Block Coordinate Descent Method Research Articles

Joint BS-RIS-User Association and Beamforming Design for RIS-Assisted Cellular Networks

Reconfigurable intelligent surface (RIS) is a revolutionary technology for sixth-generation (6G) networks owing to its ability to manipulate wireless environments. As a frequency-selective device, RIS can only effectively shape the propagation of signals within a certain frequency band. Due to this frequency-selective property, the deployment of RIS in cellular networks will introduce a complicated base station (BS)-RIS-user association issue since adjacent BSs operate at different frequency bands. In this paper, with the consideration of the frequency-selective characteristics of RIS, we aim to jointly optimize BS-RIS-user association, active beamforming at BSs, and passive beamforming of RIS to maximize the sum-rate of a RIS-assisted cellular network. We first leverage <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{0}$</tex-math></inline-formula> -norm to efficiently integrate BS-RIS-user association with active and passive beamforming. Then, we adopt fractional programming (FP) and block coordinate descent (BCD) methods to deal with logarithmic and fractional parts and decouple the joint association and beamforming design problem into several sub-problems. Efficient algorithms which combine <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{0}$</tex-math></inline-formula> -norm approximation, majorization-minimization (MM), and alternating direction method of multipliers (ADMM) are developed to alternately solve the sub-problems. Extensive simulation results illustrate the importance of BS-RIS-user association optimization in RIS-assisted cellular networks and verify the effectiveness of the proposed joint association and beamforming design algorithm.

URLLC-oriented secure communication for UAV relay-assisted network

In this paper, we investigate the unmanned aerial vehicle (UAV) relay-assisted secure short packet communication. The UAV acts as a decode-and-forward relay to transmit control signals from the source to the actuators in the presence of a ground eavesdropper (EV) whose imperfect channel state information is available at the UAV. Specially, non-orthogonal multiple access is adopted in our work to achieve more connections and improve the fairness of communication and the short packets are employed for data transmission to reduce the latency. Explicitly, we maximize the minimum average secrecy throughput among all actuators by jointly optimizing the UAV trajectory, transmit power and blocklength allocation, which generates a challenging optimization problem. Therefore, we propose an iterative algorithm based on block coordinate descent method and successive convex approximation technique to handle the non-convex problem. Numerical results show that the proposed scheme has better performance compared to the benchmark schemes.

Robust Matrix Completion Based on Factorization and Truncated-Quadratic Loss Function

Robust matrix completion refers to recovering a low-rank matrix given a subset of the entries corrupted by gross errors, and has various applications since many real-world signals can be modeled as low-rank matrices. Most of the existing methods only perform well for noise-free data or those with zero-mean white Gaussian noise, and their performance will be degraded in the presence of outliers. In this paper, based on the factorization framework, we propose a novel robust matrix completion scheme via using the truncated-quadratic loss function, which is non-convex and non-smooth, and half-quadratic theory is adopted for its optimization. By introducing an auxiliary variable, half-quadratic optimization (HO) can transform the loss function into two tractable forms, that is, additive and multiplicative formulations. Block coordinate descent method is then exploited as their solver. Compared with the additive form, the multiplicative variant has lower computational cost since we attempt to take the observations contaminated by outliers as missing entries. Numerical simulations and experimental results based on image inpainting and hyperspectral image recovery demonstrate that our algorithms are superior to the state-of-the-art methods in terms of restoration accuracy and runtime. MATLAB code is available at <uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/bestzywang</uri> .

