Parametric Subtractive Form Research Articles

Energy efficiency optimization in a parallel relay-assisted UWOC system with simultaneous lightwave information and power transfer.

In this paper, we investigate the energy efficiency optimization for a parallel relay-assisted underwater wireless optical communication (UWOC) system with simultaneous lightwave information and power transfer (SLIPT) over an aggregate channel. In this system, relay nodes are equipped with energy harvesting devices, getting energy from the direct current component of the received signal transmitted by the source node. These nodes utilize the harvested energy to transmit the signal to the destination node with the decoding and forwarding strategy. The harvested energy for each relay node is derived by the Gauss-Laguerre quadrature formula and the outage probability is deduced by the Meijer-G function. Then, the system's energy efficiency can be calculated and an energy efficiency maximization problem is built up with respect to the bias current. We propose a three-level-iteration algorithm to solve this problem. In the first level, the Dinkelbach method is used to represent energy efficiency in a parametric subtractive form. In the second level, we use the penalty function method to convert the object function and constraint. In the third level, the objective function is transformed into a quadratic function by using a successive convex approximate method, thereby solving for the bias current. The effects of system parameters on energy efficiency are also analyzed. Theoretical results and Monte Carlo simulations suggest that employing the solved bias current can significantly improve the system's energy efficiency.

Energy-efficient BS sleeping, user association, and resource allocation in full-duplex ultra-dense networks

Full-duplex ultra-dense network (FD-UDN) is a promising technology in 5G mobile networks for handling the increase in network capacity. However, interference management and energy efficiency are two of the most important challenges that must be addressed. With the small base stations (SBSs) densification, employing sleeping strategy coupled with resource management becomes an effective approach to manage interference and power consumption in FD-UDN. To the best of our knowledge, this aspect has not been addressed in previous work. To this end, we develop a framework to optimize the BS sleeping and resource management with the aim of maximizing energy efficiency and maintaining the quality of service (QoS) requirements of users. The problem is formulated as a non-convex mixed-integer non-linear programming problem, which is difficult to handle. Employing the Dinkelbach method, the objective function of the problem is converted to an equivalent parametric subtractive form. Then, the problem is decoupled into two sub-problems: user association and resource allocation, as well as BSs on/off switching. The former is solved using the iterative reweighted lq-norm minimization (IRM) method, and the latter is solved using the Lagrangian dual method and the constrained concave-convex procedure (CCCP). The simulation results demonstrate that the proposed method is more effective than traditional ones in simultaneously improving the EE, reducing power consumption, and keeping fewer SBSs active, especially in high network loads.

GA based energy efficiency resource allocation in heterogeneous networks with MRC

The energy efficiency (EE) resource allocation problem for downlink orthogonal frequency division multiple access (OFDMA) heterogeneous networks (HetNets) of wireless communication is investigated in this article. A coordinated multipoint (CoMP) network consisting of a microcell and multiple picocells interconnected via a backhaul network is considered. The mathematical form of EE maximization is a fractional, mixed-integer, nonlinear programming, and NP-hard to solve. Genetic algorithm (GA) based scheme is developed for solving the formulated maximization problem. For GA based scheme, a normal GA is used for resource blocks (RBs) allocation and for the power distribution process, instead of transforming the fractional objective function into a parametric subtractive form, a multi-objective optimization problem (MOOP) is formed and then non-dominated sorting genetic algorithm II (NSGA-II) is applied to tackle the MOOP. Finally, the simulation process is provided to verify the effectiveness of the proposed method and the results show that the performance of GA based scheme outperforms the benchmark scheme.

Resource Management for Computation Offloading in D2D-Aided Wireless Powered Mobile-Edge Computing Networks

The integration of mobile-edge computing (MEC) and energy harvesting (EH) can potentially improve the network performances and prolong the battery life of the device. In this article, we study the resource management problem in the device-to-device (D2D)-aided wireless powered MEC networks where one device can forward or execute computation data for other devices with its resources. Our problem seeks to optimize the computation offloading strategy, transmission power, energy transmit power, as well as CPU speed to maximize the long-term utility energy efficiency (UEE). UEE is defined as the achieved computation data per unit energy. Since the formulated problem is in fractional form and hard to solve, we employ the Dinkelbach algorithm to transform the problem into a parametric subtractive form. Furthermore, considering that the formulated problem is time varying and stochastic due to the dynamic task arrival rate and battery level, we transform the long-term problem into deterministic drift-plus-penalty subproblems for each time slot by introducing virtual queues and adopting the Lyapunov optimization theory. The proposed scheme can balance the optimal UEE and stable data queue by introducing the control parameter <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$V$ </tex-math></inline-formula> . Theoretically, we reveal the tradeoff between the UEE and stable queue length for wireless powered MEC systems as <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$[O(1/V), O(V)]$ </tex-math></inline-formula> . Finally, the simulations illustrate the efficiency of the proposed scheme compared with the existed work in terms of the UEE, stable queue length, and battery level.

