-cells. To partially alleviate the SINR degradation, we consider an interference avoidance technique, i.e., a resource (frequency) partitioning strategy that turns off some fraction of such resource in a macrocell and saves it for low-power base stations (BSs). Naturally, an optimal offloading scheme should be closely coupled with the resource partitioning, and in turn an optimal partition decides the offloading performance. In this paper, we maximize a sum-utility with joint offloading and interference avoidance for HCNs. Considering that the formulated problem is in a nonlinear mixed-integer form and difficult to tackle, we introduce a dual decomposition method to develop an effective distributed algorithm. We reveal that load balancing, by itself, is insufficient, and additional interference avoidance is required for improving the system performance. Meanwhile, we show that the proposed scheme can provide a load balancing gain and an interference avoidance gain.

In this paper, a massive MIMO downlink frequency division duplexing (FDD) system over correlated Rayleigh fading channel is considered. It is well known that the length of training sequence not only affects the accuracy of channel estimation but also accounts for the rate loss resulting from training overhead. However, as the number of the base station antennas becomes large, the required length of training sequence cannot increase unlimitedly. Thus, in this work we derive the analytical expression of achievable rate and investigate the impacts of the training sequence length on system asymptotic performance. It is discovered from the analytical results in two-fold that (1) the length of training sequence normalized by the antenna number approaches to zero yet the system capacity is guaranteed to positive infinity as long as the antenna number is large enough; (2) the transmission capability saturates to a certain level if the antenna number grows to very large with any given training length. Simulation results verify the theoretical derivations and demonstrate the performance limit.

This paper investigates the resource allocation issue between downlink training stage and data transmission stage for the frequency division duplexing (FDD) massive multiple-input multiple-output system from the viewpoint of energy efficiency (EE). For a given total energy budget during a coherence period, how to jointly select the training duration, training power and data power is of great significance for the system EE. Thus, an optimization problem of energy-efficient resource allocation is put forward. Since the analytical expression of the involved average spectral efficiency (SE) is intractable, a closed-form approximation of the SE is deduced using deterministic equivalent. Based on the simplified expression, the original non-convex fractional optimization problem is transformed into an equivalent problem in subtractive form by the means of fraction programming, which includes an achievable solution. Then, an iterative algorithm is proposed. Numerical results validates the benefits of the proposed resource allocation scheme.

In this paper, we design a secure transmission scheme for multiple-input single-output (MISO) broadcast channel with simultaneous wireless information and power transfer (SWIPT), where a multi-antenna transmitter simultaneously transmit independent confidential messages to multiple potentially malicious receivers, in the presence of external eavesdroppers. Our objective is to minimize the total transmit power while guaranteeing the security communication and energy harvesting constraints by jointly optimizing the transmit beamforming vectors, covariance of artificial noise, and power splitting ratios, which is non-convex optimization and hard to tackle. We first solve this non-convex problem by using the technique of semi-definite relaxation (SDR), and then prove that the relaxation is tight and thus achieves the globally optimal solution of the original problem. Simulation results are finally presented to demonstrate the performance of our proposed scheme.

Two‐way relaying systems efficiently accomplish transmissions in both directions within dual‐hop, hence, two time slots can be saved compared with one‐way relaying. However, the conventional two‐way relaying protocol requires the assumption of symmetric traffic demands, that is, each transmitter node has to act as a receiver in latter slot. This assumption restricts applying two‐way relay to general and practical scenarios. In this study, the authors release this unpractical constraint by assuming that the transmitter in slot 1 and receiver in slot 2 can be any nodes, which are not necessarily being the same. For this scenario, a novel transmission protocol exploiting the overhearing link to suppress the interference caused by asymmetric traffic, denoted as overhearing transmission, is proposed. With the overhearing transmission protocol, and in the light of green communications, the precoding matrices at the decode‐and‐forward multi‐antenna relay are optimised to improve energy efficiency in both uplink and downlink (DL) transmission directions, where the objective is to minimise the transmit power at the relay while guaranteeing a target transmission rate. The authors transform the original non‐convex problem to an equivalent form, which can be readily solved by typical semi‐definite relaxation approaches. An efficient algorithm is further proposed to implement the precoding design in practice. Simulation results show that the proposed algorithm is able to minimise the power consumption at the relay, with the minimum rate constraints of both the uplink and DL transmissions being satisfied.

In this study, the authors propose a user association scheme with quality of service support for load balancing in heterogeneous cellular networks (HCNs), which jointly considers user's achievable rate and load level of each BS instead of only utilising the former. To reveal how HCNs should self‐organise, the authors formulate it as a network‐wide weighted utility maximisation problem. Note that the formulated problem is a non‐linear mixed‐integer one, and its optimal solutions may be very difficult to be found when it is large‐scale. To solve the proposed problem, the authors design a low‐complexity distributed algorithm via dual decomposition. Numerical results show that, compared with the range expansion association (REA) and best power association (BPA), the strategy has a higher load balancing level (LBL) and a lower call blocking probability (CBP). Meanwhile, the proposed algorithm occupies a very fast convergence rate when its parameters are set properly.

