Energy Efficiency Maximization Problem Research Articles

The Optimal Power Allocation for Sum Rate and Energy Efficiency of Full-Duplex Two-Way Communication Network.

Full-duplex (FD) transmission holds a great potential of improving the sum data rate of wireless communication systems. However, the self-interference introduced by the full-duplex transmitter brings a big challenge to enhance the energy efficiency. This paper investigates the power allocation problem in a full-duplex two-way (FDTW) communication network over an OFDM channel, aiming at improving the sum data rate and energy efficiency. We first characterize the sum rate and energy efficiency achieved in a single-carrier FDTW system. The optimal transmit power that achieves the maximal sum data rate is presented. The energy efficiency maximization problem is solved by using fractional programming. Then we further formulate sum rate and energy efficiency maximization problem in a multi-subcarrier FDTW system. In particular, the sub-optimal transmit power allocation which achieves a decent sum rate improvement is found by using a proposed iterative algorithm. By combining the iterative algorithm and fractional programming, we further maximize the energy efficiency of the multi-subcarrier system. With our proposed algorithm, we can easily obtain an optimal transmit power that approximates the global optimal solution. Simulation results show that using the obtained optimal transmit power allocation algorithm can significantly improve the sum rate and energy efficiency in both single-carrier and multi-subcarrier systems.

Optimal Power Allocation in Downlink Multicarrier NOMA Systems: Theory and Fast Algorithms

In this work, we address the problem of finding globally optimal power allocation strategies to maximize the users sum-rate (SR) as well as system energy efficiency (EE) in the downlink of single-cell multicarrier non-orthogonal multiple access (MC-NOMA) systems. Each NOMA cluster includes a set of users in which the well-known superposition coding (SC) combined with successive interference cancellation (SIC) technique is applied among them. By obtaining the closed-form expression of intra-cluster power allocation, we show that MC-NOMA can be equivalently transformed to a virtual orthogonal multiple access (OMA) system, where the effective channel gain of these virtual OMA users is obtained in closed-form. Then, the SR and EE maximization problems are solved by using very fast water-filling and Dinkelbach algorithms, respectively. The equivalent transformation of MC-NOMA to the virtual OMA system brings new theoretical insights, which are discussed throughout the paper. The extensions of our analysis to other scenarios, such as considering users rate fairness, admission control, long-term performance, and a number of future next-generation multiple access (NGMA) schemes enabling recent advanced technologies, e.g., reconfigurable intelligent surfaces are discussed. Extensive numerical results are provided to show the performance gaps between single-carrier NOMA (SC-NOMA), OMA-NOMA, and OMA.

Multibeam Satellite Communications With Energy Efficiency Optimization

Energy efficiency (EE) is an important aspect of satellite communications. Different with the existing algorithms that typically use the first-order Taylor lower bound approximation to convert non-convex EE maximization (EEM) problems into convex ones, in this letter a two-step quadratic transformation method is presented. In the first step, the fractional form of the achievable rate over the total power consumption is converted into a non-fractional form based on quadratic transformation. In the second step, the fractional form of the signal power over the interference-and-noise power is further converted into a non-fractional form, still based on quadratic transformation. After the two-step quadratic transformation, the original EEM problem is converted into an equivalent convex one. Then an alternating optimization algorithm is presented to solve it by iteratively performing two stages until a stop condition is satisfied. Simulation results show that the presented algorithm can fast converge and its performance is better than that of the sequential convex approximation algorithm and the multibeam interference mitigation algorithm.

Spectral and Energy Efficiency of ACO-OFDM in Visible Light Communication Systems

In this paper, we study the spectral efficiency (SE) and energy efficiency (EE) of asymmetrically clipped optical orthogonal frequency division multiplexing (ACO-OFDM) for visible light communication (VLC). Firstly, we derive the achievable rates for Gaussian distributions inputs and practical finite-alphabet inputs. Then, we investigate the SE maximization problems subject to both the total transmit power constraint and the average optical power constraint with the above two inputs, respectively. By exploiting the relationship between the mutual information and the minimum mean-squared error, an optimal power allocation scheme is proposed to maximize the SE with finite-alphabet inputs. To reduce the computational complexity of the power allocation scheme, we derive a closed-form lower bound of the SE. Also, considering the quality of service, we further tackle the non-convex EE maximization problems of ACO-OFDM with the two inputs, respectively. The problems are solved by the proposed Dinkelbach-type iterative algorithm. In each iteration, the interior point algorithm is applied to obtain the optimal power allocation.The performance of the proposed power allocation schemes for the SE and EE maximization are validated through numerical analysis.

