Lagrange Dual Method Research Articles

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.

Joint Subchannel and Power Allocation for Energy Efficiency Optimization in NOMA Heterogeneous Networks With Energy Harvesting

Nonorthogonal multiple access (NOMA) in heterogeneous networks (HetNets) can effectively improve data rate and spectral utilization by allowing multiple users to share the same channel. However, in trying to meet various requirements of multiuser communication, maintaining a low energy becomes a serious issue in NOMA HetNets. In this article, we study a joint subchannel and power allocation scheme in order to improve the energy efficiency of small cells with energy harvesting unit in NOMA HetNets. In the scheme, we propose a modified Gale–Shapley algorithm based on the interference hypergraph for subchannel allocation that can dynamically adjust the number of small cells on the same subchannel. Furthermore, we optimize the power allocation for small cell users by the Lagrangian dual method. Numerical simulation results are presented to demonstrate that the proposed scheme achieves superior performance compared with the existing well-known methods and traditional orthogonal frequency-division multiple access system.

Energy-Efficient beyond 5G Multiple Access Technique with Simultaneous Wireless Information and Power Transfer for the Factory of the Future

In the Industrial Internet of Things (IIoT), non-orthogonal multiple access (NOMA) has emerged as a viable multiple access method due to its superior efficiency. In this paper, a new power allocation technique for NOMA-enabled IIoT devices is presented with trade-offs between increasing energy efficiency and decreasing power consumption. We present a joint optimization of transmission rate and energy harvesting in simultaneous wireless information and power transfer (SWIPT) NOMA-enabled IIoT devices. With the power splitting (PS) approach, we examine how to improve overall transmission rate and harvested energy, simultaneously, while fulfilling the minimum rate and harvested energy needs of each IIoT device in a SWIPT-enabled NOMA system. An objective function is established by adding transmission rates obtained from information decoding and the transformed throughput from energy harvesting. The combination of management approaches with Industry 4.0 technology provides a viable strategy to decrease industrial production’s energy use. Several performance metrics may be utilized to study manufacturing process optimization. The efficiency of production equipment may be measured by looking at the overall effectiveness (OE) of the equipment in use. We divide the non-convex optimization problem into two sub-problems, based on the Lagrangian duality method, and solve them to find the optimal solution for the non-convex problem. The approach is validated based on physical layer parameter settings that represent potential factory of the future scenarios. Simulation results confirm the effectiveness of the presented method in a SWIPT-enabled NOMA system, provide considerable performance gains over the classic rate maximization strategy, and demonstrate the energy efficiency of the presented method compared with the conventional system. The results show huge potential of our solutions to reduce the future huge energy demand related to factory automation.

Joint Subcarrier and Transmission Power Allocation in OFDMA-Based WPT System for Mobile-Edge Computing in IoT Environment

Mobile-edge computing (MEC) is expected to play an important role in the next-generation of Internet-of-Things (IoT) services with artificial intelligence (AI) by providing the sustainable computation capability of resource-constrained IoT devices. Since the finite battery lifetime has been a longstanding challenge of the MEC system for IoT services, the wireless power transfer (WPT) technology has been recently developed for the MEC system in order to support the perpetual operation of IoT devices. In this article, we introduce two resource allocation problems for OFDMA-based WPT-MEC systems: 1) a max–min energy fairness (MMEF) problem and 2) a power sum maximization (PSM) problem. These problems ensure high-performance computations for AI-based applications, where the network reliability and the tremendous power consumption may be required. Moreover, we incorporate a logarithmic nonlinear energy harvesting (EH) model into our formulated problems, which lead to nonconvex mixed-integer nonlinear programming (MINLP) problems. In order to resolve these NP-hard problems, we convert the proposed problems into their equivalent convex forms by applying the continuous relaxation method. The near-optimal solutions are thereby obtained in closed-form expressions by leveraging the Lagrangian duality method for each relaxed problem. Numerical results are presented to validate the merits of the proposed algorithms of MMEF&PSM over the alternative benchmark algorithm and provide significant insights on the effects of the key system parameters, including the number of IoT devices and power transmission subcarriers.