Joint User Association and Power Allocation for Hybrid Half-Duplex/Full-Duplex Relaying in Cellular Networks

For hybrid half-duplex/full-duplex relaying in a relay-aided cellular network, a joint user association, relay mode selection, and power allocation scheme is proposed to maximize the energy efficiency under the minimum spectral efficiency requirement and transmission power constraints. This combinatorial optimization problem is a mixed-integer nonconvex one, which is difficult to be solved in its original form. To circumvent this issue, the problem is first transformed into an equivalent one whose objective function is in a parametric subtractive form. Then, the equivalent problem is reformulated as a convex one by relaxing index variables, converting the nonconvexity by the successive convex approximation, and constructing auxiliary variables. In this way, the equivalent nonconvex problem is approximated by a convex one in each iteration, and the dual decomposition technique is employed to solve the convex one. An iterative algorithm is further developed to reach the solution to the primal problem. Simulation results show that the performance of the iterative algorithm can be very close to the optimal solution obtained by the exclusive searching within only a few number of iterations. Moreover, the proposed scheme outperforms existing ones, which only adhere to either the user association or the relay mode selection but not both.

Energy-efficient association mechanism designed for uplink CDMA-based HCNs

ABSTRACTTo reduce the energy consumption and prolong the battery lifetimes of mobile terminals, the design of energy-efficient association scheme is necessary and meaningful. To this end, we design a type of association mechanism (scheme) to maximize the whole energy efficiency (WEE) for uplink code-division-multiple-access (CDMA)-based heterogeneous cellular networks (HCNs), and formulate it as a WEE maximization problem with users’ SINR (signal-to-interference-plus-noise ratio) constraints. Considering that the finally formulated problem is in a fractional mixed-integer form and hard to tackle, we introduce an energy efficiency (EE) parameter to convert it into a parametric subtractive form. At last, we design two two-layer iterative algorithms for the formulated problem, whose primary difference lies in the treatment of SINR constraints. In general, the outer loop utilizes a bisection method to search the optimal EE parameter, and the inner loop alternately optimizes the association index and transmit power. At last, we give the corresponding convergence analyses for some subalgorithms, and also give some detailed complexity analyses for the whole algorithm. In the simulation, we introduce an existing energy-efficient association mechanism for comparison, and finally investigate the impacts of different network parameters on the association performance.

Robust Energy-Efficient Downlink Resource Allocation in Heterogeneous Networks with Outage Probability Constraint

With the development of the fifth generation communication technology, improving energy efficiency (EE is defined as the ratio of the system throughput over the total power consumption) of wireless communication becomes a hot topic, which has attracted wide attention from industry and academia. Heterogeneous networks (HetNets) have been considered as a new promising technique for expanding network coverage and improving EE. Robust resource allocation is a huge challenge when uncertainty parameters are involved in this issue. The problem is more significant in HetNets since perfect channel state information is not available at femtocell base station’s transmitters. In this paper, we study the downlink resource allocation in HetNets under outage probability constraint, and formulate the EE maximization problem as a nonlinear fractional programming problem. In order to solve the fractional programming problem, firstly, we transform the original problem into an equivalent optimization problem in a parametric subtractive form. Then based on the exponential distribution model under Rayleigh fading environment, the probability constraint is transformed into a deterministic constraint. Finally, we propose a two-loop iteration algorithm to find the optimal solution by using Dinkelbachs method and Lagrangian dual decomposition method. Simulation results demonstrate the convergence and the effectiveness of the proposed algorithm.