In heterogeneous cellular networks (HCNs), the user association is a challenging topic since some different base stations coexist. Moreover, because of the asymmetric uplink and downlink in HCNs, a joint uplink and the downlink association algorithm should be designed to improve the system performance. For the practical implementation, the authors need to ensure that the algorithm is highly effective. Thus, they try to design an association strategy that jointly maximises downlink sum rate and minimises uplink sum power, and formulate it as a sum‐utility maximisation problem. To solve this problem, they design a centralised association algorithm via a gradient descent method, and develop a distributed association algorithm via dual decomposition. Simulation results show that, compared with the signal strength‐based association, range expansion association and the method proposed by Ye, their scheme has some significant advantages in the mass.

This paper investigates the problem of joint base station selection and resource allocation in an orthogonal frequency division multiple access (OFDMA) heterogeneous cellular network. The original throughput maximization problem is NP-hard and we propose solving it by using game theoretic stochastic learning approaches. To this end, we first transform the original problem into a tractable form, which has a weighted utility function. Then we prove that an exact potential game applies and it exists the best Nash equilibria which is a near optimal solution of the original problem when an efficient solution method of the weights is employed. To obtain the optimal solution, we redesign the utility function by leveraging a state space to formulate the original problem into an ordinal state based potential game, which is proved that it exists a recurrent state equilibrium point that maximizes system throughput. Furthermore, we propose two different variants of Max-logit learning algorithm based on these two games respectively: one is a simultaneous learning algorithm with less information exchange, which achieves the best Nash equilibria point of the exact potential game and the other is an efficient learning algorithm for the ordinal state based potential game, which can converge to the global optimization solution. Finally, numerical results are given to validate that theoretical findings.

In this paper, we investigate joint beamforming and power allocation in multicell multiple-input single-output (MISO) downlink networks. Our goal is to maximize the utility function defined as the ratio between the system weighted sum rate and the total power consumption subject to the users’ quality of service requirements and per-base-station (BS) power constraints. The considered problem is nonconvex and its objective is in a fractional form. To circumvent this problem, we first resort to an virtual uplink formulations of the the primal problem by introducing an auxiliary variable and applying the uplink-downlink duality theory. By exploiting the analytic structure of the optimal beamformers in the dual uplink problem, an efficient algorithm is then developed to solve the considered problem. Furthermore, to reduce further the exchange overhead between coordinated BSs in a large-scale antenna system, an effective coordinated power allocation solution only based on statistical channel state information is reached by deriving the asymptotic optimization problem, which is used to obtain the power allocation in a long-term timescale. Numerical results validate the effectiveness of our proposed schemes and show that both the spectral efficiency and the energy efficiency can be simultaneously improved over traditional downlink coordinated schemes, especially in the middle-high transmit power region.

In this paper, a robust transmission scheme for simultaneous wireless information and power transfer (SWIPT) in the presence of an eavesdropper is proposed. With imperfect channel state information (CSI) at the transmitter, the optimal transmit covariance matrix is obtained based on the maximization of the worst case harvested energy for the energy receiver (ER) while guaranteeing the achievable secrecy rate constraint for the information receiver (IR). To solve such a challenging nonconvex problem, in this paper, a two-stage optimization approach is proposed. In the first stage, the original problem is transformed into a robust design problem, which can be further converted into a convex semidefinite program (SDP) problem by using S-procedure as a tool. In the second stage, the optimal transmit covariance matrix is obtained via the aid of one-dimensional search algorithm. Finally, simulation results are provided to illustrate the robustness and effectiveness of the proposed method.

Spectral efficiency (SE) and energy efficiency (EE) are both essential in future wireless communications. To improve the system performance on these two metrics, in this paper we consider the weighted sum rate maximization (WSRMax) problem subject to per-cell EE constraints and per-BS transmit power constraints in multicell multiuser downlink systems. This problem is difficult in its original form due to the introduction of new EE constraints. We first reveal that the original problem can be transformed into an equivalent parameterized polynomial form by introducing some auxiliary variables. By exploiting the concavity property with respect to each variable in the equivalent problem, an efficient block coordinate ascent algorithm is then proposed with guaranteed convergence property. Numerical results show that compared with the conventional WSRMax algorithm, in addition to fulfilling the EE requirement of each cell, our algorithm achieves a better system EE performance at the cost of a slight sum rate performance loss at a certain region and offers a new insight on the SE-EE tradeoff in wireless communication systems.

This paper investigates the performance of a two-way decode-and-forward (DF) multi-antenna relay network. A joint antenna selection scheme for all nodes is first proposed based on the maximizing the worse received signal to noise ratio (SNR) of two end users. Then, we derive the probability density function (PDF) and cumulative distribution function (CDF) of the received SNRs of both users. We also achieve the closed-form expressions of average bit error rate (BER) and outage probability of the relay system. Furthermore, we reveal the asymptotic behavior of our system when transmitting SNR or the number of antennas is large. Our analysis shows that the proposed DF antenna selection scheme achieves full diversity. The numerical results finally verify the accuracy of our analysis.

