Equivalent Convex Optimization Problem Research Articles

Collaborative Energy and Information Transfer in Green Wireless Sensor Networks for Smart Cities

Smart city is able to make the city source and infrastructure more efficiently utilized, which improves the quality of life for citizens. In this framework, wireless sensor networks (WSNs) play an important role to collect, process, and analyze the corresponding information. However, the massive deployment of WSNs consumes a significant energy consumption, which has raised the growing demand for green WSNs for smart cities. Exploiting the recent advance in collaborative energy and information transfer to power the WSNs and transmit the data has been considered a promising approach to realize the green WSNs for smart cities. We propose an architecture design of the green WSNs for smart cities, by exploiting the collaborative energy and information transfer protocol, and illustrate the challenging issues in this design. To achieve a green system design, the sensor nodes in WSNs harvest the energy simultaneously with the information decoding (ID) from the received radio frequency signals. Specifically, the energy-constrained sensor nodes partition the received signals into two independent groups to perform energy harvesting (EH) and ID. The sensor nodes then use the harvested energy to amplify and forward the information signals. We study the joint optimization of subcarrier grouping, subcarrier pairing, and power allocation such that the transmission rate performance is maximized with the EH constraint. The joint optimization problem is solved via dual decomposition after transforming it into an equivalent convex optimization problem. Simulation results tested with the real WSNs system data indicate that the performance of our proposed protocol can be significantly improved.

Resource allocation in two-way OFDM-based cognitive radio networks with QoE and power consumption guarantees

In this paper, a resource allocation algorithm in two-way orthogonal frequency division multiplexing (OFDM) based cognitive radio networks with quality of experience (QoE) and power consumption guarantees is proposed. We define the overall QoE perceived by secondary users (SUs) per power consumption as QoEW. The power consumption model consists of fixed circuit power, dynamic circuit power, and transmit power which depends on the efficiency of the power amplifiers at different terminals. Under the constraint of total maximum transmit power, the optimization objective is to maximize QoEW while meeting the minimum QoE demands of SUs and maintaining interference threshold limitations of multiple primary users. The resource allocation problem is formulated into a nonlinear fractional programming and transformed into an equivalent convex optimization problem via its hypograph form. Based on the Lagrange dual decomposition method and cross-layer (CL) optimization architecture, this convex optimization problem is separately solved in the physical layer and the application layer. The optimal QoEW is achieved through the proposed CL alternate iteration algorithm. Numerical simulation results demonstrate the impacts of system parameters on QoEW and the effectiveness and superiority of the proposed algorithm.

Robust resource allocation for cognitive relay networks with multiple primary users

A robust resource allocation (RA) algorithm for cognitive relay networks with multiple primary users considering joint channel uncertainty and interference uncertainty is proposed to maximize the capacity of the networks subject to the interference threshold limitations of primary users’ receivers (PU-RXs) and the total power constraint of secondary user’s transmitter and relays. Ellipsoid set and interval set are adopted to describe the uncertainty parameters. The robust relay selection and power allocation problems are separately formulated as semi-infinite programming (SIP) problems. With the worst-case approach, the SIP problems are transformed into equivalent convex optimization problems and solved by Lagrange dual decomposition method. Numerical results show the impact of channel uncertainties and validation of the proposed robust algorithm for strict guarantee the interference threshold requirements at different PU-RXs.

A Cooperative SWIPT Scheme for Wirelessly Powered Sensor Networks

Wireless power transfer (WPT) provides a novel solution to the painstaking power-charging issue in wireless sensor networks. However, due to the propagation loss, the fast attenuation in energy transfer efficiency over the transmission distance is the main impediment to the WPT application. In this paper, we apply the simultaneous wireless information and power transfer (SWIPT) to a wirelessly powered sensor network, where each node has two circuits, which operate on energy harvesting mode and information decoding mode separately. We propose a novel cooperative SWIPT scheme (CSS) for this system. First, we present a conflict-free schedule initialization algorithm for CSS. For a given conflict-free schedule, we formulate a resource allocation problem to maximize the network energy efficiency, which is then transformed to an equivalent convex optimization problem and resolved via dual decomposition. Finally, a heuristic algorithm is presented to achieve the transmission schedule with the maximum energy efficiency and the corresponding resource assignment policy. Simulation results indicate that the CSS can significantly improve the energy efficiency of the wirelessly powered sensor network.