Joint Device Pairing, Reflection Coefficients, and Power Control for NOMA Backscatter Systems

Non-orthogonal multiple access (NOMA) and backscatter communication are two emerging technologies for low-power communication. In this paper, we consider a NOMA backscatter system, where signals from two backscatter devices are multiplexed on a frequency resource block using NOMA in each time slot. Our objective is to maximize the average energy efficiency by optimizing backscatter device pairing, reflection coefficients of backscatter devices, and the transmit power of the reader. We formulate the average energy efficiency maximization problem subject to the minimum circuit power and the minimum data rate requirements of the backscatter devices, and the transmit power constraint of the reader. The formulated problem is nonconvex. To obtain a suboptimal solution for this problem, we use alternating optimization technique and decompose the problem into two subproblems. The subproblems are solved by using fractional programming, Dinkelbach’s algorithm, and successive convex approximation method. Simulation results show that our proposed algorithm converges quickly to a suboptimal solution. Our proposed algorithm outperforms several baseline algorithms, including the genetic algorithm, fixed device pairing scheme, conventional device pairing scheme, maximum transmit power allocation scheme, and random reflection coefficient selection scheme, in terms of the average energy efficiency. The optimality gap of our proposed algorithm is investigated by comparing with the optimal scheme, in which the optimal device pairing is obtained based on exhaustive search.

User scheduling and power allocation for downlink multi-cell multi-carrier NOMA systems

In Non-Orthogonal Multiple Access (NOMA), the best way to fully exploit the benefits of the system is the efficient resource allocation. For the NOMA power domain, the allocation of power and spectrum require solving the mixed-integer nonlinear programming NP-hard problem. In this paper, we investigate user scheduling and power allocation in Multi-Cell Multi-Carrier NOMA (MCMC-NOMA) networks. To achieve that, we consider Weighted Sum Rate Maximization (WSRM) and Weighted Sum Energy Efficiency Maximization (WSEEM) problems. First, we tackle the problem of user scheduling for fixed power using Fractional Programming (FP), the Lagrange dual method, and the decomposition method. Then, we consider Successive Pseudo-Convex Approximation (SPCA) to deal with the WSRM problem. Finally, for the WSEEM problem, SPCA is utilized to convert the problem into separable scalar problems, which can be parallelly solved. Thus, the Dinkelbach algorithm and constraints relaxation are used to characterize the closed-form solution for power allocation. Extensive simulations have been implemented to show the efficiency of the proposed framework and its superiority over other existing schemes.

Worst-Case Energy Efficiency in Secure SWIPT Networks With Rate-Splitting ID and Power-Splitting EH Receivers

This paper studies the robust beamforming design for simultaneous wireless information and power transfer (SWIPT)-enabled networks, where the rate-splitting (RS) scheme and the power-splitting (PS) energy harvesting (EH) receiver are adopted for secure information transfer and EH, respectively. In order to explore the worst-case energy efficiency (EE) performance limit of the system, an EE maximization problem is formulated with the elliptically bounded channel state information error model under the constraints of the quality of service (QoS) requirements of information decoding users, the EH requirements of EH users and the power budget at the transmitter. To tackle the formulated non-convex problem, a sequential minimal optimization-based algorithm is first proposed to construct a mapping table and the optimal PS ratios of the PS EH receiver are found by searching the table. Then, a dual-layer iterative algorithm is designed to obtain the maximal EE based on the Dinkelbach’s method in the inner loop and the successive convex approximation method in the outer loop. To accelerate the convergence of the outer loop, an efficient initialization algorithm is also designed. Simulation results show that the RS scheme contributes to the EE enhancement, and the PS EH receiver enlarges the rate-energy region restricted by the non-linear EH circuit. Moreover, traditional sum-rate maximization design and power minimization design may induce a notable worst-case EE performance loss at the high-power region and the low-QoS requirement region, respectively.