Energy Minimization for Intelligent Reflecting Surface-Assisted Mobile Edge Computing

Intelligent reflecting surface (IRS) has been increasingly considered in mobile edge computing (MEC), assisting smart terminals (STs) in offloading computationally-intense tasks to base stations (BSs). This paper presents a new IRS-assisted MEC framework, which jointly optimizes the local CPU frequencies of the STs, the receive beamformers of the BS, the ST offloading schedules, and the IRS phase configuration, to minimize the energy consumption of the STs. To this end, we reveal that the optimal CPU frequency is time-invariant for each ST. Under flat-fading channels, the IRS phases and the receive beamformers of the BS can be then decoupled from the offloading schedules. Based on this structure, we develop an alternating optimization to solve the IRS phase configuration and the receive beamformers, and then exploit the Lagrange duality method to solve the offloading schedules. We prove that the overall algorithm is guaranteed to compute a stationary point solution for the problem of interest with a low complexity. Under frequency-selective channels, we also develop a new alternating optimization algorithm to minimize the energy consumption, where manifold optimization is leveraged to effectively solve the IRS phase shifts. Numerical results show that the proposed algorithms are superior to existing techniques in terms of energy efficiency under both flat-fading and frequency-selective channels.

Joint Task Partition and Resource Allocation for Multiuser Cooperative Mobile Edge Computing

Exploiting the idle computation resources distributed at wireless devices (WDs) can enhance the mobile edge computing (MEC) computation performance. This paper studies a multiuser cooperative computing system consisting of one local user and multiple helpers, in which the user solicits multiple nearby WDs acting as helpers for cooperative computing. We design an efficient orthogonal frequency-division multiple access- (OFDMA-) aided three-phase transmission protocol, under which the user’s computation-intensive tasks can be executed in parallel by local computing and offloading. Under this setup, we study the energy consumption minimization problem by optimizing the user’s task partition, jointly with the communication and computation resources allocation for task offloading and results downloading, subject to the user’s computation latency constraint. For the nonconvex problem, we first transform the original problem into a convex one and then use the Lagrange duality method to obtain the globally optimal solution. Compared with other benchmark schemes, numerical results validate the effectiveness of the proposed joint task partition and resource allocation (JTPRA) scheme.

Energy Efficient Resource Allocation for IRS Assisted CoMP Systems

A novel intelligent reconfigurable surface (IRS) assisted coordinated multi-point (CoMP) system is proposed. Our objective is to maximize the energy efficiency (EE) of this system by jointly optimizing base station (BS) clustering, user association, sub-carrier assignment, power allocation, and optimal design of the IRS, while satisfying the users’ quality of service requirements. Considering the amplitude and phase shift characteristics, both ideal and non-ideal IRS are investigated. The formulated problem is proved to be NP-hard. By analyzing its structure, we decouple it into the power allocation sub-problem, the BS clustering, UE association, and sub-carrier assignment sub-problem, and the reflection coefficients design sub-problem. For the power allocation sub-problem, we invoke the fractional programming to find the optimal solution. For the reflection coefficients design sub-problem of ideal IRS, the optimal solution is derived with the Lagrangian dual method. Whereas quantization-based method is employed to find the discrete phase shifts for non-ideal IRS. We finally propose a genetic algorithm (GA) to represent the potential solutions of sub-carrier assignment, and combine the other two optimization algorithms as fitness estimator in GA. Numerical results validate the feasibility, fast convergence, and the flexibility of the proposed algorithm. It shows that the proposed scheme outperform the system without IRS and that with a random initialized IRS.

Proactive Eavesdropping for Wireless Information Surveillance Under Suspicious Communication Quality-of-Service Constraint

This paper investigates a proactive eavesdropping scenario where multiple suspicious communication (SC) links are eavesdropped by a full-duplex monitor who can send jamming or constructive signals on each SC link. In order to avoid being discovered by the suspicious users, the monitor restricts the SC quality-of-service (QoS) degradation caused by itself. Under this SC QoS constraint and the average transmit power constraint, the problems of optimizing the mode and transmit power of the monitor to maximize the average successful eavesdropping probability and the average eavesdropping rate are investigated for the delay-sensitive suspicious service and delay-tolerant suspicious service, respectively. By proving that the time-sharing condition is satisfied, the optimal solutions are derived based on the Lagrange duality method. Simulation results validate the effectiveness of the proposed schemes. It is shown that the proposed schemes can provide satisfactory eavesdropping performance improvement even with zero SC QoS degradation requirement.

