Lagrange Dual Decomposition Research Articles

A heuristic approach to energy efficient user association in ultra‐dense HetNets using intermittent scheduling strategies

AbstractThe ultra‐dense deployment of pico cells in 5G heterogeneous networks (HetNets) has raised serious concerns regarding interference and energy consumption. Both industry and academia are focusing on enhancing network energy efficiency (EE) while maintaining satisfactory quality of service (QoS) levels. However, finding an optimal solution to NEE is very challenging, especially in ultra‐dense HetNets. Here, a user association and power management algorithm is presented that follows a heuristic approach and aims to maximize EE while satisfying other network requirements. The proposed algorithm associates users based on criteria that consider the users’ EE and minimizes energy consumption by intermittently switching into sleep mode base stations with the highest impact on overall network EE. The performance of this solution is evaluated in a realistic multi‐cell two‐tier scenario considering both co‐tier and cross‐tier interference by comparing it with two other solutions: a heuristic approach based on standardized eICIC, and an optimization approach based on Lagrangian dual decomposition. The simulation results show that our solution outperforms benchmarking solutions in terms of EE, average user rate, and network throughput while minimizing energy consumption.

Power allocation scheme for sum rate and fairness trade-off in downlink NOMA networks

Non-orthogonal multiple access (NOMA) is an essential enabler technology that is expected to help satisfy the key requirements of increased system throughput in future wireless networks. However, another equally important aspect that should go hand-in-hand with system throughput is user fairness for any network. But, to the best of our knowledge, even though there have been works that look at system throughput or user fairness maximization for NOMA-based networks, they looked at these as a single objective optimization problem, where one is the objective and the other is one of the constraints. However, quite often, joint optimization of both system throughput and user fairness is required to make optimized decisions in the face of trade-offs between these two equally important but conflicting objectives. In this regard, this paper formulates a multi-objective optimization problem to jointly maximize the sum rate and user fairness in a downlink transmission NOMA system, through optimize power allocation (PA), under system-imposed constraints. A weighted sum approach is used to turn the multi-objective optimization problem into a single-objective optimization problem to make it analytically tractable. The optimized PA is then obtained using Lagrange dual decomposition method and Karush–Kuhn–Tucker (KKT) conditions. Using our derived expressions, we propose an iterative PA algorithm that converges fast enough to be employed in practical NOMA networks. We also present simulation results to highlight the effectiveness of the proposed solution. Further, the performance of the proposed method is compared with that of the benchmark methods.

A highly efficient resource slicing and scheduling optimization algorithm for power heterogeneous communication networks based on hypergraph and congruence entropy

New services, such as distributed photovoltaic regulation and control, pose new service requirements for communication networks in the new power system. These requirements include low latency, high reliability, and large bandwidth. Consequently, power heterogeneous communication networks face the challenge of maintaining quality of service (QoS) while enhancing network resource utilization. Therefore, this paper puts forward a highly efficient optimization algorithm for resource slicing and scheduling in power heterogeneous communication networks. Our first step involves establishing an architectural description model of heterogeneous wireless networks for electric power based on hypergraph. This model characterizes complex dynamic relationships among service requirements, virtual networks, and physical networks. The system congruence entropy characterizes the degree of matching between the service demand and resource supply. Then an optimization problem is formed to maximize the system congruence entropy through dynamic resource allocation. To solve this problem, a joint resource allocation and routing method based on Lagrangian dual decomposition is proposed. These methods provide the optimal solutions of the nodes and link mappings of service function chains. The simulation results demonstrate that the proposed algorithm in this paper can greatly enhance resource utilization and also meet the QoS requirements of various services.