Improved sparse low-rank model via periodic overlapping group shrinkage and truncated nuclear norm for rolling bearing fault diagnosis

The early faults of rolling bearings are the common causes of rotating machinery failures. Rolling bearings with local faults usually generate periodic shocks during operation, but the pulse information is easily masked by a large number of random shocks and noise. To effectively diagnose the early fault information of rolling bearings, a dual-dimensional sparse low-rank (DDSLR) model is proposed in this paper, which can simultaneously extract the sparsity within and across groups and periodic self-similarity of fault signal. In the DDSLR model, a newly developed dimension transformation operator is used to transform the fault signal between one-dimensional vector and low-rank matrix, and the periodic overlapping group shrinkage and truncated nuclear norm are used to improve the traditional sparse low-rank model. In addition, the setting rules of periodic prior and parameters in the DDSLR model are discussed, so that the DDSLR model has certain adaptive ability. Finally, the DDSLR model is proved to be a multi-convex optimization problem, and its solution algorithm is derived by using soft threshold operator and majorization-minimization algorithm under the framework of block coordinate descent method. The results of simulation analysis and experiments show that the proposed DDSLR model has higher fault signal estimation accuracy and better fault feature extraction performance than some classical sparse noise reduction models.

RIS-Aided Hybrid Precoder Design With Anti-Blocking Scheme in High-Speed Railway

Reconfigurable intelligent surface (RIS)-aided high-speed railway (HSR) communication system is an efficient and promising way to slove the signal blocking by tuning passive signal reflection or refraction. However, the complexity HSR environment lead unstable communication links and low quality of service. Therefore, this paper studies a RIS-aided hybrid precoding for anti-blocking HSR network to enhance the sum rate of mobile relays when signal blocking. To describe the blocking scenes clearly, the blocking model is established and the closed form of the blocking probability is derived. Based on the blocking model, the non-convex blocking optimal problem is decoupled by the block coordinate descent method with the jointly optimization problem about hybrid precoder and reflect angle matrix of RIS. Then, the successive convex approximation and prox-linear method are utilized to solve the constant modulus constraint of RIS and hybrid precoding constraints. Simulation results show that the proposed RIS-aided anti-blocking hybrid precoding scheme can achieve higher sum rate than the traditional methods in blockage scenarios. Moreover, the proposed algorithm brings better performance of blocking probability and outage probability in high-speed scenarios.

Multi-Sensor Image Feature Fusion via Subspace-Based Approach Using $\ell _{1}$-Gradient Regularization

Image fusion is a technique of combining two or more images into a single image which is more informative from an interpretation point of view. With the rapid development of different synthetic aperture radar sensing satellites capturing information from the earth by measuring energy in different portions of the electromagnetic spectrum (narrow/wide-band), complementary information about the area captured by different satellites is available (e.g. high-resolution spectral and RGB images). However, the estimation of the full-resolution image may not be necessary for inference approaches, including the pixel-based classification. Instead, it is desirable to extract the relevant information embedded in the available data to improve the inference capabilities. This work proposes a computational framework to estimate features with high-spatial-resolution and appropriate spectral content by combining information from a multi-sensor system. The considered multi-sensor setup is a hyperspectral imaging system with a complementary RGB sensor. The proposed framework first extracts spatial features from the RGB image using morphological profiles. Then, the fusion model assumes that the extracted features, and the hyperspectral measurements, lie in different subspaces matrices. In addition, this work developed a joint optimization scheme to solve the feature fusion problem by integrating the alternating direction method of multipliers with the block coordinate descent method. The alternating optimization method estimates the spatial features in the fusion model by penalizing the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\ell _{1}$</tex-math></inline-formula> -norm of the spatial gradient magnitudes. The quality of extracted features is measured in terms of supervised pixel-based classification methods. Extensive simulations show that the proposed approach outperforms other state-of-the-art methods in terms of classification accuracy.