Joint Cell Activation and Selection for Green Communications in Ultra-Dense Heterogeneous Networks

The densification of small cells in heterogeneous networks (HetNets) causes huge energy consumption and severe network interference. To fully exploit the potential of new network architecture, the cell selection (CS) in such HetNets should couple with reducing power consumption and network interference. To this end, we jointly perform cell activation and selection (CAS) to maximize the network energy efficiency (EE) under users’ long-term rate constraints. The formulated problem is in a mixed-integer fractional form and hard to tackle. We need to transform it into a parametric subtractive form, by which we reach its solution through a three-layer iterative algorithm. The first layer searches an EE parameter using a bisection method; the second layer alternately optimizes CAS indices; the third layer solves CS and cell activation (CA) problems using dual decomposition and fixed point iteration, respectively. At last, we give some complexity and convergence analyses for the designed algorithm, and investigate the impacts of different network parameters on system performance. The simulation results show that the CA introduced in CS is a good option to reduce energy consumption and network interference.

Energy Efficiency Optimization for Downlink Cloud RAN with Limited Fronthaul Capacity.

In the downlink cloud radio access network (C-RAN), fronthaul compression has been developed to combat the performance bottleneck caused by the capacity-limited fronthaul links. Nevertheless, the state-of-arts focusing on fronthaul compression for spectral efficiency improvement become questionable for energy efficiency (EE) maximization, especially for meeting its requirements of large-scale implementation. Therefore, this paper aims to develop a low-complexity algorithm with closed-form solution for the EE maximization problem in a downlink C-RAN with limited fronthaul capacity. To solve such a non-trivial problem, we first derive an optimal solution using branch-and-bound approach to provide a performance benchmark. Then, by transforming the original problem into a parametric subtractive form, we propose a low-complexity two-layer decentralized (TLD) algorithm. Specifically, a bisection search is involved in the outer layer, while in the inner layer we propose an alternating direction method of multipliers algorithm to find a closed-form solution in a parallel manner with convergence guaranteed. Simulations results demonstrate that the TLD algorithm can achieve near optimal solution, and its EE is much higher than the spectral efficiency maximization one. Furthermore, the optimal and TLD algorithms are also extended to counter the channel error. The results show that the robust algorithms can provide robust performance in the case of lacking perfect channel state information.

Energy-Efficient Downlink Resource Allocation in Heterogeneous OFDMA Networks

In this paper, we investigate energy-efficient downlink resource allocation in heterogeneous orthogonal frequency division multiple access (OFDMA) networks, and formulate the energy efficiency (EE) maximization problem as a mixed-integer nonlinear fractional programing (MINLFP) problem with a nonconcave nonlinear objective function and nonlinear constraints. By means of fractional programing and changing of variables, we transform the original MINLFP problem into an equivalent optimization problem in a parametric subtractive form, which is proved to be a concave mixed-integer nonlinear programing (MINLP) problem and is optimally solved by using Dinkelbach and branch-and-bound (BB) methods. In BB method, the concave MINLP problem is relaxed to a series of concave nonlinear programing problems and solved by the use of Powell–Hestenes–Rockafellar augmented Lagrangian (PHR-AL) method. The optimal solution can be used to benchmark the performance of suboptimal solutions. As the computational complexity of BB method increases exponentially with problem size, we further develop a suboptimal two-step scheme, which first allocates the resource blocks and then performs the transmit power control to give suboptimal solution with much lower complexity. Simulation results demonstrate the effectiveness of the proposed schemes and show that the proposed suboptimal two-step scheme is promising for practical applications as it makes a good tradeoff between EE performance and computational complexity.

Cooperative Downlink Max-Min Energy-Efficient Precoding for Multicell MIMO Networks

Energy efficiency (EE) optimization of wireless systems has attracted increasing attention recently due to its beneficial impacts on the environment and operational savings. Max-min user energy-efficient precoding for multicell multiple-input–multiple-output (MIMO) cooperative networks is investigated. The optimization problem is a nonconvex fractional programming problem, and optimal solutions are hard to find. Two different local optimization methods, namely, block coordinate descent and sequential convex approximation, are proposed to transform the original problem into a series of convex subproblems. In the former method, the relationship between the user rate and the minimum mean square error (MMSE) is utilized, and optimization of the transmitter matrix is formulated as a semidefinite program; the latter method is based on the convex approximation of the nonconvex rate function. The fractional subproblem is transformed into a parameterized subtractive form by exploiting the generalized fractional programming theorem in both methods. Two iterative-fairness-based energy-efficient algorithms are proposed with proved local convergence. Numerical results illustrate that the proposed max-min EE algorithms can improve EE with a performance loss in terms of the sum rate at a high signal-to-noise ratio (SNR) and achieve EE fairness among base stations with different transmit power levels.