Energy Efficient Power Allocation Scheme for Downlink Distributed Antenna System in Composite Fading Channel

In this paper, the energy efficiency (EE) of downlink distributed antenna system is investigated over composite fading channel including the path loss, shadow fading and Rayleigh fading, where both the static and dynamic circuit power consumptions are considered. Under the constraint of maximum transmit power of each remote antenna, our aim is to maximize the EE which is defined as the ratio of the transmission rate to the total consumed power to obtain effective power allocation (PA). According to the definition of EE, the optimized objective function is firstly formulated, and then utilizing the properties of fractional programming theory, the non-convex optimization problem in fractional form is transformed into an equivalent convex optimization problem in subtractive form, which makes the optimized problem become easy to handle. Based on this, using the Karush–Kuhn–Tucker conditions and mathematical calculation, an optimal energy efficient PA scheme is derived. Compared to the existing optimal schemes based on exhaustive search and the iterative calculation, this scheme may provide closed-form calculation of PA coefficients, and thus the computation complexity is lower. Moreover, it can obtain the EE performance identical to the existing optimal schemes. Simulation results verify the effectiveness of the proposed scheme.

Integrating reference point, Kuhn–Tucker conditions and neural network approach for multi-objective and multi-level programming problems

In this paper, a neural network approach is constructed to solve multi-objective programming problem (MOPP) and multi-level programming problem (MLPP). The main idea is to convert the MOPP and the MLPP into an equivalent convex optimization problem. A neural network approach is then constructed for solving the obtained convex programming problem. Based on employing Lyapunov theory, the proposed neural network approach is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the MOPP and the MLPP. The simulation results also demonstrate that the proposed neural network is feasible and efficient.

Robust Power and Bandwidth Allocation in Cognitive Radio System With Uncertain Distributional Interference Channels

In this paper, the problem of joint transmit power and bandwidth allocation over multiple channels is investigated for a secondary user in underlay mode, when partial information of interference channel is known. The target is to maximize the capacity of a secondary user under a probabilistic constraint of the interference to the primary user. A robust optimization problem is formulated, which is nondeterministic and cannot be solved directly. We then transform the original optimization problem into an equivalent convex optimization problem. For general case, an optimal solving algorithm, which is a combination of analytical and bisection-search methods, is given. For some special cases, simple and optimal solving algorithms are also devised. Numerical results are presented to show that our proposed optimal algorithm has low computation complexity when the number of channels is not large and can achieve global optimal utility in general case and our proposed simple algorithms have much lower computation complexity and can achieve global optimal utility in special cases.

A Systematic Approach to Jointly Optimize Rate and Power Consumption for OFDM Systems

In this paper, we adopt a multiobjective optimization for the bit and power allocation problem in order to meet the requirements of emerging wireless systems, i.e., achieving higher throughput without considerably increasing the transmit power. More specifically, we propose to simultaneously maximize the throughput and minimize the transmit power of an OFDM system subject to average bit error rate (BER), power budget, and maximum allocated number of bits per subcarrier constraints. The formulated optimization problem is not convex and we use an evolutionary algorithm, i.e., genetic algorithm, in order to obtain the solution. We study the structure of the problem and the obtained solution and notice that the constraint on the average BER can be replaced by a BER per subcarrier constraint. As such, we propose an approximate non-convex optimization problem. We further exploit the structure of the approximate optimization problem and notice that the BER constraint per subcarrier (i.e., the source of the non-convexity) must be satisfied with an equality sign and can be substituted; this leads to an equivalent convex optimization problem where the global optimality of the Pareto solutions is guaranteed. Closed-form expressions are obtained for the bit and power allocations with reduced complexity. Simulation results show that the proposed multiobjective optimization approach provides significant performance improvements over single objective optimization techniques presented in the literature, without incurring additional complexity.

Resource allocation in a generalized LTE air interface virtualization framework exploiting user behavior

Wireless network virtualization (WNV) is a promising technique to solve the ossification of current networks. In this paper, a generalized Long Term Evolution (LTE) air interface virtualization framework is proposed where virtual operators (VOs) are enabled to share the physical resources owned by the infrastructure provider (InP). This user-centric feature provides VOs with the flexibility to manage their own virtualized networks according to different user traffic demand. Hence, we introduce the “Gini Coefficient” to quantitatively characterize the user traffic behavior among different VOs. In addition, we consider bandwidth-power allocation to optimize system energy efficiency (EE). The resource allocation problem is formulated as a mixed combinatorial and non-convex optimization problem, which is extremely difficult to solve. To reduce the computational complexity, we decouple the problem into two steps. First, for a given power allocation, we obtain the bandwidth allocation. Adopting bankruptcy game model and the well-known Shapley value, a heuristic bandwidth allocation algorithm is devised. Second, under the assumption of known bandwidth allocation, we transform the original optimization problem into an equivalent convex optimization problem and obtain the optimal solution via fractional programming. Through simulation, the results of user behavior and resource allocation are jointly analyzed. The user behavior is proved to be effective and the proposed resource allocation outperforms conventional schemes.