An efficient implementable inexact entropic proximal point algorithm for a class of linear programming problems

We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography, and economics. To solve these generally large-scale LP problems efficiently, we design an implementable inexact entropic proximal point algorithm (iEPPA) combined with an easy-to-implement dual block coordinate descent method as a subsolver. Unlike existing entropy-type proximal point algorithms, our iEPPA employs a more practically checkable stopping condition for solving the associated subproblems while achieving provable convergence. Moreover, when solving the capacity constrained multi-marginal optimal transport (CMOT) problem (a special case of our LP problem), our iEPPA is able to bypass the underlying numerical instability issues that often appear in the popular entropic regularization approach, since our algorithm does not require the proximal parameter to be very small in order to obtain an accurate approximate solution. Numerous numerical experiments show that our iEPPA is efficient and robust for solving some large-scale CMOT problems on synthetic data. The preliminary experiments on the discrete tomography problem also highlight the potential modeling capability of our model.

Accelerating probabilistic tensor canonical polyadic decomposition with nonnegative factors: An inexact BCD Approach

Recently, Bayesian modeling and variational inference (VI) were leveraged to enable the nonnegative factor matrix learning with automatic rank determination in tensor canonical polyadic decomposition (CPD), which has found various applications in big data analytics. However, since VI inherently performs block coordinate descent (BCD) steps over the functional space, it generally does not allow integration with modern large-scale optimization methods, making the scalability a critical issue. In this paper, it is revealed that the expectations of the variables updated by the VI algorithm is equivalent to the block minimization steps of a deterministic optimization problem. This equivalence further enables the adoption of inexact BCD method for devising a fast nonnegative factor matrix learning algorithm with automatic tensor rank determination. Numerical results using synthetic data and real-world applications show that the performance of the proposed algorithm is comparable with that of the VI-based algorithm, but with computation times reduced significantly.

Sum Rate Maximization for Self-Sustainable IRS-Assisted UAV Communications

In this letter, we propose a novel time switching (TS) transmission scheme for intelligent reflecting surface (IRS)-assisted unmanned aerial vehicle (UAV)-enabled wireless powered communication network (WPCN). In the energy harvesting (EH) phase, the operation of IRS is switched between energy harvesting and reflecting to improve the energy transfer. In the information transmitting (IT) phase, the operation of IRS is switched between assisted and unassisted IT to avoid the deficient duration of IT phase when the IRS is energy starved. We formulate an achievable sum-rate maximization problem by jointly optimizing the resource allocation, IRS phase shift and location of the UAV. To address the non-convexity resulting from coupling of variables, we divide original problem into three sub-problems and solve them with the block coordinate descent (BCD) method. The numerical results testify that the proposed scheme can obtain the significant sum-rate gain compared to the traditional TS scheme.

Joint Beamforming Design for Intelligent Omni Surface Assisted Wireless Communication Systems

Intelligent reflecting surface (IRS) has been widely considered as one of the key enabling techniques for future wireless communication networks owing to its ability of dynamically controlling the phase shift of reflected electromagnetic (EM) waves to construct a favorable propagation environment. While IRS only focuses on signal reflection, the recently emerged innovative concept of intelligent omni-surface (IOS) can provide the dual functionality of manipulating reflecting and transmitting signals. Thus, IOS is a new paradigm for achieving ubiquitous wireless communications. In this paper, we consider an IOS-assisted multi-user multi-input single-output (MU-MISO) system where the IOS utilizes its reflective and transmissive properties to enhance the MU-MISO transmission. Both power minimization and sum-rate maximization problems are solved by exploiting the second-order cone programming (SOCP), Riemannian manifold, weighted minimum mean square error (WMMSE), and block coordinate descent (BCD) methods. Simulation results verify the advancements of the IOS for wireless systems and illustrate the significant performance improvement of our proposed joint transmit beamforming, reflecting and transmitting phase-shift, and IOS energy division design algorithms. Compared with conventional IRS, IOS can significantly extend the communication coverage, enhance the strength of received signals, and improve the quality of communication links.

