Intelligent air-ground integration communication is an emerging technology. Uncrewed aerial vehicles (UAVs) serve as mobile edge computing (MEC) servers in large-scale Internet of Things (IoT) applications, alleviating the computational load on ground users. Existing multi-UAV MEC approaches struggle with the complex computation and large data sizes of deep neural network tasks. To address these challenges, we propose a Deep Reinforcement Learning (DRL)-based DNN Partitioning and Dynamic Trajectory Selection (DPDTS) method, which reduces end-to-end latency and system energy consumption through task offloading and collaborative inference. Specifically, we propose an Optimal Partition Point Selection (OPPS) algorithm to minimize transmission overhead by selecting optimal partition points for DNN tasks. Then, we design a fairness-based matching algorithm to optimize user offloading and resource allocation. Finally, OPPS and matching algorithms are integrated to optimize UAV flight trajectories and user transmission power via DRL. The simulation results show that DPDTS outperforms existing benchmark methods in terms of delay and energy efficiency.

UAV path planning technology is a key technical assurance that enables unmanned aerial vehicles to navigate intelligently and complete tasks safely and smoothly. This paper presents an enhanced Spider Wasp Optimizer based on tangent guidance, specifically applied to UAV path planning. First, to address the challenge of relying on heuristic experience to determine the number of trajectory points in static global path planning, we introduce a tangent-based method for calculating the number of trajectory points. This approach enables the algorithm to dynamically calculate the number of trajectory points according to the terrain's complexity, thereby enhancing the algorithm's overall efficiency. Second, to enhance the convergence speed, accuracy, and solution quality, we design different probabilistic selection factors tailored to the characteristics of each individual. These factors guide individuals in selecting the most appropriate update model. In addition, we introduced the concept of neighborhood in the model update to prevent the deterioration of candidate solution quality caused by the random selection of individuals for position updates, thereby slowing down the convergence speed of the algorithm. Finally, to address the issue of reduced population diversity in the later stages of the original algorithm, we propose a diversion mechanism that reallocates under performing individuals to enhance population diversity. Simultaneously, we apply the Firefly Algorithm to further refine higher-performing individuals, thereby ensuring the algorithm's convergence speed. To evaluate the performance of the proposed algorithm, we designed experimental scenarios with varying levels of difficulty, demonstrating its effectiveness.

With the rapid development of autonomous driving, how to enable unmanned vehicles (UVs) to efficiently avoid multiple dynamically moving obstacles, especially obstacle vehicles (OVs), has become a vital issue in the context of the Internet of Vehicles (IoV). This requires not only high-level adaptability to dynamic and complex traffic environments, but also extraordinarily agility in reacting to possible collision hazards with safer and proactive collision avoidance. Conventional methods, e.g., artificial potential field (APF), may overreact to distant targets which have no risk in collision, generating a false evasion direction when facing multiple OVs. To this end, we propose a novel improved APF-based algorithm along with the trajectory prediction. Specifically, to measure the safety distance for vehicle maneuvering, a trajectory prediction method integrated with unscented kalman filter (UKF) is developed. Then, an obstacle filtering method utilizing sensor information and trajectory prediction results is applied for wiping off collision-free targets. Afterwards, by employing APF method combining with avoidance strategies based on virtual forces and window-based collision detection, the potential pushing effect caused by multiple OVs is mitigated. Experimental results show that, given the scenario of collision avoidance with multiple OVs, the proposed solution can achieve an obstacle avoidance success rate of around 90%, which is about 20% higher than the best benchmark algorithms, simultaneously demonstrating advantages in efficiency and safety.

In remote or high-demand wireless cellular networks, efficient data collection from ground users (GUs) with fixed infrastructure poses a significant challenge. Unmanned aerial vehicles (UAVs) have emerged as a promising solution due to their flexible deployment and cost-effectiveness. This paper focuses on a UAV-aided wireless cellular communication system comprising a UAV and multiple adjacent GUs, where the mission of the UAV is to collect data from these GUs. The objective is to minimize UAV propulsion energy consumption while ensuring fair data uploading among all GUs. Due to the non-convex and intractable nature of the above problem, we propose a novel real-time waypoint localization method based on the parallel projection method from a geometric perspective. By enhancing the projection process, this approach achieves energy-efficient and fair data collection, along with an efficient trajectory design algorithm. Further, considering the scenario of densely distributed GUs in large-scale areas, a GU-clustering algorithm is proposed based on Mean Shift. Additionally, this paper categorizes GUs into homogeneous and heterogeneous scenarios and designs distinct trajectory designing algorithms to accommodate diverse real-world situations. Simulations and comparisons validate the effectiveness and efficiency of the proposed algorithms in tackling the UAV trajectory design challenges.