A Stackelberg Game Model for Overlay D2D Transmission With Heterogeneous Rate Requirements

This paper studies the performance of overlay device-to-device (D2D) communication links via carrier sense multiple access (CSMA) protocols. We assume that the D2D links have heterogeneous rate requirements and different willingness to pay, and each of them acts non-altruistically to achieve its target rate while maximizing its own payoff. Spatial reuse is allowed if the links are not interfering with each other. A non-cooperative game model is used to address the resource allocation among the D2D links, at the same time leveraging on the ideal CSMA network (ICN) model to address the physical channel access issue. We propose a Stackelberg game in which the base station in the cellular network acts as a Stackelberg leader to regulate the individual payoff by modifying the unit service price so that the total D2D throughput is maximized. The problem is shown to be quasi-convex and can be solved by a sequence of equivalent convex optimization problems. The pricing strategies are designed so that the network always operates within the feasible throughput region. The results are verified by simulations.

Energy-Efficient Power Allocation for Cognitive Radio Networks with Joint Overlay and Underlay Spectrum Access Mechanism

Traditional designs of cognitive radio (CR) focus on maximizing system throughput. In this paper, we study the joint overlay and underlay power allocation problem for orthogonal frequency-division multiple access–based CR. Instead of maximizing system throughput, we aim to maximize system energy efficiency (EE), measured by a “bit per Joule” metric, while maintaining the minimal rate requirement of a given CR system, under the total power constraint of a secondary user and interference constraints of primary users. The formulated energy-efficient power allocation (EEPA) problem is nonconvex; to make it solvable, we first transform the original problem into a convex optimization problem via fractional programming, and then the Lagrange dual decomposition method is used to solve the equivalent convex optimization problem. Finally, an optimal EEPA allocation scheme is proposed. Numerical results show that the proposed method can achieve better EE performance.

Optimal Price‐Based Power Control Algorithm with Quality of Service Constraints in Cognitive Radio Networks

In price-based cognitive radio networks, the Primary user (PU) can allow the Secondary users (SUs) to access by pricing if their interference power is under the Interference power constraint (IPC). The interaction between the PU and the SUs is modeled as a Stackelberg game with the consideration of the Quality of service (QoS) of the SUs. The revenue maximization problem of PU is expressed as an equivalent convex optimization problem if the minimum Signal-to-interference and noise ratio (SINR) constraints for the SUs are greater than or equal to 0dB. An optimal pricing algorithm is proposed based on this equivalent convex optimization problem. Simulation results show that the proposed pricing algorithm outperforms the non-uniform pricing algorithm in terms of the revenue of the PU, the sum rate of SUs and the number of admitted SUs.

An LMI Approach to Guaranteed Cost Control Design for Teleoperation Systems

A procedure for the guaranteed cost control design of delayed bilateral teleoperation systems with nonlinear external forces is proposed. The assumption that the external forces are nonlinear functions of velocities and/or positions of local devices and that one part of these forces satisfies sector condition has been made. A stability criterion is formulated firstly and then the optimal guaranteed cost controller is obtained by solving the equivalent convex optimization problem in the form of linear matrix inequalities (LMIs). The controller preserves closed-loop stability regardless of the delay length. The behavior of the resulting teleoperation system is illustrated in simulations.

Energy-Efficiency Power Allocation for Cognitive Radio MIMO-OFDM Systems

This paper studies energy-efficiency (EE) power allocation for cognitive radio MIMO-OFDM systems. Our aim is to minimize energy efficiency, measured by Joule per bit metric, while maintaining the minimal rate requirement of a secondary user under a total power constraint and mutual interference power constraints. However, since the formulated EE problem in this paper is non-convex, it is difficult to solve directly in general. To make it solvable, firstly we transform the original problem into an equivalent convex optimization problem via fractional programming. Then, the equivalent convex optimization problem is solved by a sequential quadratic programming algorithm. Finally, a new iterative energy-efficiency power allocation algorithm is presented. Numerical results show that the proposed method can obtain better EE performance than the maximizing capacity algorithm.