Enhancing UAV-Enabled Communications via Multiple Intelligent Omni-Surfaces

This letter investigates an air-ground communication system where an unmanned aerial vehicle (UAV) communicates with multiple users with the assistance of multiple intelligent omni-surfaces (IOSs). Our goal is to maximize the minimum average expectation of the achievable rate through the joint optimization of the users’ scheduling, IOSs’ phase shifts, and UAV’s trajectory. We first show the random channel power gains follow the more tractable noncentral Chi-square distribution. Then, the resulting optimization problem is a mixed-integer non-convex problem with tightly coupled optimization variables, which is difficult to solve optimally. We propose an efficient algorithm to obtain the suboptimal solution based on block coordinate descent (BCD) and successive convex approximation (SCA) methods. Simulation results show that our proposed scheme significantly outperforms other benchmark schemes.

Editorial: Tensor numerical methods and their application in scientific computing and data science

Editorial: Tensor numerical methods and their application in scientific computing and data science

System throughput maximization in IRS-assisted phase cooperative NOMA networks

This work investigates performance of system throughput in intelligent reflecting surfaces (IRSs)-enabled phase cooperative non-orthogonal multiple access (NOMA) framework. By exploiting heterogeneous cognitive radio networks concept the aim is to maximize the sum rate of secondary users in the proposed phase cooperative downlink network configuration via optimization solutions. However, the optimization problem comes out to be NP-hard and precludes direct solution. Hence, an alternating optimization is applied at the primary network to solve the maximization problem by exploiting the transmit beamforming (BF) at the power station (PS) and phase shift optimization at the IRS. Later, sum rate maximization for secondary network is performed by utilizing phase shifts of primary network via phase cooperation. In order to find global optimal solutions for active beamformers at both PSs, a branch-reduce-and-bound (BRnB) method is used whereas, passive phase shift optimization at the primary PS is performed via a simple iterative solution, i.e., the element-wise block coordinate descent method. For the proposed framework, Monte-Carlo simulations are performed where the optimality of the global solution is compared with heuristic BF methods including minimum-mean-square-error/regularized zero-forcing-beamforming (ZFBF) and ZFBF. The BRnB algorithm sets an upper performance bound by improving the sum rate of users in comparison with the conventional heuristic BF schemes. This work signifies the utilization of phase cooperation in IRS-assisted NOMA networks for a multi-user environment.

Joint task processing/offloading mode selection and resource-allocation for backscatter-aided and wireless-powered MEC

We propose to develop the joint task processing/offloading mode selection and system resource-allocation schemes for a backscatter-aided and wireless-powered mobile edge computing (MEC), where multiple edge users (EUs), a hybrid access point (H-AP) working as a dedicated energy source and an information receiver, and several carrier emitters (CEs) coexist. We aim to maximize the residual energy of all energy harvesting based EUs while ensuring that EUs can complete their tasks, by jointly optimizing EUs’ task processing mode (local computing mode or edge computing mode), task offloading mode, and system resource-allocation. For the task offloading mode, each EU can select the bistatic backscatter (BB) communication mode or the harvest-then-transmit (HTT) mode to directly offload its task to the MEC server co-located with the H-AP. Also, each EU can select the ambient backscatter (AB)＋BB communication mode or the AB＋HTT communication mode to backscatter its data to nearby EUs through AB communication and then offload data to the MEC server with the help of nearby EUs through HTT or BB communication. First, we formulate a residual energy maximization problem for the considered system. Since the formulated optimization problem is non-convex with multiple coupled variables, we adopt the block coordinate descent (BCD) method to decompose it into several subproblems. Then, we utilize the alternating directions method of multipliers (ADMM) to transform the non-convex subproblems into convex subproblems, and propose the distributed joint task processing/offloading mode selection and system resource-allocation schemes. Finally, we verify and evaluate the performance of our proposed scheme through numerical analyses, which show that our proposed scheme outperforms the other benchmark schemes in terms of the residual energy and the task completion rate of EUs by jointly selecting the task processing mode and the task offloading mode for each EU.