Energy-Efficient Optimization for Downlink Massive MIMO FDD Systems With Transmit-Side Channel Correlation

The energy-efficient resource allocation problem is investigated for the downlink massive multiple-input–multiple-output (MIMO) frequency-division duplexing (FDD) system under a correlated Rayleigh fading channel. Our objective is to maximize energy efficiency by adjusting the training duration, training power, and data power, under the constraint of the total transmit energy and spectral efficiency requirement for the user, which evaluates the impacts of the training and data transmission phases simultaneously. The optimization problem is established in a complicated form, where the difficulties lie in the nonanalytic expression of the involved objective function, as well as the nonconvex nature of the optimization problem. To solve it, the deterministic equivalent approximation methodology is introduced to obtain an accurate analytical expression of the cost function. Based on this, the optimization problem in a nonconvex fractional form is transformed into an equivalent optimization problem with a parametric subtractive form, which is still nonconvex. Thus, the objective function is lower bounded by a concave function, which leads to the availability of standard convex theory, and finally, an iterative resource allocation algorithm is proposed. Moreover, we obtain the closed-form solutions using the Lambert W function for some special channel cases. Numerical results validate the benefits of the proposed scheme and illustrate the tradeoff between training and data transmission.

Resource Efficiency: A New Beamforming Design for Multicell Multiuser Systems

Apart from spectral efficiency (SE), energy efficiency (EE) has become an important metric for future wireless communication systems. However, how to achieve balance between SE and EE for a multicell multiuser coordinated beamforming system remains an open problem. In this paper, we propose a new paradigm for EE–SE balancing, namely, using a new metric called resource efficiency (RE) as the objective function to achieve a reasonable tradeoff between SE and EE. The considered optimization problem is more complex than traditional problems and, in general, is NP-hard for finding the globally optimal solution. To obtain insight into the problem, we first equivalently transform the original problem into a parameterized subtractive form optimization problem with some auxiliary variables by using the fraction programming theory. Then, a successive convex approximation method and the classical second-order cone programming method are jointly used to solve the equivalent problem. Finally, an effective algorithm with proven convergence is proposed to obtain the solution to the considered RE optimization. In addition, the algorithm is further extended to consider imperfect channel state information (CSI) using the worst-case design. Extensive numerical simulations are given to validate the effectiveness of our algorithm.

Energy efficient coordinated precoding design for a multicell system with RF energy harvesting

This paper investigates multicell multiuser downlink systems with simultaneous wireless information and power transfer. We study the energy efficient transmission design for maximizing the system energy efficiency of data transmission (bits/Joule delivered to the receivers) which is defined as the ratio of the weighted sum rate to the total power consumption. In particular, we focus on the energy efficient coordinated precoding for the downlink of multicell system using the power splitting technique where each receiver divides the received signal into two power streams for concurrent information decoding and energy harvesting. To solve the non-convex optimization problem under consideration, first, we transform the primal optimization problem in fractional form into a tractable parameterized subtractive form optimization problem. Then, the tractable problem is solved by applying the technique of the Lagrangian optimization technique and semidefinite relaxation. An efficient solution to the considered optimization problem is finally developed. Numerical results validate the effectiveness of the proposed algorithm and reveal that the proposed algorithm can achieve better energy efficiency performance than the traditional energy efficient transmission.

Coordinated Beamforming for Energy Efficient Transmission in Multicell Multiuser Systems

In this paper we study energy efficient joint power allocation and beamforming for coordinated multicell multiuser downlink systems. The considered optimization problem is in a non-convex fractional form and hard to tackle. We propose to first transform the original problem into an equivalent optimization problem in a parametric subtractive form, by which we reach its solution through a two-layer optimization scheme. The outer layer only involves one-dimension search for the energy efficiency parameter which can be addressed using the bi-section search, the key issue lies in the inner layer where a non-fractional sub-problem needs to tackle. By exploiting the relationship between the user rate and the mean square error, we then develop an iterative algorithm to solve it. The convergence of this algorithm is proved and the solution is further derived in closed-form. Our analysis also shows that the proposed algorithm can be implemented in parallel with reasonable complexity. Numerical results illustrate that our algorithm has a fast convergence and achieves near-optimal energy efficiency. It is also observed that at the low transmit power region, our solution almost achieves the optimal sum rate and the optimal energy efficiency simultaneously; while at the middle-high transmit power region, a certain sum rate loss is suffered in order to guarantee the energy efficiency.