Transmission Investment Coordination Using MILP Lagrange Dual Decomposition and Auxiliary Problem Principle

Transmission Investment Coordination Using MILP Lagrange Dual Decomposition and Auxiliary Problem Principle

A Distributed Scheme for the Taxi Cruising Route Recommendation Problem Using a Graph Neural Network

Despite considerable research efforts being devoted to the taxi cruising route recommendation (TCRR) problem, existing studies still have some shortcomings. To begin with, the competition and collaboration between taxis are not sufficiently taken into account. Furthermore, the TCRR is heavily reliant on potential taxi demand, which is time-variant and difficult to accurately predict due to the underlying spatiotemporal correlation and dynamic traffic patterns. Moreover, the consideration of competition and cooperation among taxis increases the complexity of the TCRR problem, making conventional centralized algorithms computationally expensive. In this paper, we first formulate TCRR as a biobjective optimization problem to balance the collaboration and competition between taxis. Subsequently, we forecast short-term taxi demand using the proposed long-short-term-memory-based graph convolutional network (LSTM-GCN), which considers diverse factors such as road topology, points of interest (POIs), and multiple time-scale features. Lastly, we propose a distributed algorithm based on a Lagrange dual decomposition. The experimental and simulation results demonstrate that our TCRR scheme performs better than any other counterpart, (i) resulting in a 3% reduction in idle taxis per hour, (ii) performing four times faster than the centralized algorithms to obtain the optimal solution, and (iii) resulting in a 7% increase in average profit.

Learning-Based Multi-UAV Assisted Data Acquisition and Computation for Information Freshness in WPT Enabled Space-Air-Ground PIoT

The explosion of information data in the power Internet of Things (PIoT) poses difficulties for data acquisition and computation of power devices located in remote areas with limited computing capability and energy. Therefore, we propose a multi-unmanned aerial vehicle (UAV) assisted wireless power transmission (WPT) enabled space-air-ground PIoT framework, in which the UAVs provide energy for data acquisition of power devices through WPT, and use mobile edge computing (MEC) technology to calculate the data. Finally, they act as relays to forward the data to the low earth orbit (LEO) satellite. For keeping the data fresh, we jointly optimize the number of UAV hovering positions, the hovering positions, the connection between UAVs and power devices, the energy transmission and data acquisition time of power devices, the computing resources, flight speed and trajectories of UAVs, aiming to minimizing the average age of information (AoI) of power devices. Through theoretical derivation the problem is decoupled into five independent subproblems, which are solved using improved K-means algorithm, Lagrangian dual decomposition method, interior point method, adaptive optimization, and Q-Learning algorithm, respectively. Extensive numerical simulations demonstrate the superior properties of our solution comparing to benchmark algorithms.

Resource management for sum-rate maximization in SCMA-assisted UAV system

This work presents a resource management framework for optimizing the sum-rate in a sparse code multiple access (SCMA)-assisted UAV downlink system. We formulate two optimization problems for maximizing the overall sum-rate: the first problem addresses UAV 3D deployment and trajectory optimization with energy constraints, while the second focuses on optimizing SCMA subcarrier and power allocation optimization, subject to factor graph matrix (FGM) constraints and a minimum user data rate. Since the optimization problems are non-convex, the complexity of finding the global optimal solutions is prohibitive. We propose a gradient ascent-based iterative algorithm to compute the optimal UAV 3D deployment and trajectory. Further, an effective channel state information-based algorithm is proposed for FGM assignment, followed by a Lagrange dual decomposition method to solve the power allocation problem efficiently. Our research findings demonstrate that the optimization of the UAV trajectory gives improved sum-rate within the specified energy budget. Further, employing CSI-based multiple subcarrier allocation and strategic power allocation can significantly improve system performance compared to the benchmark schemes.