Electroencephalography (EEG) biometrics draws increasing attention in high-security requirements due to its advantages of anti-spoofing, live traits, and non-duplicated. However, existing EEG datasets, which rely on external stimuli or task-specific instructions for data collection, often intertwine identity-related information with biases such as emotional states, cognitive tasks, and disease markers. Besides, EEG signals are time-varying, while identity information within EEG signals is relatively fixed, which poses challenges for extracting identity features from EEG to perform accurate person identification. This high correlation hampers the promotion of brainprint recognition in real-life applications. In this paper, we propose a disentangled representation learning based identity recognition framework, which disentangles the EEG signal into intrinsic identity-related information and biased identity-invariant information, thus enhancing the performance of EEG biometrics. First, two parallel encoders are used to extract intrinsic identity-relevant and bias identity-irrelevant factors, respectively, and each encoder consists of a temporal filter module and a novel spatial-temporal attention module. Then, we further refine the disentanglement process through a correlation-driven loss that minimizes factor similarity across spatial-temporal and global representational domains. Adversarial training and reconstruction regularization are introduced to facilitate the identity and biased representations to be independent and complementary to each other. Additionally, we extend supervised contrastive learning to the component level, minimizing cross-component similarity and encouraging each component to independently reflect its unique information, thereby improving the disentanglement efficacy. Our proposed framework achieves state-of-the-art performance on diverse datasets encompassing emotional, motor imagery, and pathological conditions, demonstrating the robustness and effectiveness of our proposed brainprint identity recognition model.

Drones have become an indispensable tool in our daily lives. While fixed-wing and rotary-wing drones are common types, each comes with its own set of advantages and disadvantages. Hybrid drones, however, combine the strengths of both types, enabling vertical takeoff and landing, hovering, and remote flight. Nonetheless, the aerodynamics of hybrid drones are exceedingly intricate, leading to a sluggish pace in their development. In this article, we propose a neural network controller design, employing the reinforcement learning Proximal Policy Optimization (PPO) algorithm to train the controller. Additionally, we integrate an attention mechanism into the network's input section to emphasize the speed variable, thereby enhancing the data processing and improving the model performance and efficiency. Experimental results demonstrate that our approach yields a controller with superior stability and optimal value.

Federated learning, as a distributed machine learning method, has gained extensive adoption within resource-constrained Internet of Things (IoT). However, the challenge of client selection has persistently remained a pivotal concern in federated learning. This problem faces the dual challenges of statistical heterogeneity and systematic heterogeneity. Selecting representative clients while preserving privacy and reducing client dropout has become a pressing concern. Neglecting the constraints of client resources can lead to a heightened client dropout rate and a decline in model accuracy. In order to address this challenge, this paper introduces FedCDRC, a federated learning client selection framework tailored for resource-constrained IoT devices. FedCDRC clusters clients using representative gradients and divides them into groups based on clustering results. Each group considers various resource factors, such as CPU cycle frequency, transmission rate, and remaining energy, to calculate selection costs. These costs, combined with dataset sizes, determine client sampling probabilities. We conducted experiments on both MNIST and CIFAR-10 datasets, considering scenarios of both independent and identically distributed (IID) and non-IID clients. The experimental results demonstrate that FedCDRC outperforms two baseline methods in achieving the fastest convergence rate while improving test accuracy by 7.23% - 18%. Additionally, it effectively reduces the client dropout rate, highlighting its suitability for resource-constrained IoT devices.

As an aerial service platform for Internet of Things (IoT), unmanned aerial vehicle (UAV) can provide integrated sensing, computing and communication (ISCAC) services for the IoT nodes. In this paper, a UAV-enabled ISCAC system is proposed for IoT to meet the evolving requirements of emerging services in 6G networks. This system has three functions: sensing user equipments (UEs) for acquiring radar sensing information, executing computing tasks, and offloading incomplete tasks to the access point (AP) for further processing. Through jointly optimizing UAV CPU frequency, UAV radar sensing power, transmit power of UEs, and UAV trajectory, the weighted total energy consumption of both the UAV and the UEs can be minimized. We present a three-layer iterative optimization algorithm to tackle the original non-convex optimization problem. Finally, the effectiveness of the algorithm and its superiority in energy consumption compared to other benchmark schemes are verified through simulation results.