In this paper, we propose a load-aware and QoS- aware user association strategy that jointly considers the load of each BS and user's achievable rate instead of only utilizing the latter, and formulate it as a network-wide weighted utility maximization problem to reveal how a heterogeneous cellular network should self-organize. This is a nonlinear mixed-integer optimization problem, and its optimum solutions are very difficult to be obtained when it is large scale one. To solve the proposed problem, we relax association indicator variables and adopt a gradient descent method to find optimum solutions. Then, each user is associated with some BS with a maximum association indicator taken from solutions of the relaxed optimization problem. Experimental results show that, compared with the best power association and range expansion association, our strategy has a lower call blocking probability and a higher load balancing level.

This study considers the joint transmission precoding design for downlink multicell multiuser multiple‐input single‐output systems where imperfect channel variances are available at the base stations. The authors aim to tackle the robust signal‐to‐interference‐plus‐noise ratio (SINR) balancing problem to maximise the minimum worst‐case user rate. To solve the non‐convex problem, a duality relationship between the downlink max–min worst‐case SINR optimisation problem and the virtual uplink min–max worst‐case SINR optimisation problem is first revealed. Based on this, a new algorithm is developed to solve the virtual problem by using jointly the sub‐gradient method and the geometric programming methods, whose achieved solution is finally converted to the downlink. Their analysis shows that the proposed algorithm is guaranteed to converge and has lower computational complexity than conventional approaches. Moreover, computer simulations validate the effectiveness of the proposed method and show that the proposed algorithm has fast convergence and achieves a performance close to that of the brute search method.

Energy-efficient communications has attracted much interest in the research of 5G cellular systems. In this paper, we study energy-efficient coordinated beamforming design for heterogeneous multicell multiuser downlink systems. The considered problem is formulated as maximizing the weighted sum per-cell energy efficiencies (WSPEEMax) subject to predefined per-user target rate demands, maximum leakage interference power constraints, and per-BS transmit power constraints. This formulation is more general than the conventional EE optimization problem and provides a unified way to consider the EE of heterogeneous networks. However, it is hard to tackle due to the weighted sum-of-ratios form of the objective function and the non-convex nature of per-user target rate constraints. To address it, we propose to first transform the original problem into a polynomial form optimization by introducing some auxiliary variables and then further reveal their equivalence in finding the solution. Then, an efficient block coordinate ascent optimization algorithm is developed to solve the equivalent problem by exploiting the concave nature of the considered problem with respect to each optimization variable. To further improve the network EE, we also develop an energy-efficient transmission method for each small-cell network. Finally, extensive numerical results are provided to verify the effectiveness of the proposed schemes and show that both the EE and spectral efficiency (SE) of heterogeneous network can be significantly improved by energy-efficient coordinated multiple-input multiple-output (MIMO) transmission.

This paper investigates the coordinated beam-forming design for multi-cell MISO downlink beamforming system, aiming at maximizing the sum rate. In the proposed scheme, convex approximation approach is used to first recast the primal non-convex problem into an approximate problem of minimizing the sum of weighted inverse SINR. Then, an alternating optimization method is developed to address the approximate problem based on uplink-downlink duality. We show that our solution is globally optimal in the case of two-BS cooperation with a total power constraint, and is also effective in a general case. When extending to per-BS power constraints, an alternating optimization algorithm with provable convergence to stationary point is proposed following a similar procedure. Our simulation results show that the proposed scheme has a fast convergence and achieves a sum rate performance very close to the optimal performance obtained by exhaustive search.

In this paper we analyze the performance of a small cell network where the locations of the base stations are generated according to Poisson distribution and linear multiuser precoding is employed. The performance metrics of both the overall outage probability (OOP) and the symbol error probability (SEP) are investigated for this small cell network. Tight closed-form expressions for the OOP and the average SEP are derived, and an asymptotic approximation to the OOP and the average SEP are also obtained, respectively. Their accuracy are validated via our numerical results. In addition, we propose a new access mechanism to maximize the energy efficiency and further evaluate its performance analytically. Both theoretical and numerical results show that the proposed scheme could effectively improve the efficiency of the small cell heterogeneous network.

This paper considers robust beamforming design for coordinated multiple point joint transmission systems with imperfect channel state information at the base stations (BSs). A robust lower bound duality relation between the downlink max-min worst-case SINR optimization problem and the virtual uplink min-max worst-case SINR optimization problem is first revealed. Based on this, an iterative optimization method is then proposed using the subgradient theory to solve the virtual uplink problem, by which the solution to the downlink optimization problem is easily obtained. It is proved that the convergence of the proposed algorithm can be guaranteed with monotonic boundary sequence theorem and the subgradient theory. Numerical simulation verifies the effectiveness of the proposed method.

