Equivalent Convex Optimization Problem Research Articles

Energy-efficient UAV communication: A NOMA scheme with resource allocation and trajectory optimization.

This work investigates a downlink nonorthogonal multiple access (NOMA) scheme with unmanned aerial vehicle (UAV) aided wireless communication, where a single UAV was regarded as an air base station (ABS) to communicate with multiple ground users. Considering the constraints of velocity and maneuverability, a UAV energy efficiency (EE) model was proposed via collaborative design resource allocation and trajectory optimization. Based on this, an EE maximization problem was formulated to jointly optimize the transmit power of ground users and the trajectory of the UAV. To obtain the optimal solutions, this nonconvex problem was transformed into an equivalent convex optimization problem on the basis of three user clustering algorithms. After several alternating iterations, our proposed algorithms converged quickly. The simulation results show an enhancement in EE with NOMA because our proposed algorithm is nearly 99.6% superior to other OMA schemes.

Joint Resource and Trajectory Optimization for Energy Efficiency Maximization in UAV-Based Networks

The explosive growth of unmanned aerial vehicles (UAVs)-based networks has accelerated in recent years. One of the crucial tasks of a UAV-based network is managing and allocating resources, including time, power, fly trajectory, and energy resources. We investigate a UAV-based network that gathers information from smart devices, sensor devices, and IoT devices (IDs) with respect to energy efficiency (EE) maximization. The EE of users served by the UAV over the time slots of a cycle is maximized through three categories: UAV trajectory optimization, power allocation, and time slot assignment. However, these are non-convex problems that are very difficult to solve. To solve the problem efficiently, we divide it step by step and convert the non-convex optimization problem into an equivalent convex optimization problem, optimizing each equivalent problem over each variable while other variables are fixed. Firstly, we perform a UAV trajectory optimization with a different number of ground users. Secondly, the Dinkelbach method is used to construct a non-convex fractional power allocation problem. In addition, we develop an algorithm to distribute time slots to all users, which continually raises the EE value. Eventually, a scheme is provided to sequentially update the method to each equivalent problem. The numerical results provide evidence that by solving the proposed sum-rate maximization problem, the performance of ground users has significantly improved with the support of the UAV-based network.

A Smoothing SAA Method for Solving a Nonconvex Multisource Supply Chain Stochastic Optimization Model

We construct a new multisource supply chain stochastic optimization model when the supply and demand are both uncertain. This model is nonconvex because the decision variables are truncated by the random variable in the objective function. It is a common technical challenge encountered in many operations management models. To address this challenge, we adopt a novel transformation technique to transform the nonconvex problem into an equivalent convex optimization problem. Then, we provide a smoothing sample average approximation (SAA) method to solve the transformed problem. The SAA model is a good approximation for the expected value function in the objective function when the number of samples is large enough. The smoothing technique can transfer the nonsmooth plus function into a smoothing function in the model, and thus, we can use the numerical methods for the common nonlinear integer programming to solve the transformed model. Numerical tests verify the effectiveness of the new model and the smoothing SAA method.

Robust Secure Beamforming for Intelligent Reflecting Surface Assisted Full-Duplex MISO Systems

This paper investigates a full-duplex (FD) secure communication system with the assistance of an intelligent reflecting surface (IRS). Compared with the traditional FD system, the IRS-assisted FD communication not only greatly improves the spectrum efficiency but also provides a new way to enhance physical layer security due to the overlapping of multiple signals at the eavesdropper. Furthermore, we consider a more practical scenario without perfect channel state information (CSI) because it is very difficult to obtain the perfect CSI especially for cascaded channels via IRS. In addition, the eavesdropper is usually passive and hidden which will not actively exchange CSI with the user, which leads to an obstacle for obtaining the perfect CSI of eavesdropping channels. To this end, a worst-case achievable security rate (ASR) optimization problem is formulated under the bounded CSI error model. Due to the existence of non-convexity and highly coupled variables, this problem is extremely challenging. To directly tackle the nonconvexity of the considered optimization problem, similar to successive convex approximation (SCA), we first transform the original problem into its equivalent convex optimization problem directly, and finally obtain the optimal solution of the original non-convex problem by iteratively calculating the convex optimization problem. On this basis, we iteratively solve the transmission beamforming and IRS phase shift through Alternate Optimization (AO). In particular, when optimizing the phase shift coefficient, a penalty convex-concave procedure solution is proposed. Simulation results demonstrate that our proposed robust secure beamforming scheme can effectively improve ASR, and also outperforms the nonrobust one.