An Energy-Efficient Multimode Transmission Scheme for Underwater Sensor Network

Underwater sensor network plays a critical role in the ocean data collection owing to its capability of providing reliable and wide communication coverage. How to assure lifetime performance of the network with limited energy supply has always been a key research issue. In this paper, we propose an underwater acoustic sensor network model which supports data delivery from each underwater sensor node (USN) to sea surface sink node (SN) in either direct or relay-assisted transmission mode, i.e., transmission mode between each USN and the SN can be dynamically selected according to network’s current state. To optimize its lifetime performance, we model the mode selection and resource allocation issue jointly into a non-convex and mixed integer programming problem. In order to efficiently solve it, we further divide the original problem into two subproblems: resource allocation subproblem and joint mode and relay selection subproblem. We prove that the reformulated non-convex resource allocation problem can be equivalent to a convex optimization problem, and its optimal solution can be found by using Lagrange dual decomposition method. For the second subproblem, some critical conditions are analyzed to determine optimal relays with the criterion of balancing energy consumption between USNs and a matching approach is designed to obtain the mode and relay selection results based on USNs’ priorities. Simulation results validate that the proposed transmission scheme is effective and superior to the traditional time division multiple access scheme.

Energy-Efficient Beamforming Design for RIS-Aided MIMO Downlink Communication With SWIPT

This paper investigates an energy/power-efficient simultaneous wireless information and power transfer (SWIPT)-enabled reconfigurable intelligent surface (RIS)-assisted multi-input multi-output (MIMO) communication network, where a base station (BS) communicates with multiple information receivers (IRs) and energy receivers (ERs) simultaneously with the aid of a RIS. We formulate a power minimization problem and jointly optimize the active beamforming matrix at the BS and passive beamforming matrix at the RIS subject to the constraint of the minimum required rate at each IR while ensuring the minimum energy harvesting requirement of ERs. Due to the non-convex nature of the formulated problem, we transform the minimum rate constraint into a simpler form by adopting a mean square error (MSE) based approach. Next, an alternating optimization (AO) method is adopted to transform the main non-convex problem into two simpler sub-problems, for obtaining the optimal active and passive beamforming matrices, respectively. Thereafter, computationally efficient algorithms are proposed to determine the optimal solutions of each sub-problem utilizing optimization tools such as Lagrangian dual decomposition, sub-gradient method, majorization-minimization (MM) and pricing-based approaches. Then, we also propose an AO-based iterative algorithm that obtains the optimal values of both matrices iteratively by repeatedly using the aforementioned sub-optimal solutions. We also discuss the impact of imperfect channel state information (CSI) on the performance of the considered network and demonstrate the effectiveness of the proposed algorithm in providing an efficient beamforming design for the same. In addition to this, we highlight the impact of key system parameters such as the number of reflecting elements, and the minimum rate constraint. Finally, we establish that the use of an RIS in such a network along with the proposed algorithm provides a power saving of approximately 10%-26% compared to the other traditional schemes to achieve the same quality of service.

Joint computation offloading and resource allocation in space-air-terrestrial integrated networks for IoT Applications

Internet of Things (IoT) devices can reduce their energy consumption by computation offloading. However, IoT devices located in areas without deployed ground communication facilities face significant challenges in computation offloading. For this reason, we propose the space-air-terrestrial integrated networks (SATINs) and design a three-tier computing framework for providing computing services to IoT devices. In the computing framework, device's task can be computed locally, on mobile edge computing (MEC) servers in the air layer, or on cloud servers in the ground. In this article, we jointly optimize the computation offloading decisions of tasks and computing resource allocation of MEC servers. We aim at minimizing the total cost of executing tasks while satisfying both the time constraints of tasks and capacity constraints of MEC servers. And the total cost includes the energy cost of IoT devices and the usage cost of servers. Since the computation offloading decisions are binary variables, the joint optimization problem is a mixed integer nonlinear programming (MINLP) problem and is NP-hard. To tackle this problem, we use relaxation technique and Majorize-minimize (MM) method to transform the optimization problem into a series of convex problems for solving. Moreover, we propose a distributed algorithm based on Lagrange dual decomposition method with low time complexity. Experimental results demonstrate that our proposed distributed algorithm can effectively reduce the total cost of the system compared with other benchmark algorithms.