We investigate pilot contamination problem for very large MIMO multi-cell TDD system. The asymptotic sum rate of two typical precoding schemes, i.e., the single-cell zero forcing (ZF) precoding and the multi-cell minimum mean square error (MMSE) based coordinated precoding are first derived. Results show that these two schemes have the same asymptotic sum rate expression as the number of the base station antenna going to infinity, revealing that coordinated precoding based on local channel state information (CSI) only provides marginal gain in the presence of pilot contamination. Based on our derivations, a pilot scheduling scheme is further proposed to mitigate pilot contamination, which could provide much better performance. Numerical results finally verify our derivations and the proposed scheme.

In this paper we study energy efficient joint power allocation and beamforming for coordinated multicell multiuser downlink systems. The considered optimization problem is in a non-convex fractional form and hard to tackle. We propose to first transform the original problem into an equivalent optimization problem in a parametric subtractive form, by which we reach its solution through a two-layer optimization scheme. The outer layer only involves one-dimension search for the energy efficiency parameter which can be addressed using the bi-section search, the key issue lies in the inner layer where a non-fractional sub-problem needs to tackle. By exploiting the relationship between the user rate and the mean square error, we then develop an iterative algorithm to solve it. The convergence of this algorithm is proved and the solution is further derived in closed-form. Our analysis also shows that the proposed algorithm can be implemented in parallel with reasonable complexity. Numerical results illustrate that our algorithm has a fast convergence and achieves near-optimal energy efficiency. It is also observed that at the low transmit power region, our solution almost achieves the optimal sum rate and the optimal energy efficiency simultaneously; while at the middle-high transmit power region, a certain sum rate loss is suffered in order to guarantee the energy efficiency.

In this paper, a new analytical expression of the max-min SINR duality between the multi-cell downlink and the virtual uplink subject to per-BS power constraints is firstly given. Based on that, a hierarchical iterative scheme is proposed to solve the virtual uplink optimization problem. The uplink solution is then converted to achieve the solution to the multi-cell downlink beamforming problem. Simulation results show that, in contrast to existing multi-cell beamforming schemes, the proposed scheme achieves better performance in terms of both the worst-user rate and the rate per energy.

A joint source-and-relay beamforming scheme is proposed for multiple-input multiple-output (MIMO) systems with distributed single-antenna relays. First, a lower-bound of the signal-to-noise ratio at the destination is derived as an objective function to formulate a constrained beamforming optimisation problem. The joint beamforming problem is then divided into two sub-optimisation problems corresponding to the source and the relay beamforming, respectively. The first sub-problem is shown to be a quadratic concave minimisation, and is tackled by developing an iterative algorithm with each iteration solving a linear problem. The second one corresponds to a Rayleigh–Ritz ratio problem which is then solved by the generalised singular-value decomposition in a closed form. Based on the solutions to the subproblems, a global iterative algorithm is designed to implement the joint source-and-relay beamforming. Simulation results show that the proposed method outperforms some existing relaying schemes in terms of the capacity and outage probability of the whole MIMO relay system.

In this paper, we address the problem of the coordinated beamforming design for multi-cell multiple input single output (MISO) downlink system subject to per-BS power constraints. The objective is taken as the maximization of the minimum signal-to-interference plus noise ratio (SINR), while a complete analysis of the duality between the multi-cell downlink and the virtual uplink optimization problems is provided. A hierarchical iterative scheme is proposed to solve the virtual uplink optimization problem, whose solution is then converted to derive the one of the multi-cell downlink beamforming problem. The proposed algorithm is proved to converge to a stable point. Additional, the complexity of the proposed algorithm is analyzed. Simulation results show that, in contrast to existing multi-cell beamforming schemes, the proposed algorithm achieves better performance in terms of both rate per energy (RPE) and the worst-user rate.

This paper addresses coordinated downlink beamforming optimization in multicell time division duplex (TDD) systems where a small number of parameters are exchanged between cells but with no data sharing. With the goal to reach the point on the Pareto boundary with max-min rate fairness, we first develop a two-step centralized optimization algorithm to design the joint beamforming vectors. This algorithm can achieve a further sum-rate improvement over the max-min optimal performance, and is shown to guarantee max-min Pareto optimality for scenarios with two base stations (BSs) each serving a single user. To realize a distributed solution with limited intercell communication, we then propose an iterative algorithm by exploiting an approximate uplink-downlink duality, in which only a small number of positive scalars are shared between cells in each iteration. Simulation results show that the proposed distributed solution achieves a fairness rate performance close to the centralized algorithm while it has a better sum-rate performance, and demonstrates a better tradeoff between sum-rate and fairness than the Nash Bargaining solution especially at high signal-to-noise ratio.

By employing the amplify-and-forward relaying strategy, a relay selection method with simplified precoding is proposed for two-hop multi-relay channels. The proposed method consists of two parts. In the first part, the authors present an optimal beamforming scheme with full channel state information (CSI) and derive a simplified and analytic expression for the output SNR through each relay, thereby selecting the best relay. The second part considers the transmiit precoding problem with the CSI known to the receiver only and provide a selection strategy with Grassmannian beamforming. The new algorithm chooses only one relay based on the maximal received SNR to assist in transmission. It can significantly reduce the system consumption, achieve excellent bit-error-rate and average throughput and maintain full diversity order. Simulation results demonstrate that the performance of the proposed schemes with low complexity approaches towards the optimal iteration method. For practical situations with a distance attenuation factor, the performance gain of the authors schemes is also evident.