Compared to single unmanned aerial vehicle (UAV), multi-UAVs formation has garnered significant attention due to their advantages in collaborative task execution, task allocation, as well as heightened redundancy and reliability. This paper investigates a UAV rendezvous system comprising multiple UAVs with random positions and velocities. We introduce the concept of a virtual leader, with the objective of transforming the formation control problem of UAVs into tracking the positional movements of the virtual leader. We model the exploration of the optimal position for the virtual leader as a Markov decision process and propose a variablestep exploration algorithm combined with deep reinforcement learning techniques, guiding the virtual leader towards its optimal position from its initial location. The experimental simulation results ultimately demonstrate the effectiveness of our approach.

As an essential part of mobile networks, vehicular ad hoc networks (VANETs) are beneficial to the improvement of traffic efficiency and safety through real-time information sharing between vehicles. Digital Twins (DT) have been utilized to facilitate the design, testing, and deployment of VANETs. However, constructing Digital Twins still faces interference from malicious vehicles. Despite most vehicles following communication rules honestly, the reliability and authenticity of traffic messages cannot be guaranteed due to the network’s openness and vulnerability. Meanwhile, vehicles may suffer tracking attacks during the interaction without an effective privacy-preserving method, leading to the leakage of sensitive data. To address these issues, a decentralized trust management scheme embedded with blockchain that considers identity authentication is proposed to detect malicious DT-vehicles. In our method, each vehicle in the Digital Twin of VANETs (DT-VANETs) is equipped with a certificate recorded on the blockchain as a legal identity, which is also served as a pseudonym for security during message transmission. The trustworthiness of the vehicle is evaluated based on direct trust and recommendation trust. Direct interaction between vehicles consists of message authenticity verification and active detection, which are the basis of direct trust calculation. For other vehicles, these direct trust opinions are treated as second-hand information to obtain recommendation trust. Unreliable recommendations are filtered by our proposed RTF algorithm, further resisting cooperation attacks. Vehicles judged to be malicious will have their certificates revoked and removed from DT-VANETs, providing a guarantee for the establishment of trust in DT-VANETs. Experimental results show that the proposed scheme can effectively resist malicious attacks in DT-VANETs.

Network Functions Virtualization (NFV) replaces the specialized hardware with the software-based forwarding to promise the flexibility, scalability and automation benefits. With an increasing range of applications, NFV must ultimately forward packets at rates that are comparable to the native and specialized hardware-based approaches. However, the transition packet forwarding from specialized hardware to software-based has turned out to be more challenging than expected. Thus, NFV acceleration is desperately needed to play a crucial role in the development of NFV. It is an interesting issue how to address the persistent performance tuning in a way that provides far greater flexibility to meet the demands of power. The existing developments are very inefficient, since that the uncontrollable and unanticipated performance regressions frequently occur. Besides, the environments for full system simulations are traditionally expensive and time consuming to evaluate the system performance. In this paper, we propose the methodology named as “NFV Acceleration via Lean Measurements (NALM)” to tune the performance for the NFV acceleration. NALM provides a holistic measurement approach through combining individual measures to quickly identify the bottlenecks, which can help developers with a better understanding of the design tradeoffs. Moreover, the environments for large scale performance simulation are replaced by a debugger. Thus, the waste is eliminated in terms of time consumption and infrastructure costs of the full system simulation. The systematic analysis of the multi-cores speedup ratio highlights the potential optimization space and rules. We further propose the improvement recommendations on efficient practices. The experiments evaluate the specific effects, and the relationship between the metrics and forwarding performance.