Joint Trajectory Planning, Time and Power Allocation to Maximize Throughput in UAV Network

Due to the advantages of strong mobility, flexible deployment, and low cost, unmanned aerial vehicles (UAVs) are widely used in various industries. As a flying relay, UAVs can establish line-of-sight (LOS) links for different scenarios, effectively improving communication quality. In this paper, considering the limited energy budget of UAVs and the existence of multiple jammers, we introduce a simultaneous wireless information and power transfer (SWIPT) technology and study the problems of joint-trajectory planning, time, and power allocation to increase communication performance. Specifically, the network includes multiple UAVs, source nodes (SNs), destination nodes (DNs), and jammers. We assume that the UAVs need to communicate with DNs, the SNs use the SWIPT technology to transmit wireless energy and information to UAVs, and the jammers can interfere with the channel from UAVs to DNs. In this network, our target was to maximize the throughput of DNs by optimizing the UAV’s trajectory, time, and power allocation under the constraints of jammers and the actual motion of UAVs (including UAV energy budget, maximum speed, and anti-collision constraints). Since the formulated problem was non-convex and difficult to solve directly, we first decomposed the original problem into three subproblems. We then solved the subproblems by applying a successive convex optimization technology and a slack variables method. Finally, an efficient joint optimization algorithm was proposed to obtain a sub-optimal solution by using a block coordinate descent method. Simulation results indicated that the proposed algorithm has better performance than the four baseline schemes.

Joint energy and throughput optimization for MEC-enabled multi-UAV IoRT networks

In this paper, we study an Unmanned Aerial Vehicle (UAV) enabled Mobile Edge Computing (MEC) service provisioning to the Internet of Remote Things (IoRT) devices spread randomly on the ground in a remote area. The data generated by the IoRT devices is collected by the UAVs, which immediately relay the data collected to an MEC device installed on the ground at a nearby location. The MEC device receives the data from the UAVs, and sends the results back to the UAVs, which in turn relay them to IoRT devices. We aim to minimize the energy consumption by the IoRT devices and the UAVs, while maximizing the system throughput subject to bandwidth, power, information-causality, and UAVs’ trajectory constraints. We formulate the problem as a Mixed Integer Non Linear Programming problem, which is a complex and non-convex optimization problem. To make the problem tractable, we use variable relaxation. We further develop an iterative algorithm based on Block Coordinate Descent method, to jointly optimize the connection scheduling, power control, bit transmission scheduling, bandwidth allocation, and trajectories of the UAVs. Numerical results demonstrate the convergence of the algorithm and superiority of the proposed model with respect to conventional methods. Our proposed system model of placing MEC at ground shows 9% improvement in energy consumption when compared to carrying out computations at MEC carried by UAV and a 99% improvement when compared to placing MEC at the satellite. The proposed system model shows a 0.2% lower system throughput on average, compared to placing MEC at UAV, which is tolerable considering gains in terms of energy consumption.

Secure computation offloading assisted by intelligent reflection surface for mobile edge computing network

As an novel paradigm, computation offloading in the mobile edge computing (MEC) system can effectively support the resource-intensive applications for the mobile devices (MD) equipped with limited computing capability. However, the hostile radio transmission and data leakage during the offloading process may erode the MEC system’s potential. To tackle these hindrances, we investigate an IRS-assisted secure MEC system with eavesdroppers, where the intelligent reflecting surface (IRS) is deployed to enhance the communication between the MD and the AP equipped with edge servers and the malicious eavesdroppers may attack the wireless data offloaded by MD. The MD opt for offloading part of the tasks to the edge server for execution to support the computation-intensive applications. Moreover, the relevant latency minimization problem is formulated by optimizing the offloading ratio, the allocation of edge server computing capability, the multiple-user-detection (MUD) matrix and the IRS phase shift parameters, subject to the constraints of edge computation resource and practical IRS phase shifts. Then, the original problem is decouple into two subproblem, and the computing and communication subproblems are alternatively optimized by block coordinate descent (BCD) method with low complexity. Finally, simulation results demonstrate that the proposed scheme can significantly enhance the performance of secure offloading in the MEC system.