A maximum mean squared error optimal relay beamformer is proposed here for two-way single-antenna distributed relaying systems. A constrained optimisation problem with respect to the relay beamforming vector is first formulated. It is then shown that the design problem of such a relay beamformer supporting both downlink and uplink transmissions simultaneously can be converted to convex optimisation when full channel state information (CSI) is available at the relays. By employing the Lagrangian multiplier method, a closed-form solution for the relaying vector is obtained. The proposed relay beamforming method is also extended to the situation where only the statistics of the CSI are available. A simulation study is conducted to confirm the merit of the proposed two-way relaying scheme.

In this paper, we first derive an optimal precoder for amplify-and-forward (AF) multiple-antenna relay systems with single-antenna source and destination terminals by maximizing the output signal-to-noise ratio (SNR). Then, the resulting maximum SNR expression and its approximation at high transmission SNR are analyzed to obtain their statistical properties for independently identically distributed (i.i.d.) Rayleigh fading channels. Based on the properties of the approximate maximum SNR, the average symbol error probability (ASEP) is investigated, leading to an explicit diversity order and array gain. The ergodic achievable rate is also studied, giving a tight closed-form upper bound. The theoretical analysis is finally validated by Monte Carlo simulations.

We consider a wireless relay network where two pairs of nodes exchange information with their partners through a single amplify-and-forward two-way relay with each node equipped with multiple antennas. We propose a new relaying scheme employing OFDMA for the multiple access transmission in the first time slot and OFDM/SDMA for the broadcast transmission in the second time slot to improve the sum rate of the network. To fully utilize spatial diversity, we design the relay beamforming matrices according to two methods respectively, i.e., signal to leakage and noise ratio (SLNR) and block diagonalization based zero-forcing (BDZF), on per subcarrier basis. We also derive the upper bound on the capacity region of this two-way relay network by using cut-set theory. Simulation results show that the proposed scheme outperforms three other relaying schemes in terms of sum rate and can approach the upper bound of capacity region.

This paper presents an optimal relay precoding scheme for two-hop amplify-and-forward based MIMO relay networks with one source, one destination and multiple relays. A constrained optimization problem for relay precoder is formulated by using the mutual information criterion along with a total relay transmitting power constraint. It is shown that due to the block-diagonal structure of the precoding matrix, the optimization problem can not be solved directly by the existing methods. We then simplify it into an equivalent problem involving scalar optimization variables only. Through an in-depth study of the problem formulation, it is revealed that the objective function is convex only when the relay power is larger than a certain threshold, which can be determined mainly by the system configurations and the channel condition. Finally, under the convex condition, the simplified problem is solved by a convex optimization method. The effectiveness of the proposed precoder is validated by Monte-Carlo simulations with comparison to some of the existing methods.

We address the problem of combining limited feedback information with long-term channel statistical information in the design of downlink SDMA schemes. A novel combining method is developed to improve the quality of channel knowledge at the base station. More specifically, a set of novel feedback parameters is proposed and a related method is developed to estimate a representation of the multiuser channel vectors at the base station. This method utilizes the hybrid information by combining instantaneous channel feedback and long-term channel statistics, and is based on a channel phase codebook designed using the generalized Lloyd algorithm. The estimated channel knowledge at the base station can be used for joint design of multiuser precoding and opportunistic scheduling. The advantage of the proposed scheme over existing CSI quantization based SDMA schemes is further confirmed by computer simulations.

In this paper, a robust optimal distributed relay beamforming scheme is presented for two-way wireless relay systems with two sources (one base station and one mobile terminal) and multiple relays, each having a single antenna. Considering that the perfect channel state information (CSI) between the mobile terminal and the relays is usually not available, the new beamforming problem, based on the minimization of the sum MSE (mean squared error) subject to a total relay power, is formulated such that only the CSI between the base station and the relays is required. The constrained beamforming optimization problem is then solved by the Lagrangian multiplier method, leading to a closed-form solution for the distributed relay beamforming. Monte Carlo simulations show that the proposed scheme performs better than the conventional relaying method in terms of both sum rate and the bit-error-rate (BER).

Some of the existing relay schemes for cooperative networks based on one-way relaying protocol are not applicable to the case of two-way relaying protocol. In this letter, a cooperative relay scheme for distributed amplify-and-forward relays working under the two-way relaying protocol is designed in a closed-form, which is asymptotically optimal in the high levels of signal-to-noise ratio (SNR). An upper-bound of the mean squared error (MSE) is derived via a tight approximation of the SNR expression. Based on the minimization of this upper-bound, the two-way relay scheme is then derived as a Rayleigh-Ritz ratio problem. The new relay scheme achieves the minimum MSE for both directional transmissions. Simulation results illustrate the effectiveness of the proposed scheme especially in the high SNR regime.