UAV-Aided Vehicular Short-Packet Communication and Edge Computing System Under Time-Varying Channel

In this paper, a novel UAV-aided vehicular edge computing (VEC) network is proposed, where the vehicle and on-board UAV provide multi-access edge computing (MEC) service for the roadside Internet of Things (IoT) devices. In this system, considering the time-varying channel, we derive the lower bound of signal-to-noise ratio (SNR) based on the first-order Gauss-Markov process. Then, with the short-packet transmission, we maximize the total amount of computation by jointly optimizing the communication scheduling, the trajectories of the vehicle and on-board UAV, and the computing resource, subject to the mobility, connection and computation constraints. The formulated optimization problem is a mix-integer non-convex problem. To efficiently solve it, we propose an alternative algorithm based on the Lagrangian dual decomposition and successive convex approximation technique. Extensive simulation results are provided to show the performance gain of the proposed algorithm.

Federated Learning Over Fully-Decoupled RAN Architecture for Two-Tier Computing Acceleration

Two-tier computing paradigm that takes full advantage of both the end-user and the cloud computation capabilities has emerged as a promising way to deal with computationally-intensive tasks in the next generation wireless networks. For promoting the integration of the two-tier computing, federated learning (FL) provides an effective framework to enable the collaboration between the end-user and the cloud. However, the key performance metric, i.e., FL training latency, will be severely affected by the worst wireless link quality in both uplink and downlink. In this paper, aiming at accelerating the FL enabled end-cloud two-tier computing over the wireless networks, we introduce the uplink and downlink fully-decoupled radio access network (FD-RAN) architecture to enhance the minimum wireless link rate via multiple base stations (BSs) access collaboration and power management solution. First, the Lagrange dual decomposition and the binary variable relaxation methods are leveraged to obtain an optimal multiple BS access scheme for the enhancement of minimum uplink and downlink SINR. Subsequently, we exploit the successive convex approximation (SCA) algorithm to deal with the uplink power control and downlink power allocation with a proved data rate lower bound. Furthermore, considering the dynamic channel realizations, a stochastic optimization technique with a convex surrogate function is utilized to find the best end-cloud two-tier computing scheme for FL applications. Simulation results have demonstrated the effectiveness of our proposed joint multiple access collaboration and power management solution over FD-RAN for achieving a faster FL enabled two-tier computing task.

Joint Communication, Computing, and Caching Resource Allocation in LEO Satellite MEC Networks

Driven by the urgent requirement of ubiquitous and reliable coverage for global users, the low earth orbit (LEO) satellite network has attracted numerous attentions from the academic and industry circles. By deploying multi-access edge computing (MEC) servers in LEO satellites, computation offloading and content caching services can be provided for remote Internet-of-Things (IoT) devices without proximal servers. In this paper, the joint optimization of computation offloading, radio resource allocation and caching placement in LEO satellite MEC networks are investigated. The problem is formulated to minimize the total delay of all ground IoT devices while ensuring the energy, computing and caching constraints. To solve this mixed-integer and non-convex problem, a Lagrange dual decomposition (LDD)-based algorithm is proposed to obtain the closed-form optimal solution. Then, a heuristic algorithm is proposed to further reduce the computation complexity. Numerical results validate that both algorithms are effective compared to the optimal exhaustive search, the full local computing and the full MEC methods. Besides, the offloading ratio and the average delay of all IoT devices with different numbers and computing capacities of devices and satellites are also demonstrated.

Joint Trajectory Plan and Resource Allocation for UAV-Enabled C-NOMA in Air-Ground Integrated 6 G Heterogeneous Network