Sum Rate Maximization for Cooperative NOMA with Hardware Impairments

This paper investigates the sum rate (SR) maximization problem for downlink cooperative non-orthogonal multiple access (C-NOMA) systems with hardware impairments (HIs). The source node communicates with users via a half-duplex amplified-and-forward (HD-AF) relay with HIs. First, we derive the SR expression of the systems under HIs. Then, SR maximization problem is formulated under maximum power of the source, relay, and the minimum rate constraint of each user. As the original SR maximization problem is a non-convex problem, it is difficult to find the optimal resource allocation directly by tractional convex optimization method. We use variable substitution method to convert the non-convex SR maximization problem to an equivalent convex optimization problem. Finally, a joint power and rate allocation based on interior point method is proposed to maximize the SR of the systems. Simulation results show that the algorithm can improve the SR of the C-NOMA compared with the cooperative orthogonal multiple access (C-OMA) scheme.

Robust resource allocation for NOMA-assisted heterogeneous networks

As a promising technology to improve spectrum efficiency and transmission coverage, Heterogeneous Network (HetNet) has attracted the attention of many scholars in recent years. Additionally, with the introduction of the Non-Orthogonal Multiple Access (NOMA) technology, the NOMA-assisted HetNet cannot only improve the system capacity but also allow more users to utilize the same frequency band resource, which makes the NOMA-assisted HetNet a hot topic. However, traditional resource allocation schemes assume that base stations can exactly estimate direct link gains and cross-tier link gains, which is impractical for practical HetNets due to the impact of channel delays and random perturbation. To further improve energy utilization and system robustness, in this paper, we investigate a robust resource allocation problem to maximize the total Energy Efficiency (EE) of Small-Cell Users (SCUs) in NOMA-assisted HetNets under imperfect channel state information. By considering bounded channel uncertainties, the robust resource optimization problem is formulated as a mixed-integer and nonlinear programming problem under the constraints of the cross-tier interference power of macrocell users, the maximum transmit power of small base station, the Resource Block (RB) assignment, and the quality of service requirement of each SCU. The original problem is converted into an equivalent convex optimization problem by using Dinkelbach's method and the successive convex approximation method. A robust Dinkelbach-based iteration algorithm is designed by jointly optimizing the transmit power and the RB allocation. Simulation results verify that the proposed algorithm has better EE and robustness than the existing algorithms.

Optimal Dynamic Duct Static Pressure Method in a Multi-Zone Variable Air Volume System

Reducing the energy consumption of a variable air volume (VAV) system in heating, ventilation, and air-conditioning (HVAC) systems attracts many attentions. In this letter, a novel method, namely, optimal dynamic duct static pressure (ODSP) method is proposed to find the globally optimal solutions of the original non-convex multi-zone VAV system energy optimization problem. Our method is based on the primal dual interior point method to solve an equivalent convex optimization problem of the multi-zone VAV system energy optimization problem. Different from existing methods, our method is a real-time optimization method and explicitly considers the duct network model to find the energy saving strategy. Numerical simulations illustrate the effectiveness of our method compared with current methods, which show that our method provides better energy efficiency and nearly 20% energy is saved. Our method also has the guarantee to find the optimal solutions.

Trade-off between spectral efficiency and normalized energy in Ad-hoc wireless networks

With the ever-increasing deployment of wireless communication technologies, effective management of scarce power and radio spectrum resources is of primary concern. The available bandwidth spectrum should be utilized in the most efficient and controlled way for practical economic growth of industries in conformity with the evolving demand of energy for powering wireless devices. In the proposed optimization scheme, energy management and limited spectrum sharing are distributively implemented for handling quality of service provisioning and potential resource allocation across multiple nodes with inherent operational capability deficiencies. We employ cross-layer information exchange and convex optimization techniques to simultaneously achieve more efficient radio spectrum usage and optimal energy consumption in ad-hoc wireless networks with distributed scenarios. We consider the time-invariant additive white Gaussian noise channel and the time-varying Rayleigh fading channel to study the trade-off between the two network design objectives of achieving improved spectrum efficiency and minimizing the energy overhead in data routing paradigm. The original problem is transformed into an equivalent convex optimization problem through logarithmic processing to obtain the approximate global optimal solution. Moreover, the robustness and efficiency of the proposed framework is evaluated in large-scale set ups to provide the scalability analysis on both the employed performance objectives. The developed optimization scheme is compared with the machine learning models previously proposed in literature by employing the computational and/or time complexity metrics. Finally, the effectiveness of the proposed optimization model is substantiated through the simulation comparison results with the existing schemes in terms of various key performance parameters such as throughput, energy efficiency, and average bit errors.