Robust Energy Efficiency Power Allocation for Uplink OFDM-Based Cognitive Radio Networks

This paper studies the energy efficiency power allocation for cognitive radio networks based on uplink orthogonal frequency-division multiplexing. The power allocation problem is intended to minimize the maximum energy efficiency measured by Joule per bit metric, under total power constraint and robust aggregate mutual interference power constraint. However, the above problem is non-convex. To make it solvable, an equivalent convex optimization problem is derived that can be solved by general fractional programming. Then, a robust energy efficiency power allocation scheme is presented. Simulation results corroborate the effectiveness of the proposed methods.

Consistent formulation of network equilibrium with stochastic flows

Traffic flows in real-life transportation systems vary on a daily basis. According to traffic flow theory, such variability should induce a similar variability in travel times, but this “internal consistency” is generally not captured by existing network equilibrium models. We present an internally-consistent network equilibrium approach, which considers two potential sources of flow variability: (i) daily variation in route choice and (ii) daily variation in origin–destination demand. We particularly aspire to a flexible formulation that permits alternative statistical assumptions, which allows the best fit to be made to observed variability data in particular applications. Joint probability distributions of route—and therefore link—flows are derived under several assumptions concerning stochastic driver behavior. A stochastic network equilibrium model with stochastic demands and route choices is formulated as a fixed point problem. We explore limiting cases which allow an equivalent convex optimization problem to be defined, and finally apply this method to a real-life network of Kanazawa City, Japan.

Energy-Efficient Resource Allocation for OFDM-Based Cognitive Radio Networks

In this paper, we investigate the energy-efficient resource allocation in orthogonal frequency division multiplexing (OFDM)-based cognitive radio (CR) networks, where we try to maximize the system energy-efficiency under the consideration of many practical limitations, such as transmission power budget of the CR system, interference threshold of primary users and traffic demands of secondary users. Our general objective formulation leads to a challenging mixed integer programming problem that is hard to solve. To make it computationally tractable, we employ a time-sharing method to transform it into a non-linear fractional programming problem, which can be further converted into an equivalent convex optimization problem by using its hypogragh form. Based on these transformations, it is possible to obtain (near) optimal solution by standard optimization technique. However, the complexity of the standard technique is too high for this real-time optimization task. By exploiting the structure of the problem extensively, we develop an efficient barrier method to work out the (near) optimal solution with a reasonable complexity, significantly better than the standard technique. Numerical results show that our proposal can maximize the energy efficiency of the CR system, whilst the proposed algorithm performs quickly and stably.

A primal-dual interior point method for optimal zero-forcing beamformer design under per-antenna power constraints

In this paper, we consider an optimal zero-forcing beamformer design problem in multi-user multiple-input multiple-output broadcast channel. The minimum user rate is maximized subject to zero-forcing constraints and power constraint on each base station antenna array element. The natural formulation leads to a nonconvex optimization problem. This problem is shown to be equivalent to a convex optimization problem with linear objective function, linear equality and inequality constraints and quadratic inequality constraints. Here, the indirect elimination method is applied to reduce the convex optimization problem into an equivalent convex optimization problem of lower dimension with only inequality constraints. The primal-dual interior point method is utilized to develop an effective algorithm (in terms of computational efficiency) via solving the modified KKT equations with Newton method. Numerical simulations are carried out. Compared to algorithms based on a trust region interior point method and sequential quadratic programming method, it is observed that the method proposed is much superior in terms of computational efficiency.

Solving a class of geometric programming problems by an efficient dynamic model

In this paper, a neural network model is constructed on the basis of the duality theory, optimization theory, convex analysis theory, Lyapunov stability theory and LaSalle invariance principle to solve geometric programming (GP) problems. The main idea is to convert the GP problem into an equivalent convex optimization problem. A neural network model is then constructed for solving the obtained convex programming problem. By employing Lyapunov function approach, it is also shown that the proposed neural network model is stable in the sense of Lyapunov and it is globally convergent to an exact optimal solution of the original problem. The simulation results also show that the proposed neural network is feasible and efficient.

Design of Affine Controllers via Convex Optimization

We consider a discrete-time time-varying linear dynamical system, perturbed by process noise, with linear noise corrupted measurements, over a finite horizon. We address the problem of designing a general affine causal controller, in which the control input is an affine function of all previous measurements, in order to minimize a convex objective, in either a stochastic or worst-case setting. This controller design problem is not convex in its natural form, but can be transformed to an equivalent convex optimization problem by a nonlinear change of variables, which allows us to efficiently solve the problem. Our method is related to the classical -design procedure for time-invariant, infinite-horizon linear controller design, and the more recent purified output control method. We illustrate the method with applications to supply chain optimization and dynamic portfolio optimization, and show the method can be combined with model predictive control techniques when perfect state information is available.