In this paper, a two-way relay precoder is designed for multiple-input multiple-output (MIMO) distributed cooperative relay systems. A constrained optimization problem with respect to (w.r.t.) the relay precoder is formulated for the most general relay and antenna scenario, namely, multiple relays each with multiple antennas, It is shown that due to the difficulty of two-way distributed relaying mechanism as well as the block-diagonal nature of the relay precoding matrix, this optimization problem cannot be solved by existing one-way relaying methods. It is then proved that with full channel state information available at relays, the underlying problem can be converted to a convex optimization w.r.t. the non-zero entries of the relay precoding matrix only, such that the Lagrangian multiplier method is applicable to the relay precoder design, leading to a closed-form relay precoding solution. A simulation study is conducted to justify the superior performance of the proposed two-way relaying scheme.

A new optimization criterion is proposed to minimize error probability for the proposed joint optimal power allocation (PA) of the MIMO systems enhanced by relay in this paper. It is proved that the cost function obtained is only convex with respect to (w.r.t.) the power parameters of the source or those of the relay separately, but not convex w.r.t. the whole parameters. In order to use convex optimization methods with high efficiency to solve this complicated problem, a tight upper bound of the sum MSE (mean squared error) is derived, and employed to modify the cost function in order to obtain a convex problem. It is verified through simulation results that the proposed PA scheme outperforms the existing one.

In this paper, new dynamic resource allocation algorithms are presented for the downlink of multi-user MIMO-OFDMA/SDMA systems. Since it is difficult to obtain the optimal solution to the joint optimization problem, the whole procedure is divided into two steps, namely, the subcarrier-user scheduling and the resource allocation. In the first step, a new metric is proposed to measure the spatial compatibility of multiple users each with multiple receive antennas, based on which a new subcarrier-user scheduling algorithm is designed. In the second step, two dynamic resource allocation algorithms are developed to assign radio resources to the scheduled users accordingly. Simulation results demonstrate the superiority of the proposed algorithms in terms of the system throughput.

The analysis shows that the conventional codebook construction of Grassmannian subspace packing can not control the performance loss caused by a linear receiver, while a proper unitary perturbation to the codebook is capable of compensating for this performance loss. This paper therefore proposes a novel hierarchical codebook to exploit the gain of unitary perturbation. The hierarchical codebook consists of a Grassmannian subcodebook and a proposed perturbation subcodebook. To implement precoding, this paper also presents a successive codeword selection scheme, thus the receiver would successively selects two preferred codewords from Grassmannian and perturbation subcodebooks. With the feedback binary indices of these selections, the transmitter uses the product of two preferred codewords as the precoder. The theoretical analysis of the proposed precoding technique shows that the usage of the perturbation subcodebook can improve to a certain degree the system performance in terms of throughput as well as BER, with a small additional feedback overhead, and the proposed codebook would reduce the computational and storage requirements in contrast to the conventional codebook. It is also shown via computer simulations that the proposed technique gives a better BER performance than the single Grassmannian codebook based precoding technique does, even if the feedback overhead remains the same.

In this paper, a new transmit scheme combining beamforming (BF) with space-time block coding (STBC) is proposed for correlated fading channels. Based on maximizing the output mean signal-to-noise ratio (SNR) at the receiver, the transmitter BF weight vectors are first derived. Then, utilizing the minimal bit error rate (BER) upper bound as the design criterion, a simple power allocation algorithm is developed. Next, the BER performance of the system with the proposed transmit scheme is analyzed by considering an M-QAM constellation. Finally, computer simulation results are given to verify the effectiveness of the proposed scheme.

An iterative linear transceiver design scheme under sum mean squared error minimization criterion is proposed. By modifying the structure of transceiver, the complex computation of Lagrangian multiplier within traditional MMSE transceiver design can be effectively obviated, and thus the whole system complexity can be greatly reduced. Because the Lagrangian multiplier has analytical solution, transmit preceding matrix also has closed-form solution, and can be solved easily with fixed- point iterations. The receiver filter is worked out independently with MMSE criterion at each terminal, and the downlink signaling of each receive filter from base station is not necessary- Simulations demonstrate that the proposed scheme is effective.

Adaptive transmission which adjusts optimally transmit power level, preceding matrix, modulation and coding schemes at the cost of perfect channel state information (CSI) , can greatly improve the performance of a communication link under fading environment. As the perfect CSI is difficult to be available at transmitter, it is valuable to study the adaptive design with partial CSI. Previous works showed that preceding with limited feedback proves effective in increasing transmission rate in the multiple-input multiple-output (MIMO) systems, and further performance gain can be achieved if power control is used along with quantized preceding. However, adaptive modulation and coding (AMC) has not been considered in previous works with partial CSIT. In order to maximize transmission rate under the constraint of fixed transmit power and target quality-of-service (QoS), we develop a novel adaptive preceding scheme along with joint power and bit loading for finite-rate feedback MIMO systems. What's more, the preceding matrix and power information are fed back through double codebooks for reducing the feedback overhead. In addition, codebook design for power information is given. Simulation results show that the proposed scheme greatly improves the transmission rate with low feedback overhead.