Research on energy-efficient routing algorithm based on SWIPT in multi-hop clustered WSN for 5G system

As one of the basic supporting technologies of 5G system, wireless sensor networks technology is facing a new challenge to improve its transmission energy efficiency. This paper considers combining simultaneous wireless information and power transfer (SWIPT) technique and routing technique, and applying them to multi-hop clustered wireless sensor networks (MCWSN), where each node can decode information and harvest energy from a received radio-frequency signal. And the relay nodes in MCWSN can utilize the harvest energy to forward data to their next hop nodes according to the routing scheme. First, we formulate an energy-efficient routing problem of MCWSN with SWIPT. Then, a heuristic energy efficient cooperative SWIPT routing algorithm (EECSR) is presented to find a transmission path with the maximum energy efficiency. Specifically, in EECSR, the resource allocation problem in each hop of the path is transformed to some equivalent convex optimization problems, which are resolved via dual decomposition. Moreover, a distributed routing protocol based on EECSR is proposed. As far as we know, this is the first solution that considers energy efficiency optimization based on routing and SWIPT in MCWSN. Simulation results show that our EECSR algorithm has high energy efficiency and good robustness. And our distributed routing protocol has better real-time performance than traditional protocols.

Optimal resource allocation for multiclass services in peer-to-peer networks via successive approximation

Peer-to-peer (P2P) networks support a wide variety of network services including elastic services such as file-sharing and downloading and inelastic services such as real-time multiparty conferencing. Each peer who acquires a service will receive a certain level of satisfaction if the service is provided with a certain amount of resource. The utility function is used to describe the satisfaction of a peer when acquiring a service. In this paper we consider optimal resource allocation for elastic and inelastic services and formulate a utility maximization model which is an intractable and difficult non-convex optimization problem. In order to resolve it, we apply the successive approximation method and approximate the non-convex problem to a serial of equivalent convex optimization problems. Then we develop a gradient-based resource allocation scheme to achieve the optimal solutions of the approximations. After a serial of approximations, the proposed scheme can finally converge to an optimal solution of the primal utility maximization model for resource allocation which satisfies the Karush–Kuhn–Tucker conditions.

Energy Efficiency Maximization for Multi-Cell Multi-Carrier NOMA Networks.

As energy efficiency (EE) is a key performance indicator for the future wireless network, it has become a significant research field in communication networks. In this paper, we consider multi-cell multi-carrier non-orthogonal multiple access (MCMC-NOMA) networks and investigate the EE maximization problem. As the EE maximization is a mixed-integer nonlinear programming NP-hard problem, it is difficult to solve directly by traditional optimization such as convex optimization. To handle the EE maximization problem, we decouple it into two subproblems. The first subproblem is user association, where we design a matching-based framework to perform the user association and the subcarriers’ assignment. The second subproblem is the power allocation problem for each user to maximize the EE of the systems. Since the EE maximization problem is still non-convex with respect to the power domain, we propose a two stage quadratic transform with both a single ratio quadratic and multidimensional quadratic transform to convert it into an equivalent convex optimization problem. The power allocation is obtained by iteratively solving the convex problem. Finally, the numerical results demonstrate that the proposed method could achieve better EE compared to existing approaches for non-orthogonal multiple access (NOMA) and considerably outperforms the fractional transmit power control (FTPC) scheme for orthogonal multiple access (OMA).

Large Scale Resource Allocation for the Internet of Things Network Based on ADMM

Large scale deployment of Internet of Things (IoT) devices poses challenges in resource allocation. In this paper, alternating direction method of multipliers (ADMM) is adopted to solve such large scale resource allocation problems. Based on this, three optimization problems are investigated in a hierarchical IoT network. Considering ADMM could not solve a non-convex optimization problem directly, a non-convex fractional programming problem i.e., energy efficiency maximization problem for IoT region server, is formulated. Faced with this problem, we introduce the Dinkelbach algorithm to transfer the energy efficiency maximization problem into an equivalent convex optimization problem. Then the classic ADMM with two blocks is employed to solve the equivalent convex optimization problem. On the other hand, the classic ADMM with two blocks could not satisfy the convergence speed demands of the high-dimensional convex optimization problems any more. Thus, the network latency minimization problem for controller is designed and then solved by the Jacobian-ADMM algorithm in parallel. It is hard to satisfy controller and IoT region servers’ objectives at the same time. Given this, an incentive mechanism on the basis of Stackelberg game is designed. Thus a game-based resource allocation problem is proposed to deal with the contradiction between the centralized objective of the controller and the individual objectives from the IoT region servers. Based on the Dinkelbach algorithm and Jacobian-ADMM algorithm, a two-layer iterative resource allocation algorithm is posed to solve the game-based resource allocation problem. Last but not least, the convergence of the proposed algorithms are analyzed with numerous simulation results.