RIS Assisted Wireless Powered IoT Networks With Phase Shift Error and Transceiver Hardware Impairment

Considering a reconfigurable intelligent surface (RIS) aided wireless powered Internet of Things (WP IoT) network. To address the energy-limitation issue, IoT devices in such a network can be wirelessly powered by a power station (PS) first and then connect with an access point (AP) using their own harvested energy. The RIS helps enhance energy and information receptions in the downlink wireless energy transfer (WET) and uplink wireless information transfer (WIT), respectively. This work unveils the impact of phase shift error (PSE) and transceiver hardware impairment (THI) on the considered network. Our investigation starts with a scenario where only the impact of the PSE on system under study is considered, then moves toward a scenario with the compound effect of both PSE and THI. A maximization problem of the system sum throughput is formulated to evaluate the overall performance for these two scenarios, subject to the constraints of the adjustable RIS phase shifts, the statistical PSE and the transmission time scheduling. To handle the non-convexity of the formulated problem due to those coupled variables, we first adopt the Lagrange dual method and Karush-Kuhn-Tucker (KKT) conditions to derive the optimal time scheduling in closed-form. Next, we recast the stochastic PSE into the deterministic counterpart for its tractability. Then, we adopt a successive convex approximation (SCA) to iteratively derive the optimal WIT’s phase shifts, and element-wise block coordinate decent (EBCD) and complex circle manifold (CCM) methods to iteratively derive the optimal WET’s phase shifts. Finally, we complete our solution approach for the scenario with both PSE and THI. Simulation results highlight the performance of the proposed scheme and the benefits induced by the RIS in comparison to benchmark schemes.

Fast Approximations for Job Shop Scheduling: A Lagrangian Dual Deep Learning Method

The Jobs Shop Scheduling problem (JSP) is a canonical combinatorial optimization problem that is routinely solved for a variety of industrial purposes. It models the optimal scheduling of multiple sequences of tasks, each under a fixed order of operations, in which individual tasks require exclusive access to a predetermined resource for a specified processing time. The problem is NP-hard and computationally challenging even for medium-sized instances. Motivated by the increased stochasticity in production chains, this paper explores a deep learning approach to deliver efficient and accurate approximations to the JSP. In particular, this paper proposes the design of a deep neural network architecture to exploit the problem structure, its integration with Lagrangian duality to capture the problem constraints, and a post-processing optimization, to guarantee solution feasibility. The resulting method, called JSP-DNN, is evaluated on hard JSP instances from the JSPLIB benchmark library and is shown to produce JSP approximations of high quality at negligible computational costs.

Improving Quality of Service for Cell-Edge Users in D2D-Relay Networks

In this paper, we build a D2D-relay communications model where the D2D user is selected as a relay to forward data for the users at the edge of the networks. We aim at maximizing the achievable data rates of the cell-edge users, a resource allocation problem is formulated and an iterative power allocation algorithm is proposed. We derive the optimal closed-form power allocation expressions by the Lagrange dual method. Simulation results show that our communication scheme can achieve greater spectral efficiency than the traditional cellular-relay communication scheme.

Optimal management of DC pension fund under the relative performance ratio and VaR constraint

This paper investigates the optimal management of defined contribution pension plan under the Omega ratio and Value-at-Risk (VaR) constraint. Interest and inflation risks are considered, and the financial market consists of cash, a zero-coupon bond, an inflation-indexed zero-coupon bond, and a stock. The goal of the pension manager is to maximize the performance ratio of the real terminal wealth under the VaR constraint. An auxiliary process is introduced to transform the original problem into a self-financing problem. We obtain the optimal terminal wealth under different cases by combining the linearization method, the Lagrange dual method, the martingale method, and the concavification method. There are fourteen cases for the convex penalty function, and there are six cases for the concave penalty function. Besides, when the penalty and reward functions are both power functions, the explicit forms of the optimal investment strategies are obtained. Numerical examples are shown to illustrate the impacts of the performance ratio and VaR constraint.

Resource Allocation for IRS-Assisted Wireless-Powered FDMA IoT Networks

This article investigates intelligent reflecting surface (IRS)-assisted wireless-powered Internet of Things (IoT) networks. Specifically, multiple IoT devices first collect energy radiated from a power station (PS), then each device uses its harvested energy to support data transmission to an access point (AP) via frequency-division multiple access (FDMA). In addition, an IRS aims to improve wireless energy transfer (WET) and wireless information transfer (WIT) capabilities using passive reflection beamformers. The system sum throughput, as a performance metric, is maximized evaluate the overall performance of the considered model, which is subject to the constraints of IRS phase shifts, transmission time scheduling, and bandwidth allocation. This problem is not convex with respect to multiple coupled variables, and cannot be directly solved. To circumvent this nonconvexity, the transmission time scheduling and the bandwidth allocation are optimally designed in the closed form by the Lagrange dual method and the Karush–Kuhn–Tucker (KKT) conditions. Moreover, an alternating optimization (AO) algorithm is used to optimally design the IRS’s phase shifts during the WET and WIT phases in an alternating fashion. Specifically, we propose elementwise block coordinate decent (EBCD) and complex circle manifold (CCM) algorithms to iteratively derive the optimal phase shifts in the closed form. We also characterize the convergence behavior of the proposed algorithms. Finally, numerical results are presented to validate the performance of the proposed scheme, where the benefits of the IRS are highlighted in terms of sum throughput, transmission time scheduling, and energy harvesting, compared with the benchmark schemes.