Leveraging unmanned aerial vehicles (UAVs) for access and high altitude platform stations (HAPSs) for data backhaul to construct the Air-Ground Integrated Network (AGIN), is a feasible solution to achieve seamless network coverage for remote IoT devices in future 6 G era. However, since the number of terminals increases exponentially, it is essential to improve spectrum efficiency and throughput of the system. In addition, the limited on-board energy storage of UAVs and finite battery of IoT terminals make the system energy efficiency (EE) a new concern. To cope with the above mentioned challenges, in this study we first put forward a clustered-NOMA (C-NOMA)-enabled heterogeneous AGIN model for remote areas including one HAPS for backhaul and multiple UAVs for access, where C-NOMA is used to obtain both improved system throughput and terminal complexity. Then, we study the joint UAV trajectory plan and resource allocation problem in order to maximize the system EE. Since it is a mixed integer nonlinear programming (MINLP) issue coupled with transmission power, subchannel allocation, UAV trajectory and speed control, this problem is decoupled into two subproblems and solved iteratively. For the first one, the optimal channel and power strategy is obtained by our subchannel allocation and power control for AGIN EE (SAPAE) maximum algorithm according to Lagrange dual decomposition method. For the second, for transforming the nonconvex problem into a convex one, we provide the successive convex approximation-based UAV trajectory and speed optimization for AGIN EE (SUTSAE) maximum algorithm, and then the near-optimal UAV trajectory and flight speed are obtained. We conduct extensive experiments to compare with other benchmark methods. It is shown that the proposed approach is better in EE and spectrum efficiency.

Joint Mode Selection and Resource Allocation for D2D and Femtocell Users in Dense Heterogeneous Networks with Full Frequency Reuse

We consider the problem of joint mode selection and resource allocation for D2D and femtocell users in a three-tier dense heterogeneous network in which all the users can reuse the spectrum. The goal is to maximize their total weighted sum rate, subject to minimum rate requirements and maximum tolerable interference on the cellular system. Since the spectrum can be fully reused, the co-tier and cross-tier interferences among the users result in a mixed integer non-linear, non-convex program that is difficult to solve directly. Using insights into the structure of the interference, we derive a close, conservative approximation of the joint problem that has a convex relaxation that is tight. That enables good solutions to the joint problem to be obtained using a customized iterative algorithm employing the Lagrange dual decomposition method. Since the proposed iterative scheme is semi-distributed, the signaling overhead is mitigated. To further reduce the computational complexity, a low-complexity (primal) decomposition-based method is also introduced, in which we select the transmission mode heuristically based on the traffic level in the network, and then sequentially perform admission control, power control, and sub-channel allocation for the femtocell users and D2D users. Our simulation results indicate that the proposed iterative and heuristic algorithms, on average, achieve around 94% and 82% of the sum rate of the optimal Branch & Bound method, respectively, and do so at much lower computational costs.

Secure Energy Efficiency Maximization for Untrusted Wireless-Powered Full-Duplex Relay Networks Under Nonlinear Energy Harvesting

In this article, we raise the concern on secure energy efficiency (SEE) over the wireless-powered untrusted relay networks with nonlinear energy harvesting (EH). To achieve data confidentiality and secrecy performance enhancement concurrently, the untrusted relay can enable simultaneous energy signal reception and confidential information forwarding during the second phase, where no dedicated energy transmission phase or relaying signal splitting is needed for the energy supply. In particular, with the help of destination jamming, the relay can also harvest energy from source signal and jamming signal during the first phase, which is different from conventional relaying protocol that only harvests energy from source and recycled energy. Considering the nonlinear EH efficiency, our objective is to maximize the SEE through piecewise region selection and power allocation. To address this intractable nonconvex problem, a two-layer algorithm based on optimization decoupling, fractional programming, Lagrange dual decomposition and difference of convex functions (DC) programming is proposed. The core idea of the proposed algorithm is to convert the primary problem into simple subproblems by sequentially exploiting the above-mentioned optimization methods. Simulation results reveal the superior secrecy performance of the proposed scheme. The proposed algorithm achieves near-optimal solutions with faster convergence rate.