An Energy Sharing Game With Generalized Demand Bidding: Model and Properties

This paper proposes a novel energy sharing mechanism for prosumers who can produce and consume. Different from most existing works, the role of individual prosumer as a seller or buyer in our model is endogenously determined. Several desirable properties of the proposed mechanism are proved based on a generalized game-theoretic model. We show that the Nash equilibrium exists and is the unique solution of an equivalent convex optimization problem. The sharing price at the Nash equilibrium equals to the average marginal disutility of all prosumers. We also prove that every prosumer has the incentive to participate in the sharing market, and prosumers' total cost decreases with increasing absolute value of price sensitivity. Furthermore, the Nash equilibrium approaches the social optimal as the number of prosumers grows, and competition can improve social welfare.

Resource configuration for minimizing source energy consumption in multi-carrier networks with energy harvesting relay and data-rate guarantee

Simultaneous wireless information and power transfer (SWIPT) is a promising technique for wireless energy harvesting, which enables a relay node to overcome its unwillingness due to the energy awareness, with essentially protecting it from excessively depleting energy reserves. To further improve the energy efficiency, the energy consumption minimization problem aims at minimizing the energy consumption of an active source node, which drives the passive relay node with energy harvesting capability to forward data to the destination. This is studied by jointly considering transmission power limits, time switching factors, and data-rate demand, etc., in a decode-and-forward relay network with SWIPT. The energy consumption minimization problem is formulated as a non-convex optimization problem. The facilitation of the derivation of the optimal solution is through transforming it into an equivalent convex optimization problem by variable substitution. Since the problem is not always feasible, a feasibility assessment problem is then developed by introducing an assessing factor. Simultaneously solving the above inter-related problems, i.e., energy consumption minimization and feasibility assessment, they are unified in a convex-optimization framework, in which both the result about the feasibility assessment and the optimal solution (if it exists) can be obtained. Even if the problem is not feasible, the achievable maximum data rate that network resources can support can be obtained as well. Simulation results further validate that energy consumption minimization-feasibility assessment algorithm is effective in minimizing source energy consumption and in realizing optimal resource configuration.

Price-Based Resource Allocation in Wireless Power Transfer-Enabled Massive MIMO Networks.

This paper considers the price-based resource allocation problem for wireless power transfer (WPT)-enabled massive multiple-input multiple-output (MIMO) networks. The power beacon (PB) can transmit energy to the sensor nodes (SNs) by pricing their harvested energy. Then, the SNs transmit their data to the base station (BS) with large scale antennas by the harvesting energy. The interaction between PB and SNs is modeled as a Stackelberg game. The revenue maximization problem of the PB is transformed into the non-convex optimization problem of the transmit power and the harvesting time of the PB by backward induction. Based on the equivalent convex optimization problem, an optimal resource allocation algorithm is proposed to find the optimal price, energy harvesting time, and power allocation for the PB to maximize its revenue. Finally, simulation results show the effectiveness of the proposed algorithm.

Collaborative Cloud and Edge Computing for Latency Minimization

By performing data processing at the network edge, mobile edge computing can effectively overcome the deficiencies of network congestion and long latency in cloud computing systems. To improve edge cloud efficiency with limited communication and computation capacities, we investigate the collaboration between cloud computing and edge computing, where the tasks of mobile devices can be partially processed at the edge node and at the cloud server. First, a joint communication and computation resource allocation problem is formulated to minimize the weighted-sum latency of all mobile devices. Then, the closed-form optimal task splitting strategy is derived as a function of the normalized backhaul communication capacity and the normalized cloud computation capacity. Some interesting and useful insights for the optimal task splitting strategy are also highlighted by analyzing four special scenarios. Based on this, we further transform the original joint communication and computation resource allocation problem into an equivalent convex optimization problem and obtain the closed-form computation resource allocation strategy by leveraging the convex optimization theory. Moreover, a necessary condition is also developed to judge whether a task should be processed at the corresponding edge node only, without offloading to the cloud server. Finally, simulation results confirm our theoretical analysis and demonstrate that the proposed collaborative cloud and edge computing scheme can evidently achieve a better delay performance than the conventional schemes.