Unmanned Aerial Vehicles (UAVs) can be used as aerial base stations for data collection in next-generation wireless networks due to their high adaptability and maneuverability. This paper investigates the scenario where multiple UAVs cooperatively fly over heterogeneous ground users (GUs) and collect data without a central controller. With the consideration of signal-to-interference-and-noise ratio (SINR) and fairness among users, we jointly optimize the trajectories of UAVs and the GUs associations to maximize the total throughput and energy efficiency. We formulate the long-term optimization problem as a decentralized partially observed Markov decision processes (DEC-POMDP) and derive an approach combining the coalition formation game (CFG) and multi-agent deep reinforcement learning (MADRL). We first formulate the discrete association scheduling problem as a non-cooperative theoretical game and use the CFG algorithm to achieve a decentralized scheme converging to Nash equilibrium (NE). Then, a MARL-based technique is developed to optimize the trajectories and energy consumption continuously in a centralized-training but decentralized-execution manner. Simulation results demonstrate that the proposed algorithm outperforms the commonly used schemes in the literature, regarding the fair throughput and energy consumption in a distributed manner.

In this paper, an energy-efficient resource management framework for industrial Internet of Things (IIoT) with closed-loop control on end devices, edge servers (ESs) and cloud center (CC) is studied. In the considered model, each ES aggregates the data collected by industrial sensors (i.e., end devices) and forms computation tasks for corresponding data analysis. In order to minimize the system-wide energy consumption, while maintaining a guaranteed service delay and a satisfied data processing accuracy for each IIoT application, a joint optimization of i) sensors’ sampling rate adaption, ii) ESs’ preprocessing mode selection and iii) edge-cloud communication and computing resource allocation, is formulated. Further taking into account the time-varying channel conditions and randomness of data arrivals, we propose a low-complexity online algorithm, which solves the problem in a dynamic manner. Performance analyses and simulation results show that the proposed algorithm is superior compared to counterparts in terms of energy efficiency and delay performance under service satisfaction constraints.

Unmanned aerial vehicles (UAVs) can serve as mobile base stations (MBSs) to provide wireless communication for ground terminals (GTs). This paper proposes a novel polynomial-time method to place MBSs, in order to minimize the number of MBSs ensuring each GT is within the wireless coverage of at least one MBS. The proposed algorithm transforms the deployment problem of MBSs into a minimum clique partition problem with the minimum enclosing circle coverage constraint. Based on the distance between GTs and the coverage radius of MBSs, the algorithm constructs an undirected graph $G(V,E)$ to denote the adjacent information between GTs. In our algorithm, the GT with the minimum degree is given a higher priority to deploy MBSs, and the location of each MBS will be refined gradually to cover as many as possible GTs. Numerical results show that, in the case where there are no capacity constraints for MBSs, the proposed algorithm performs advantageously over other algorithms in terms of the required number of MBSs as well as runtime overhead. Besides, we also analyze the impact of the capacity constraint of MBSs on the number of required MBSs, and compare the proposed algorithm with the Edge-prior algorithm on the case with the capacity constraint, showing that our algorithm requires fewer MBSs especially when the capacity of MBSs is high.

Due to the flexible deployment and low cost of unmanned aerial vehicle (UAV), the integration of UAV and wireless cellular networks is widely regarded as a promising technology to enhance the performance of wireless cellular communications. This paper considers a UAV-aided wireless cellular communication system with multiple adjacent ground users (GUs), where the primary mission of UAV is to collect data from all of the GUs. We take the GUs as the topological nodes and combine their communication ranges to construct a ground topology structure (GTS), with the purpose of designing a reasonable trajectory for the UAV to execute the data collection tasks, while ensuring the fairness of transmission among all of GUs. In order to solve these problems, we utilize parallel projection algorithm onto homogeneous and heterogeneous GTS respectively to obtain a group of waypoints which construct the UAV trajectory, we formulate the fairness of data collection as a min-max problem. Finally, simulation experiments show the trajectory design results of the homogeneous and heterogeneous GTS respectively. Numerical results further vaildate the effectiveness of our proposed algorithms.

The traditional ground industrial Internet of Things (IIoT) cannot supply wireless interconnections anywhere due to its small-scale communication coverage. In this article, a multibeam satellite IIoT in Ka-band is proposed to realize wide-area coverage and long-distance transmissions, which uses nonorthogonal multiple access (NOMA) for each beam to improve transmission rate. To guarantee Quality of Service (QoS) for the satellite IIoT, the beam power is optimized to match the theoretical transmission rate with the service rate. The NOMA transmission rate for each beam is maximized by optimizing the power allocation proportion of each node subject to the constraints of the total power for the beam and the minimal transmission rate for each node within the beam. Satellite-ground integrated IIoT is proposed to use the ground cellular network to supplement the satellite coverage in the blocked areas. The power allocation and network selection for the integrated IIoT are proposed to decrease the transmission cost. Simulation results are provided to validate the superiority of employing NOMA in the satellite IIoT and show higher transmission performance for the QoS-guarantee resource allocation.