Intelligent Omni Surface-Assisted Secure MIMO Communication Networks With Artificial Noise

Intelligent omni surface (IOS) technology that can provide both reflection and refraction for signals impinging on its surface, was recently proposed to overcome the coverage area limitation of reconfigurable intelligent surfaces (RISs). This letter investigates the efficacy of IOS in the context of physical layer security (PLS) over wireless channels. In particular, we consider a scenario where the IOS is utilized to enhance the secrecy performance of a legitimate receiver in the presence of a multi-antenna eavesdropper. In addition, artificial noise (AN) aided beamforming is implemented to provide additional security robustness. The resultant optimization problem is non-convex and difficult to solve. Accordingly, the block coordinate descent (BCD) optimization approach is adopted, and the Lagrangian dual method is applied to reduce the complexity of the AN-aided beamforming design. Furthermore, the reflecting and refracting phase shifts are optimized via the quadratically constrained quadratic programming (QCQP) method. Simulation results validate the efficacy of the proposed algorithm and confirm the superiority of IOS over traditional RIS.

Energy Efficient Power Control for Cognitive Multibeam-Satellite Terrestrial Networks With Poisson Distributed Users

With great potential to alleviate spectrum scarcity in the next generation wireless communication, cognitive satellite terrestrial networks (CSTNs) have attracted considerable attention recently. To realize efficient spectrum sharing between satellite and terrestrial networks, in this paper, we propose an energy efficient power control scheme for CSTNs, where a multibeam satellite network acts as the secondary system and the cellular network acts as the primary system. Especially, satellite users and primary base stations are spatially Poisson distributed and the channel state information (CSI) of satellite interference link is assumed to be outdated. We firstly analyze the statistical characteristic of the terrestrial aggregate interference with probabilistic stochastic geometry. On this basis, to guarantee reliable communications for both networks, we formulate the power control scheme as an energy efficiency maximization problem subjected to interference power constraints imposed by terrestrial communications and outage constraints of satellite communications. Further, by employing the Dinkelbach and Lagrange duality method, we solve the nonlinear concave optimization problem and derive the optimal solution of the transmit power. Finally, simulation results demonstrate the validity of the theoretical results, reveal the trade-off between the performance of two networks, present the impacts of aggregate interference on the performance of satellite networks, and show the performance superiority of considering outdated CSI compared with perfect CSI assumption in terms of interference violation probability.

A Smart Cross-System Framework for Joint Allocation and Scheduling With Vehicle-to-Grid Regulation Service

The growing popularity and penetration of electric vehicles (EVs) bring in challenges and opportunities to the power grid. They represent a huge aggregate electricity consumption from the city power grid, while it is possible to make use of their batteries for supporting vehicle-to-grid (V2G) regulation service. Besides, there is a need to coordinate a collection of EVs in an intelligent manner through the smart transportation system in a smart city. In this paper, we propose a novel smart cross-system framework to support V2G regulation service in a smart city. Specifically, by considering electric buses (EBs) as a particular group of EVs with large battery packs installed and predictable operation schedules, we jointly solve the problems of EB allocation and scheduling with V2G regulation service. First of all, by using the deep learning approach, the short-term city traffic conditions can be predicted via the gated recurrent units (GRUs) neural network. With the predicted traffic conditions, we then formulate the EB allocation and V2G scheduling as a mixed-integer quadratic programming (MIQP) problem. In order to solve this problem effectively, we utilize the Lagrangian dual decomposition method to decouple the main problem into subproblems for EBs and devise a distributed algorithm to solve each subproblem. The simulation results show that our proposed approach is effective in EB allocation and V2G scheduling for the regulation service. Through efficient EB routing strategies under accurate predicted traffic conditions, the power fluctuations of the city power grid can be well flatten by providing the V2G regulation service.