Secure and Energy Efficient Transmission for IRS-Assisted Cognitive Radio Networks

The spectrum efficiency (SE) and security of the secondary users (SUs) in the cognitive radio networks (CRNs) have become two main issues due to the limitation interference to the primary users (PUs) and the shared spectrum with the PUs. Intelligent reflecting surface (IRS) has been recently proposed as a revolutionary technique which can help to enhance the SE and physical layer security of wireless communications. This paper investigates the application of IRS in an underlay CRN, where a multi-antenna cognitive base station (CBS) utilizes spectrum assigned to the PU to communicate with a SU via IRS in the presence of multiple coordinated eavesdroppers (Eves). To achieve the trade-off between the secrecy rate (SR) and energy consumption, we investigate the secrecy energy efficiency (SEE) maximization problem by jointly designing the transmit beamforming at the CBS and the reflect beamforming at the IRS. To solve the non-convex problem with coupled variables, we propose an iterative alternating optimization algorithm to solve the sub-problems alternately, by utilizing an iterative penalty function based algorithm for sub-problem 1 and the difference of two-convex functions method for sub-problem 2. Furthermore, we provide a second-order-cone-programming (SOCP) approximation approach to reduce the computational complexity. Finally, the simulation results demonstrate that IRS can help significantly improve the SE and enhance the physical layer security in the CRNs. Moreover, the effectiveness and superiority of our proposed algorithm in achieving the trade-off between the SR and energy consumption are verified.

Secrecy Energy Efficiency Maximization in UAV-Enabled Wireless Sensor Networks Without Eavesdropper’s CSI

Unmanned aerial vehicles (UAVs) are anticipated to be a potential data collection solution for wireless sensor networks (WSNs). The main challenges of integrating UAVs in WSNs are security threats and UAV’s onboard energy limitation. To cope with these two challenges, this article examines the secrecy energy efficiency (SEE) maximization problem in UAV-enabled WSN. Specifically, a full-duplex (FD) UAV gathers confidential information from ground sensor nodes (SNs) in the uplink while sending jamming signals to confound a ground eavesdropper (Eve) in the downlink. Considering a passive eavesdropping scenario lacking Eve’s instantaneous channel state information (CSI), the resulting problem is subject to the constraints of connection outage probability (COP), secrecy outage probability (SOP), securely collected bits, and flight trajectory. To tackle the intractable nonconvex problem, we first derive the optimal codeword rate and redundancy rate in closed-form expressions and then develop a low-complexity algorithm using the block coordinate descent (BCD) approach to alternatively optimize the SN scheduling, SN transmit power, UAV transmit power, and UAV trajectory. Simulation results verify the performance gains of the proposed scheme compared with the benchmark schemes. In particular, the proposed scheme achieves nearly the same secrecy rate gains at a lower UAV’s energy consumption cost than the sum secrecy rate maximization (SSRM) baseline. Moreover, it is revealed that trajectory optimization of the proposed scheme plays a crucial role in improving SEE performance compared with the circle trajectory (CT) baseline.

Joint user association and energy efficiency maximization in beyond 5G heterogeneous networks

SummaryHeterogeneous networks (HetNets) seem to be the future of data networks supported by macrocells, small cells, relays, and D2D communication. The main purpose of HetNets is to facilitate maximum users while keeping energy efficiency (EE) to its peak. In this research work, we have formulated joint users association and EE maximization problem for HetNets, where our main goal is to increase the number of users associated with HetNets while keeping EE to its maximum. Formulated problem is a concave fractional problem in nature. We have used Charnes–Cooper Transformation to convert it to the concave optimization problem. We have used the (MADS) algorithm to solve the formulated optimization problem. Results have been analyzed after extensive simulations. Performance of MADS algorithm have been shown with respect to different system parameters, that is, the number of users associated, the minimum required data rate, and joint maximization of users associated and EE.