In this paper, the conventional Grassmannian codebook for precoding is first analyzed, showing that the performance loss caused by linear receivers was not taken into account. To tackle the performance loss issue, a novel hierarchical codebook consisting of a Grassmannian subcodebook and a perturbation subcodebook is then proposed for precoding systems with linear receivers. A two-step codeword selection scheme that uses the product of two codewords selected from the subcodebooks as the precoder is also presented. Our analysis shows that the perturbation subcodebook is able to compensate for the performance loss from linear receivers. Compared with the Grassmannian codebook, the superiority of the proposed codebook in terms of search complexity as well as throughput/ BER is further confirmed by computer simulations.

This paper proposes a robust precoding for the space time block codes (STBC) and spatial multiplexing (SM) hybrid system. The overall precoding is disassembled into independent precoder optimization of different STBC groups by decomposing the overall channel matrix into several independent virtual channel matrices, this method will considerably reduce the amount of the required feedback information. Also, the precoder optimization is based on a new derived SER bound and considers the uncertainty of the channel feedback. Simulation results demonstrate the performance of the proposed technique.

Automatic facial expression recognition is the kernel part of emotional information processing. This paper dedicates to develop an automatic facial expression recognition approach based on confusion-crossed support vector machine tree (CSVMT) to improve recognition accuracy and robustness. After the pseudo-Zernike moment features were extracted, they were used to train a CSVMT for automatic recognition. The structure of CSVMT enables the model to divide the facial recognition problem into sub-problems according to the teacher signals, so that it can solve the sub-problems in decreased complexity in different tree levels. In the training phase, those sub-samples assigned to two internal sibling nodes perform decreasing confusion cross, thus, the generalization ability of CSVMT for recognition of facial expression is enhanced. The compared results on Cohn-Kanade facial expression database also show that the proposed approach appeared higher recognition accuracy and robustness than other approaches.

In this paper, we present an open-loop transmit scheme for MIMO communications. We first use the uplink channel correlation matrix (UCCM) to calculate the array weight vectors for downlink beamforming (DLBF). Then based on the symbol error rate (SER) upper bound as design criterion, we derive an algorithm for adaptive power allocation among multiple beams, and thus develop the transmit scheme joint adaptive beamforming (ABF) with space-time block coding (STBC). The main benefit of the scheme is that it can almost achieve the optimal performance with low complexity. Next, using the moment generation function (MGF) approach and the Gauss-Chebyshev integration, we derive a simple and accurate numerical analysis method for the proposed scheme under three widely used modulations. Finally, computer simulation results demonstrate the superiority of the open-loop transmit scheme.

Channel estimation for OFDM systems in rapidly time-varying environments is challenging. In this paper, relying on a basis expansion channel model, we propose a scheme for estimating channel parameters varying within a transmission block. Along with the estimation scheme, we also derive the optimal pilot sequence and optimal placement of pilot tones with respect to the mean square error (MSE) of the channel estimate. It is shown that the optimal pilot sequence consists of some adjacent equipowered and equispaced subsequences that are constrained by certain phase conditions. Simulation results demonstrate the performance of the proposed scheme in rapidly time-varying scenarios.

This paper proposes a subspace-based blind channel estimation method for space-time coded OFDM system. Using only the redundancy induced by OFDM modulation and space-time block coding (STBC), channel state information (CSI) can be blindly estimated, up to two scalar ambiguities for Alamouti STBC or one for 4T4A3K STBC, even when a single receiving antenna is equipped. Compared with other blind channel estimation method for STBC-OFDM, this method needs neither pre-coding nor over-sampling, and thus has higher system data rate and lower complexity. Simulation results demonstrate the effectiveness of this method.

We propose a subspace-based blind channel estimation method for space-time coded OFDM system. Using only the redundancy induced by OFDM modulation and space-time block coding (STBC), channel state information (CSI) can be blindly estimated up to two scalar ambiguities, even with single receiving antenna. Compared with other blind channel estimation method for space time OFDM systems, this method needs neither pre-coding nor over-sampling, and thus has higher system data rate and lower complexity.

In orthogonal frequency division multiplexing (OFDM) systems, some subcarriers at the borders of the allocated bandwidth are usually used as guard band. Since these subcarriers, which are often referred to as virtual subcarriers, are not used for transmission, approach of conventional uniformly placed pilot tones is not applicable any more in some situations. Therefore, it is necessary to derive the optimal pilot sequences based on the nonuniform placement of pilot tones. In this paper, we first compute the mean square error (MSE) of the least squares (LS) channel estimate for multiple-input multiple-output (MIMO) OFDM systems. Then, based on nonuniform pilot tone placement, we derive the optimal pilot sequences with respect to this MSE. Simulation results demonstrate the effectiveness of the proposed approach

The differential unitary space-time modulation (DUSTM) scheme provides full diversity without channel knowledge at either the transmitter or the receiver. However, the complexity of maximum-likelihood decoding is exponential in the number of transmit antennas and the data rate. For the case where the number of transmit antennas is even, we propose a new DUSTM scheme which preserves full diversity while reducing the decoding complexity. Moreover, our scheme simplifies the constellation design. Theoretical analysis and simulation results show that for some typical scenarios, the proposed scheme achieves better bit-error-rate performance than the original DUSTM scheme.