Adaptive resource management for cognitive power line communication system

The authors investigate the adaptive resource allocation problem for cognitive power line communication system. The dynamic optimisation model is employed to maximise the energy-aware network utility, which is defined as the difference of the weighted network throughput and the power consumption. Then, the authors decompose the stochastic optimisation into a traffic management subproblem and a joint subchannel and power allocation subproblem. Since the joint subchannel and power allocation subproblem is a mixed integer non-linear optimisation, a continuity relaxation and Lagrange dual method is proposed to obtain the optimal solution of the mixed integer non-linear optimisation subproblem. After that, the authors develop an adaptive power line communication resource allocation algorithm to cope with the power line communication network dynamics only according to the current network state information. Finally, we derive a trade-off mechanism between network utility and network delay, in which the network delay is proportional to the control parameter V and the network utility is proportional to the parameter 1 / V $1/V$ . Simulation results not only show the effectiveness but also verify the theoretical analysis of our proposed algorithm.

Resource Allocation Optimization Based on Energy Efficiency in Green Cloud Radio Access Network

Compared with traditional cellular networks, cloud wireless access network (C-RAN) can save more energy consumption because it centrally processes the signals in the baseband unit (BBU) pool served by the cloud platform. Aiming at the limited fronthaul capacity of the fronthaul link caused by massive data and the huge energy consumption caused by the explosive growth of mobile traffic, an energy-saving resource management scheme that is powered by a mixture of on-grid and green energy is proposed in this paper. Specifically, a new network energy efficiency (EE) model is constructed. The RRH with hybrid energy to supply power of the model in response to green communication and the model can also realize two functions: information decoding and wireless charging at the same time. The total power consumption including remote radio head (RRH), fronthaul link, BBU pool, and wireless charging equipment of user equipment is considered. Based on network energy efficiency model, in addition to considering the user’s quality of service (QoS), data rate requirements, transmission power of RRHs, and maximum battery capacity constraints, the constraints of fronthaul link capacity constraints also are considered in this paper. In order to solve the proposed optimization problem, a joint strategy of power allocation, resource block (RB) allocation, and power allocation ratio adjustment is proposed in this paper. However, the objective function of energy efficiency optimization problem is nonconvex and cannot be solved directly. Therefore, an equivalent convex feasibility problem is reconstructed, and the optimal solution is obtained by Lagrange dual decomposition method. Simulation results show that the proposed resource allocation scheme can provide higher energy efficiency for the network.

Resource Allocation for Intelligent Reflecting Surface Assisted Wireless Powered IoT Systems With Power Splitting

This paper proposes a new transmission policy for intelligent reflecting surface (IRS) empowered wireless powered internet of things systems. Particularly, an energy station (ES) wirelessly charges for multiple IoT devices during downlink wireless energy transfer (WET) and then these devices deliver their own message to an access point (AP) during uplink wireless information transfer (WIT). Also, an IRS is deployed to improve energy harvesting and data transmission capabilities. To enhance self-sustainability of the IRS, the IRS harvests energy from the ES based on the harvest-then-transmit protocol. In this paper, we maximize the sum throughput via optimizing the phase shifts of the IRS, the transfer time scheduling as well as the power splitting ratio. Due to the non-convexity of the formulated problem, we divide the problem into two sub-problems, each of which can be handled separately. Then, we adopt an alternating optimization (AO) algorithm with the semidefinite programming (SDP) relaxation. Also, we consider a special case where the circuit power consumption of IoT devices can be neglected. In this case, we derive a closed form solution for the optimal transmission time slots, power allocation and phase shift by the Lagrange dual method. Finally, numerical evaluations validate effectiveness of the proposed scheme, which significantly benefits from the IRS in improving network throughput.

CoMP Enhanced Subcarrier and Power Allocation for Multi-Numerology Based 5G-NR Networks

With proliferation of fifth generation (5G) new radio (NR) technology, it is expected to meet the requirement of diverse traffic demands. We have designed a coordinated multi-point (CoMP) enhanced flexible multi-numerology (MN) for 5G-NR networks to improve the network performance in terms of throughput and latency. We have proposed a CoMP enhanced joint subcarrier and power allocation (CESP) scheme which aims at maximizing sum rate under the considerations of transmit power limitation and guaranteed quality-of-service (QoS) including throughput and latency restrictions. By employing difference of two concave functions (D.C.) approximation and abstract Lagrangian duality method, we theoretically transform the original non-convex nonlinear problem into a solvable maximization problem. Moreover, the convergence of our proposed CESP algorithm with D.C. approximation is analytically derived with proofs, and is further validated via numerical results. Simulation results have demonstrated that our proposed CESP algorithm outperforms the conventional non-CoMP and single-numerology mechanisms along with other existing benchmarks in terms of lower latency and higher throughput under the scenarios of center and edge users.