Along with the exponentially increasing quantity of intelligent terminals connected to the Internet, the spectrum competition among users becomes more and more severe in wireless networks. The network have not the ability to satisfy all communication requirements due to the significantly increasing users and demanded rates. Energy-aware admission control has been proved to be an efficient way to tackle the infeasibility caused by the severe spectrum competition among users. However, the traditional admission control is limited by gradually removing chosen users, and pays less attention to the fairness. In this article, we elaborate the concept of the fairness in a max-min optimization problem with respect to the transmission rates, by leveraging the model of bit error rates with Q-function for general fading communications. Then, we make use of the max-min rate fairness to smartly determine the subset of users to be admitted in wireless networks. Meanwhile, the overall energy consumption is minimized and the network fairness is guaranteed. In particular, the algorithms can tackle more than one user at each iteration. Numerical evaluations show the effectiveness of the algorithms.

In recent years, the Internet of Things (IoT) has developed rapidly after the era of computers and smart phones, which is expected to be applied to cities to improve the quality of life and realize the intelligence of smart cities. In particular, with the outbreak of coronavirus disease 2019 (COVID‐19) last year, in order to reduce contact, some IoT devices, such as robots, unmanned aerial vehicles (UAVs), and unmanned vehicles, have played a great role in temperature monitoring, goods delivery, and so on. In this paper, we study the real‐time task allocation problem of heterogeneous UAVs searching and delivering goods in the city. Considering the resource requirement of task and resource constraints of the UAV, when the resource of a single UAV cannot meet the requirement of the task, we propose a method of forming a UAV coalition based on contract net protocol. We analyze the coalition formation problem from two aspects: mission completion time and UAV’s energy consumption. Firstly, the mathematical model is established according to the optimization objective and condition constraints. Then, according to the established mathematical model, different coalition formation algorithms are proposed. To minimize the mission completion time, we propose a two‐stage coalition formation algorithm. Aiming at minimizing the UAV’s energy consumption, it is transformed into a zero‐one integer programming problem, which can be solved by the existing solver. Then, considering both mission completion time and energy consumption, we propose a coalition formation algorithm based on a resource tree. Finally, we design some simulation experiments and compare with the task allocation algorithm based on resource welfare. The simulation results show that our proposed algorithms are feasible and effective.

With rapid development of Internet of Things (IoT) and pervasive computing, indoor localization and tracking has attracted considerable attentions. This work aims at designing an effective and scalable indoor tracking system based on smart phones embedded with Wi-Fi interfaces and inertial sensors. Specifically, we first propose a zero site-survey overhead algorithm (ZSSO), which includes a step detection mechanism, a map constraint construction method and a customized particle filter. The step detection mechanism is used to count user steps based on raw data extracted from inertial sensors. The map constraint construction method is adopted to generate obstacle constraints of the indoor environment based on a two-step conversion method designed for indoor map. Finally, a customized particle filter is proposed to track user's positions continuously. Further, we propose an enhanced version of ZSSO (i.e., E-ZSSO) to improve tracking performance by incorporating with Wi-Fi fingerprint based localization technique. First, an automatic Wi-Fi fingerprint collection mechanism is developed for building the fingerprint database without extra site-survey overhead. Then, the Wi-Fi fingerprint based localization results are further adopted to speed up the convergence of the particle filter as well as to better calibrate the localization results. We have implemented the indoor tracking system in real-world environments and conducted comprehensive performance evaluation. The field testing results conclusively demonstrate the scalability and effectiveness of our proposed algorithms.

Adapting the data rate is an important performance in mobile cloud networking, especially for the fast growth of intelligent terminals. We study a max-min fairness problem for the mobile cloud networking to guarantee the minimal transmit data rate, by leveraging the bit error rate (BER) with Q-function for modeling achievable data rates. We propose a distributed power control algorithm to obtain the optimal solution. Then, we address a total power minimization problem with the given rate requirement constraints. When there are plenty of users and excessive interferences, its feasibility issue is solved by making use of the max-min fairness of the networks. We propose a dynamic algorithm that adapts the rate requirements to minimize the total energy consumption and to simultaneously provide fairness guarantees. Numerical simulations show the efficient performance of the proposed algorithms.