Energy-Aware Relay Optimization and Power Allocation in Multiple Unmanned Aerial Vehicles Aided Satellite-Aerial-Terrestrial Networks

With the explosive growth of various connected devices and the supported services, the satellite-aerial-terrestrial network (SATN) can fulfill the requirements of the increasing data traffic with enlarged coverage and enhanced capacity. In particular, utilizing multiple unmanned aerial vehicles (UAVs) as relays in the SATN holds great promise for bringing lots of benefits in terms of high flexibility and high reliability. However, due to the limited power of UAVs and the long distance of the aerial-satellite links, how to improve system energy efficiency (EE) is still a challenging issue since existing works mainly paid their attentions to resource while neglecting relay strategy optimization among multiple UAVs. Toward this end, in this article we explore the problem of system EE maximization through jointly optimizing relay selection and power allocation as well as UAV deployment. An iterative algorithm is presented as our solution via alternately leveraging coordinate ascent and Lagrangian dual decomposition methods. Extensive simulation results demonstrate that our devised optimization strategy can significantly improve system EE and obtain the optimal relay selection and power allocation decisions.

Cloud-Edge-End Collaboration in Air–Ground Integrated Power IoT: A Semidistributed Learning Approach

The combination of air–ground integrated power Internet of Things (AGI-PIoT) and cloud-edge-end collaboration enables flexible coverage and real-time data processing. However, how to achieve intelligent cloud-edge-end collaboration in AGI-PIoT faces several challenges such as dynamics of aerial networks, coupling of resource allocation in multiple layers, timescales, and dimensions, incomplete information, and dimensionality curse. In this article, we propose a FEderated Deep rEinforcement leaRning-based multi-lAyer multi-Timescale multi-dImensional resOurce allocatioN algorithm (FEDERATION). The multilayer multitimescale multidimensional resource allocation problem is decomposed into three subproblems based on Lyapunov optimization. For the subproblem of joint task offloading and power control, a federated deep actor-critic-based semidistributed algorithm is developed. The subproblem of admission control is solved by quadratic programming. The third subproblem is addressed through smooth approximation and Lagrange dual decomposition. Simulation results indicate that FEDERATION outperforms existing algorithms in queuing delay, energy consumption, and convergence.

Autonomous Vehicle Intelligent System: Joint Ride-Sharing and Parcel Delivery Strategy

Autonomous vehicle (AV) integration poses a significant challenge for intelligent transportation systems (ITSs). The ability to automatically coordinate complex AV operations at scale is crucial for advancing the quality of core transportation services, such as ride-sharing and parcel delivery. However, existing studies have only considered either of these two services independently from the other, disregarding the potential benefits of their combined optimization. To address this open problem, we design an autonomous vehicle intelligent system (AVIS) providing joint ride-sharing and parcel delivery services under realistic ride and route constraints. We formulate the joint optimization problem through the scope of mixed-integer linear programming and solve it using the Lagrangian dual decomposition method to ensure scalability. We conduct extensive case studies to evaluate the performance of the proposed AVIS and its constituting components. Our experimental results demonstrate that AVIS can effectively provide both ride-sharing and parcel delivery services while satisfying service requests in transportation networks of various scales. In addition, the distributed method is shown to generate near-optimal solutions in reduced computation time.

Joint CCI Mitigation and Power Control for MC-DS-CDMA in LEO Satellite Networks

We investigate a novel downlink multicarrier direct-sequence code division multiple access (MC-DS-CDMA) resource allocation scheme in the context of low earth orbit (LEO) satellite-ground integrated networks (SGINs). In contrast to the existing MC-DS-CDMA works which mainly focus on delay-tolerant services in terrestrial networks, we consider the heterogeneous delay traffic and take the unique characteristics of LEO satellite systems into account. Specifically, we exploit the channel information, the delay requirement, the buffer state, and the visible time of users to construct a utility function and formulate the resource allocation optimization problem in presence of co-channel interferences (CCI) in LEO satellite-ground heterogeneous systems. We transform the original nonconvex optimization problem into two convex ones and use the Lagrange dual decomposition method to derive the solution. We also design an efficient algorithm dynamically scheduling subcarriers, codes, and transmission power of MC-DS-CDMA. The simulation results confirm the superiority of our work in terms of lower average delay and higher overall throughput.