Resource Allocation for Uplink NOMA-Based D2D Communication in Energy Harvesting Scenario: A Two-Stage Game Approach

Energy harvesting (EH) endows device-to-device (D2D) communication and cellular equipment with the ability of continuous communication to provide internet-of-things (IoT) services in natural areas. While the available energy, which relies on EH, becomes an extra nonnegligible factor in resource allocation. Besides, we integrate uplink non-orthogonal multiple access (NOMA) with D2D communication to provide multiple access for D2D transmitters for more efficient IoT service and more efficient utilization of limited spectrum. In this scenario, ingenious resource allocation approach is a key focus for utilizing the advantages in energy and spectral efficiency. Aiming to investigate the inherent resource allocation issue, we set our goal as maximizing the energy efficiency for both NOMA-based D2D groups and cellular users (CUs), where the power and spectrum allocation are both considered. Then we propose a two-stage game approach, which is theoretically proved to be capable of obtaining the equilibrium and a stable result, to solve the unilateral energy efficiency maximization problems. Besides, an energy-aware screening method is proposed to reduce the computations based on the available energy of user equipment. Finally, the effectiveness of our proposed method is verified through elaborated simulation results.

Energy Efficiency Optimization of Reconfigurable Intelligent Surfaces With Electromagnetic Field Exposure Constraints

This work considers the problem of energy efficiency maximization in a RIS-based communication link, subject to not only the conventional maximum power constraints, but also additional constraints on the maximum exposure to electromagnetic radiations of the end-users. The RIS phase shifts, the transmit beamforming, the linear receive filter, and the transmit power are jointly optimized, and two provably convergent and low-complexity algorithms are developed. One algorithm can be applied to the general system setups, but does not guarantee global optimality. The second algorithm is provably optimal in a notable special case. The numerical results show that RIS-based communications can ensure high energy efficiency while fulfilling users' exposure constraints to radio frequency emissions.

Energy-Efficient UAV-Relaying 5G/6G Spectrum Sharing Networks: Interference Coordination With Power Management and Trajectory Design

As massive ground users access wireless networks with limited available spectrum, coexisting users that share the same spectrum band severely interfere with each other. Moreover, communication pairs without direct communication links may suffer from severe outage issues. In this paper, unmanned aerial vehicle (UAV) relaying-assisted interference coordination is proposed to enhance data transmission reliability by 1) relaying transmission, and 2) alleviating mutual interference among ground users. To efficiently utilize confined UAV energy such that the UAV relaying service life can be significantly prolonged, the full-duplex (FD) technique is exploited. An exact energy efficiency (EE) maximization problem is formulated, which jointly optimizes throughput and UAV energy consumption. Different from the traditional offline method, online power management and trajectory designs are performed under the information causality and rate constraints. Considering that power management and trajectory are coupled, we design a block coordinate descent method to efficiently solve the optimization problem. Numerical results demonstrate that the proposed scheme outperforms existing schemes, and the EE is about 30% and 46% higher than those of the genetic algorithm and half-duplex scheme, respectively. Moreover, impacts of different positions and the maximum power of ground users on the EE have been demonstrated.

Energy-Efficient Interference-Aware Cognitive Machine-to-Machine Communications Underlaying Cellular Networks

Machine-to-machine (M2M) communications can effectively utilize cognitive radio (CR) to coexist with cellular users in what is known as cognitive M2M (CM2M) communications. In this system, underlay CR is used to manage spectrum sharing among machine type communication devices (MTCDs) and cellular user equipment (CUE) where the CUE are considered to be primary users (PUs) and the MTCDs are secondary users (SUs). Moreover, due to the limited battery capacity of MTCDs and diverse quality-of-service (QoS) requirements of both MTCDs and CUE, energy efficiency (EE) is critical to prolonging network lifetime. This paper investigates the power allocation problem for energy-efficient CM2M communications underlaying cellular networks. Underlay CR is employed to manage the coexistence of MTCDs and CUE and exploit spatial spectrum opportunities to improve spectrum utilization. Two power allocation problems are proposed where the first targets MTCD power consumption minimization while the second considers MTCD EE maximization subject to MTCD transmit power constraints, MTCD minimum data rate requirements, and CUE interference limits. The proposed power consumption minimization problem is transformed into a geometric programming (GP) problem and solved iteratively. The proposed EE maximization problem is a nonconvex fractional programming problem. Hence, a parametric transformation is used to convert it into an equivalent convex form and this is solved using an iterative approach. Simulation results are presented which show that the proposed algorithms provide MTCD power allocation with lower power consumption and higher EE than the equal power allocation (EPA) scheme while satisfying the constraints.