Joint User Scheduling and RRU Association for ODFMA-Based Networks With Inter-BBU Coordination

This paper investigates the joint user scheduling (US) and user association (UA) problem for OFDMA-based networks under the centralized radio access network (C-RAN) architecture. We first formulate the joint optimization problem for US and UA, which is intractable in its exact form, and therefore, we propose a corresponding upper bound problem, with much lower computational complexity, with the help of a novel continuous rate function. We show that the upper bound problem can be further converted into an equivalent convex optimization problem via geometric programming (GP) that can be solved with inter-baseband unit coordination, which is viable in the C-RAN architecture. Furthermore, we show that the solutions of the convex upper bound problem can be mapped into the solution space of the original joint US and UA problem with a small gap. As a practically implementable solution to the original problem, a heuristic-based scheduler has been developed to obtain quasi-optimal UA and US solutions for the uplink (UL) as well as the downlink (DL) transmissions. Through extensive numerical simulations, we verify that the performance of the proposed heuristic-based scheduler is quasi-optimal on both UL and DL.

Secrecy Energy Efficiency Optimization for Downlink Two-User OFDMA Networks With SWIPT

Simultaneous wireless information and power transfer (SWIPT), as a promising technology by which mobile devices are designed by both information decoding and energy harvesting at the same time, has recently drawn significant interests. However, in multiuser scenario, a challenging physical layer security issue arises as the confident messages sent to the intended information receivers may be eavesdropped by other receivers. To address this problem, in this paper, secrecy energy efficiency maximization (SEEM) problem is investigated for two-user orthogonal frequency-division multiple access networks with SWIPT. Specifically, a power splitting scheme is adopted for each user, which would split received radio frequency signals into two independent parts for information decoding and energy harvesting, respectively. Taking both the individual secrecy quality of service requirement and the individual harvested energy constraint into consideration, the SEEM problem is formulated as a nonlinear fractional programming problem. Moreover, according to Dinkelbach's method, a power allocation and power splitting (PAPS) algorithm is proposed by solving the equivalent convex optimization problem. Finally, numerical results verify the impact of static circuit power consumption, maximum transmit power, power split ratio, subcarrier bandwidth, and path loss on secrecy energy efficiency of our PAPS algorithm.

Power- and Rate-Adaptation Improves the Effective Capacity of C-RAN for Nakagami-$m$ Fading Channels

We propose a power-and rate-adaptation scheme for cloud radio access networks (C-RANs), where each radio remote head (RRH) is connected to the baseband unit pool through optical links. The RRHs jointly support the users by efficiently exploiting the enhanced spatial degrees of freedom. Our proposed scheme aims at maximizing the effective capacity (EC) of the user subject to both per-RRH average- and peak-power constraints, where the EC is defined as the maximum arrival rate that can be supported by the C-RAN under the statistical delay requirement. We first transform the EC maximization problem into an equivalent convex optimization problem. By using the Lagrange dual decomposition method and solving the Karush–Kuhn–Tucker equations, the optimal transmission power of each RRH can be obtained in the closed form. Furthermore, an online tracking method is provided for approximating the average power of each RRH. For the special case of two RRHs, the expression of the average power of each RRH can be calculated in the explicit form. Hence, the Lagrange dual variables can be computed in advance in this special case. Furthermore, we derive the power allocation for two important extreme cases: first, no delay constraint and, second, extremely stringent delay requirements. Our simulation results show that the proposed scheme significantly outperforms the conventional algorithm without considering the delay requirements. Furthermore, when appropriately tuning the value of the delay exponent, our proposed algorithm is capable of guaranteeing a delay outage probability below $10^{-9}$ when the maximum tolerable delay is 1 ms. This is suitable for the future ultra-reliable low-latency communications.

Heterogeneous quality of experience guarantees over wireless networks

Quality of experience (QoE), which is very critical for the experience of users in wireless networks, has been extensively studied. However, due to different human perceptions, quantifying the effective capacity of wireless network subject to diverse QoE is very difficult, which leads to many new challenges regarding QoE guarantees in wireless networks. In this paper, we formulate the QoE guarantees model for cellular wireless networks. Based on the model, we convert the effective capacity maximization problem into the equivalent convex optimization problem. Then, we develop the optimal QoE-driven power allocation scheme, which can maximize the effective capacity. The obtained simulation results verified our proposed power allocation scheme, showing that the effective capacity can be significantly increased compared with that of traditional QoE guarantees based schemes.