Neural network tree (NNTree) is a modular neural network with the overall structure being a decision tree (DT), and each non-terminal node being an expert neural network (ENN). One advantage of using NNTrees is that they are actually gray-boxes because they can be interpreted easily if the number of inputs for each ENN is limited. To design interpretable NNTrees, we have proposed a multiple objective optimization based genetic algorithm. This algorithm, however, is good only for solving problems with binary inputs. In this paper, we propose a method to solve problems with continuous inputs. The basic idea is to find a small number of critical points for each continuous input using self-organized learning, and quantize the input using the critical points. Experimental results with several public databases show that the NNTrees built from the quantized data are much more interpretable, and in most cases they are as good as those obtained from the original data.

The population-based incremental learning (PBIL) algorithm is extended to a form where multiple traits for each gene reflect the pleiotropic and polygenic characteristics in natural evolved systems. This method is used to solve the traveling salesman problem. Some results are better than the best existing algorithms for evolutionary computation of the problem. The results show that the method proposed is comparable to the advanced level of solvers for the traveling salesman problem.

Statistical complexity measures are proposed as general indicators of structure or correlation. Lopez-Ruiz (1995) introduced another measure of statistical complexity C/sub LMC/ that, like others, satisfies the boundary conditions of vanishing in the extreme ordered and disordered limits. Feldman examined some properties of C/sub LMC/ and found that it is neither an intensive nor extensive thermodynamic variable, and proposed a simple alteration of C/sub LMC/ that renders it extensive. However the remedy results in a quantity that is a trivial function of the entropy density and hence of no use as a measure of structure or memory. We alter the disequilibrium term by the information of time irreversibility (information of nonlinear dynamics) and present a novel statistical complexity measure which is used to quantify the complexity caused by nonlinear dynamics. This statistical complexity measure allows reliable detection of periodic, quasi-periodic, linear stochastic and chaotic dynamics. When applied to the analysis of heart rate data, correlational structure in heart rate series is found, and the estimated statistical complexity appears to be correlated with different cardiac dynamics.

In this paper binary population-based incremental learning is extended to an integer form, and a new approach to the traveling salesman problem (TSP) is proposed based on linkage relations between cities. The properties of this method are distributed stochastic tour construction, probability distribution initialization, accelerated search based on some power of probability, decision of entropy of probability distribution for terminate condition on process of evolution, and improvement of population solutions using 2-opt/3-opt. Thirteen TSP problems are solved, including ten international contest problems on symmetric and asymmetric TSP problems. The results show that the method proposed in this paper is comparable to the international advanced level on TSP problems and is capable of finding high quality solutions to TSP problems in short times, particularly for large TSP instances.

Chaotic behavior can be found in nonautonomous cellular neural networks (CNNs). The impulsive control method to control this kind of chaos is used and some satisfactory result are achieved. The condition which ensure existence of periodic solution in the impulse controlled system is provided and proved, and numerical simulation shows the chaos can be eliminated by adding a very small external force. Through observing the time waveform diagram of some controlled periodic orbits, we find the time waveform is very similar to encephalic electric activity or cardiac electric activity in biomedical field study. This illustrate that the nonautonomous CNNs model can successfully model physiological electric response activity signals. Moreover, the physiological explanation is given for the nonautonomous CNNs model.

It is by now widely appreciated that normal heart rhythms show features of deterministic chaos, and it is also corrupted by a great deal of physiological noises from surroundings as the inputs to the chaotic system. We study the effects of measurement and dynamical noises on low-dimensional chaotic systems, and present a numerical algorithm for estimating to what extent heart rhythm is corrupted by dynamical noises. Further analysis shows that adding increasing amounts of dynamical noise increasingly develops the complexity of chaotic dynamics. The method need not fully reconstruct an attractor, thus it is robust to measurement noises. Finally, the ECG of 53 subjects falling into three groups were used to test the algorithm. From the measured R-R intervals, a time series of 1000 first order difference points was used to estimate dynamical noise levels. We found that the estimated dynamical noise levels were correlated to the different classes of ECG.

In this paper, we addressed a theoretical analysis for the capacity of parallel intra-connected bidirectional associative memory (MIBAM) and proved the conclusions: two MIBAM with the equal total number of neurons have the equal recalling probability for m pairs of stored pattern pairs if m is not too large. The results of computer simulation support the conclusions well.

By computer simulation, we detect a new type of strange attractor in a three-cell cellular neural network which defers from that found by other researchers. Bifurcation phenomena are analyzed.