Active Reconfigurable Intelligent Surface: Fully-Connected or Sub-Connected?

To overcome the “multiplicative fading effect” introduced by passive reconfigurable intelligent surface (RIS), the concept of active RIS has been recently proposed to amplify the radiated signals. However, the existing fully-connected architecture of active RIS consumes high power due to the additionally integrated active components. To address this issue, we propose the sub-connected architecture of active RIS. Different from fully-connected architecture, where each element integrates a dedicated power amplifier, in the sub-connected architecture, multiple elements control their phase shifts independently but share a same power amplifier, which significantly reduces the number of power amplifiers for power saving at the cost of fewer degrees of freedom (DoFs) for beamforming design. Fortunately, our analysis reveals that performance loss introduced by the sub-connected architecture is slight, indicating that it can achieve much higher energy efficiency (EE). Furthermore, we formulate the EE maximization problem in the active RIS-aided system for both architectures and develop a corresponding joint beamforming design. Simulation results verify the proposed sub-connected architecture as an energy-efficient realization of active RIS.

On Energy Efficiency of Wideband RIS-Aided Cell-Free Network

Cell-free (CF) network is a favorable technique against inter-cell interferences to improve the network capacity. However, to further improve the network capacity, a large number of base stations (BSs) are required to be deployed with high cost and power consumption. To tackle this problem, an energy-efficient technique called reconfigurable intelligent surface (RIS)-aided CF network has been recently proposed. By replacing some of the required power-hungry BSs with low-power RISs, the energy efficiency of CF network can be enhanced with guaranteed performance. To achieve this goal, in this paper, we first formulate a joint active and passive beamforming problem to maximize the energy efficiency of RIS-aided CF networks. Then, we propose an alternate optimization algorithm to solve this problem. Specifically, we decompose the original energy efficiency maximization problem into multiple subproblems and solve them alternatively. Particularly, we adopt the zero-forcing (ZF) beamforming scheme to optimize the active beamforming at BSs, while the sequential programming (SP) method is adopted to realize the passive beamforming at RISs. Moreover, a realistic energy-consumption model for wideband RIS-aided CF networks is provided, and the effectiveness of the proposed scheme is evaluated by simulations. Finally, simulation results verify that, the proposed scheme is able to achieve a higher energy efficiency than the existing benchmark solution.

Maximizing lower bound of energy efficiency in multi-tier heterogeneous cellular network via stochastic geometry

In this paper, an optimization method is proposed to maximize the lower bound of energy efficiency (EE) in the multi-tier heterogeneous cellular network (HCN) and resolved by adjusting Base Station (BS) density and BS transmit power. Firstly, we derive the mathematical formulation of network coverage probability and the average user rate. We prove that the network coverage probability and the average user rate monotonically increase with the cumulative sum of the product of BS density and BS transmit power. Then, the network coverage probability and the average user rate requirements are converted to the BS density and the BS transmit power constraints. An EE maximization problem is formulated. Nevertheless, the intractable problem is reformulated by maximizing the lower bound of EE since the coupled parameters are tight. The simplified optimization problem can be converted to a standard form of geometric programming (GP) by a convex approximation method. The problem in GP form can be further transformed into the traditional convex problem and can be fully solved using the interior point method. Numerical simulations show that the optimal solutions can be determined with fast convergence, while the network EE is significantly improved. The gap between the approximate and the original solutions is analyzed through simulations.