The exponential increase of the intelligent connected devices and the dramatic growth of the wireless data traffic have motivated the development of the green wireless networks as well as the Internet of Things (IoT). In this paper, we study the minimization problem of the total power to satisfy the required rate constraints in IoT, where the users simultaneously communicate through multiple independent channels. This problem is complicated due to the nonlinear data rate function based on the Shannon capacity formula. To this end, we first transfer the initial problem in power domain to an equivalent problem in rate domain instead of direct approximation for the high data rate. Then, we approximate it to a convex problem with the spectral radius constraints by the use of the Neumann expansion and nonlinear Perron-Frobenius theorem. By doing so, we achieve the close upper bound for this total power minimization problem. Moreover, we obtain the lower bound by making use of the convex relaxation technique, and finally get the global optimal solution by leveraging the branch-and-bound method. Simulation results verify that our proposed algorithms have a good approximation to the global optimal value for the power and rate allocations.

Energy efficiency is one important consideration in designing wireless mobile networks to support a large number of battery-powered mobile terminals. To provider a wider coverage to serve more users, wireless carrier infrastructure from various mobile network operators (MNOs) can be pooled together. For example, a cellular system user can access different kinds of cellular broadband networks with multiple transceivers. MNOs however have different heterogeneous rate function characteristics, and thus present new challenges to wireless network optimization. In this paper, we study the design of energy-efficient power control algorithms in a network with multiple MNOs using a unique log- convexity property of the standard interference function approach. Furthermore, the power control algorithms can be enhanced using the congestion level at each MNO.

This paper studies the joint beamforming and power control in a multiuser multi-input single-output network by utilizing the only statistical channel distribution information. Such information consists of slowly varying covariance matrices in the beamforming network that can be employed to reduce instantaneous feedback overhead in transmission. Utilizing solely the statistical channel information, we study how to minimize the maximum outage probability under a weighted sum power constraint that guarantees max-min fairness to all users. This problem is, however, generally hard to solve due to the nonconvexity and nonlinear coupling between beamformer and power variables. First, assuming a fixed beamformer set, we use the nonlinear Perron-Frobenius theory to design a decentralized algorithm with provable geometrically fast convergence rate to compute the optimal power. Then, for the general case, we examine a certainty-equivalent margin counterpart with outage-mapped thresholds that incorporate the statistical channel information. We show that a network duality for this certainty-equivalent problem can be useful to decouple the coupling between the beamformer and power variables. This nonlinear Perron-Frobenius theory motivated approach yields a feasible beamformer and power allocation that are near-optimal as compared to Monte Carlo averaging simulations.

We study the feasibility of the total power minimization problem subject to power budget and Signal-to-Interference-plus-Noise Ratio (SINR) constraints in cognitive radio networks. As both the primary and the secondary users are allowed to transmit simultaneously on a shared spectrum, uncontrolled access of secondary users degrades the performance of primary users and can even lead to system infeasibility. To find the largest feasible set of secondary users (i.e., the system capacity) that can be supported in the network, we formulate a vector-cardinality optimization problem. This nonconvex problem is however hard to solve, and we propose a convex relaxation heuristic based on the sum-of-infeasibilities in optimization theory. Our methodology leads to the notion of admission price for spectrum access that can characterize the tradeoff between the total energy consumption and the system capacity. Price-driven algorithms for joint power and admission control are then proposed that quantify the benefits of energy-infeasibility balance. Numerical results are presented to show that our algorithms are theoretically sound and practically implementable.

Epidemic evolution is the spread of a computer or biological virus over a network. The goal is to control the speed of the epidemic evolution with limited network control resources and to study how users in the network can be infected. The epidemic evolution can be modeled by a probabilistic dynamical system over a connected graph. We consider several epidemic evolution models in the literature, and formulate their evolution control under a common framework that requires solving a non convex optimization problem with an objective that is the spectral radius function of a nonnegative matrix. We propose two algorithms to tackle this optimization problem. The first one is a suboptimal but computation ally fast algorithm based on successive convex relaxation, while the second one can compute a global optimal solution using branch-and-bound techniques that leverage some key inequalities in non negative matrix theory.