Cooperative task offloading and resource allocation for UAV-enabled mobile edge computing systems

Unmanned aerial vehicle (UAV)-enabled mobile edge computing (MEC) systems can provide flexible computation services to user equipments (UEs). On the one hand, the UAV can be flexibly deployed to provide computation services to UEs in remote areas or where intensive computing is required. On the other hand, the UAV can approach UEs conveniently to enhance the offloading performance. However, when UEs are widely distributed, the UEs will consume high energy to offload tasks to the UAV, or the UAV will need to consume significant energy to fly close to different UEs to ensure reliable computation offloading, which is unfriendly to the energy-constrained UAV. To tackle these issues, in this paper, we propose a cooperative task offloading scheme for the UAV-enabled MEC systems. Specifically, we consider a UAV-enabled MEC system consisting of a UAV serving as a MEC server for multiple near and far UEs, where each UE has a dividable computation task to be computed and can offload a part of the task to the UAV for computing. The task offloading of each far UE is proposed to be assisted by an associated near UE, where each far UE first sends its task to the associated near UE, and then the near UE offloads its own task and the task from the far UE to the UAV. An iterative algorithm based on the block coordinate descent method is proposed to optimize the UAV’s trajectory, the computation and communication resources for minimizing the weighted sum energy consumption of the UEs and the UAV. Specifically, the UAV’s trajectory is optimized based on the successive convex approximation method, and the computation and communication resources are optimized via the Lagrangian dual method. Simulation results are presented to verify the effectiveness of the proposed algorithm. It is shown that compared to the state-of-the-art algorithms in existing literature, the proposed algorithm achieves much lower energy consumption, especially when the UEs carry more task data.

Toward Multiple Federated Learning Services Resource Sharing in Mobile Edge Networks

Federated Learning is a new learning scheme for collaborative training a shared prediction model while keeping data locally on participating devices. In this paper, we study a new model of multiple federated learning services at the multi-access edge computing server. Accordingly, the sharing of CPU resources among learning services at each mobile device for the local training process and allocating communication resources among mobile devices for exchanging learning information must be considered. Furthermore, the convergence performance of different learning services depends on the hyper-learning rate parameter that needs to be precisely decided. Towards this end, we propose a joint resource optimization and hyper-learning rate control problem, namely <inline-formula><tex-math notation="LaTeX">${{\sf MS-FEDL}}$</tex-math></inline-formula> , regarding the energy consumption of mobile devices and overall learning time. We design a centralized algorithm based on the block coordinate descent method and a decentralized JP-miADMM algorithm for solving the <inline-formula><tex-math notation="LaTeX">${{\sf MS-FEDL}}$</tex-math></inline-formula> problem. Different from the centralized approach, the decentralized approach requires many iterations to obtain but it allows each learning service to independently manage the local resource and learning process without revealing the learning service information. Our simulation results demonstrate the convergence performance of our proposed algorithms and the superior performance of our proposed algorithms compared to the heuristic strategy.

Joint Waveform and Beamforming Design for RIS-Aided ISAC Systems

In this paper, we consider the problem of joint waveform and passive beamforming design for MIMO integrated sensing and communication (ISAC) systems, where a reconfigurable intelligent surface (RIS) is deployed to assist the downlink communication. The objective is to maximize the signal-to-interference-and-noise-ratio (SINR) for radar and meanwhile minimizing the multi-user interference for communication. To address this problem, a block coordinate descent (BCD) method is proposed. Specifically, given the fixed waveform, an Element-wise Closed-Form (ECF) technique is derived for the reflection coefficients optimization, where the high-dimensional problem is divided into multiple one-dimensional problems with closed-form solution. Then, given fixed reflection coefficients, a dinkelbatchs-ECF algorithm is developed to optimize the waveform. Simulation results show that the proposed method achieves joint sensing and communication improvement and presents a clear performance advantage over existing methods.