Energy-efficient opportunistic multi-carrier NOMA-based resource allocation for beyond 5G (B5G) networks

The interplay between the non-orthogonal multiple access (NOMA) and the opportunistic cognitive radio (CR)-based orthogonal frequency multiple access (OFDMA) has been recently realized as a promising paradigm to support the unprecedented massive connectivity demands of future beyond fifth-generation (B5G) wireless communication systems. In such systems, which are called multi-carrier NOMA CR-based systems, each licensed band reserved for primary users can be opportunistically utilized based on power-domain NOMA to serve a group of secondary users simultaneously. An important challenge in this domain is how to provide energy-efficient resource allocation techniques that attempt to strike a balance between the total throughput (i.e., the achieved sum-rate) and the power required to achieve that rate while satisfying network QoS demands and being aware of the unique characteristics of the CR operating environment. In this paper, we propose an energy-efficient resource allocation technique for multi-carrier NOMA CR-based systems, which aims at maximizing the overall energy efficiency (EE) of the system under a set of CR and NOMA constraints. The EE maximization problem is shown to be a fractional non-convex optimization, which is, in general, hard to optimize. To deal with the fractional and the non-convexity nature of the formulated EE maximization problem, we exploit the Dinkelbach’s algorithm to transfer the EE problem to a parameterized optimization problem. Then we use an iterative optimization approach to obtain the solution for the EE maximization problem. Simulation results reveal that this EE maximization-based resource allocation technique outperforms the existing resource allocation techniques in terms of the overall EE of the system while striking a good balance between the sum-rate and the transmit power consumption.

Robust Resource Allocation Algorithm for Energy-Harvesting-Based D2D Communication Underlaying UAV-Assisted Networks

Energy efficiency (EE) is a significant performance indicator in unmanned aerial vehicle (UAV)-assisted communication networks for providing a balance between power consumption minimization and transmission rate maximization. However, most of the current works focus on the transmission rate maximization under perfect channel state information (CSI) and exact coordinate information, which is too ideal in practical systems due to channel estimation errors and coordinate estimation errors. Thus, robust resource allocation algorithms with imperfect CSI and coordinate information are critically important to reduce users’ outages and improve system robustness. In this article, a robust EE maximization problem with channel uncertainties and coordinate uncertainties is formulated for an energy harvesting-based device-to-device (D2D) communication underlaying UAV-assisted network under some necessary constraints, which involve the outage probability constraints of ground terminals, the flight altitude constraint of the UAV, the minimum harvested energy constraints of D2D users, and the transmission time constraint. Both radio resource allocation and the flight altitude are jointly optimized based on the worst case approach. The considered nonconvex problem is transformed into a convex one by exploiting variable relaxation and variable substitution approaches. The Lagrange dual theory is used to derive the closed-form expressions of robust resource allocation. Simulation results demonstrate the effectiveness of the proposed algorithm by comparing it with the benchmark algorithms in terms of EE and robustness.

Energy Efficiency Analysis in Modified GoF Spectrum Sensing-Based AF Relay Cooperative Cognitive Sensor Network with Energy Harvesting

In this paper, we propose a joint sensing duration and transmission power allocation scheme to maximize the energy efficiency (EE) of the secondary user (SU) in a cooperative cognitive sensor network (CSN). At the initial time slot of the frame, the secondary transmitter (ST) performs energy harvesting (EH) and spectrum sensing simultaneously using power splitting (PS) protocol. The modified goodness of fit (GoF) spectrum sensing algorithm is employed to detect the licensed spectrum, which is not sensitive to an inaccurate noise power estimate. Based on the imperfect sensing results, the ST will act as an amplify-and-forward (AF) relay and assist in transmission of the primary user (PU) or transmit its own data. The SU’s EE maximization problem is constructed under the constraints of meeting energy causality, sensing reliability, and PU’s quality of service (QoS) requirement. Since the SU’s EE function is a nonconvex problem and difficult to solve, we transform the original problem into a tractable convex one with the aid of Dinkelbach’s method and convex optimization technique by applying a nonlinear fractional programming. The closed-form expression of the ST’s transmission power is also derived through Karush-Kuhn-Tucker (KKT) and gradient method. Simulation results show that our scheme is superior to the existing schemes.