EE-SE Tradeoff Research Articles

Energy Efficiency Optimization with SINR Constraints in Downlink MIMO-NOMA Systems

In downlink multiple-input, multiple-output, (MIMO) and non-orthogonal multiple access (NOMA) systems, the inter-cluster interference can be cancelled by optimizing pre-coding and detection matrices. Thus, the MIMO-NOMA channel is decomposed into multiple single-input, single-output and (SISO)-MOMA channels. Then, we formulate an energy efficiency (EE) optimization problem subject to the signal-to-interference-plus-noise ratio (SINR) constraints which is non-convex. To solve the problem, we propose the algorithm based on one-dimensional linear search and first-order Taylor expansion. Moreover, as in conventional communication systems, EE and spectrum efficiency (SE) cannot always be improved simultaneously. Thus, the trade-off between EE and SE is investigated based on the formulated problem. Numerical analyses and simulation results verify the proposed algorithm. In addition, the performance in terms of EE and the EE-SE trade-off can be improved by optimizing the user pairing method.

Rate-Splitting Multiple Access for Multi-Antenna Downlink Communication Systems: Spectral and Energy Efficiency Tradeoff

Rate-splitting (RS) has recently been recognized as a promising physical-layer technique for multi-antenna broadcast channels (BC). Due to its ability to partially decode the interference and partially treat the remaining interference as noise, RS is an enabler for a powerful multiple access, namely rate-splitting multiple access (RSMA), that has been shown to achieve higher spectral efficiency (SE) and energy efficiency (EE) than both space division multiple access (SDMA) and non-orthogonal multiple access (NOMA) in a wide range of user deployments and network loads. As SE maximization and EE maximization are two conflicting objectives in the moderate and high signal-to-noise ratio (SNR) regimes, the study of the tradeoff between the two criteria is of particular interest. In this work, we address the SE-EE tradeoff by studying the joint SE and EE maximization problem of RSMA in multiple input single output (MISO) BC with rate-dependent circuit power consumption at the transmitter. To tackle the challenges coming from multiple objective functions and rate-dependent circuit power consumption, we first propose two models to transform the original problem into two single-objective problems, namely, weighted-sum method and weighted-power method. A low-complexity algorithm with closed-form solution is proposed to solve each single-objective problem in the two-user system. For the generalized <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$K$ </tex-math></inline-formula> -user system, a successive convex approximation (SCA)-based algorithm is then proposed to optimize the precoders of each transformed problem. Numerical results show that our algorithm converges much faster than existing algorithms. In addition, the performance of RSMA is superior to or equal to SDMA and NOMA in terms of SE, EE and their tradeoff.

Spectral-Energy Efficiency Trade-Off Based Design for Hybrid TDMA-NOMA System

The combination of time division multiple access (TDMA) and non-orthogonal multiple access (NOMA), referred to as hybrid TDMA-NOMA system, is considered as a potential solution to meet the unprecedented requirements for future wireless networks. While recent resource allocation techniques aiming to individually maximize either spectral efficiency (SE) or energy efficiency (EE), this paper considers an SE-EE trade-off based technique for a hybrid TDMA-NOMA system. This design offers an additional degree of freedom in resource allocation. The proposed design is formulated as a non-convex multi-objective optimization (MOO) problem. The MOO framework is reformulated as a single-objective optimization (SOO) problem by combining the multi-objectives through a weighted-sum objective function. With this, each of the original objectives is assigned with a weight factor to reflect its importance in the design. Then, the sequential convex approximation (SCA) and a second-order cone (SOC) approach are jointly utilized to deal with the non-convexity issues of the SOO problem. Simulation results reveal that the proposed trade-off based design strikes a good balance between the objective functions, while meeting the instantaneous requirements of the system.

How Many Reflecting Elements Are Needed for Energy- and Spectral-Efficient Intelligent Reflecting Surface-Assisted Communication

This paper investigates and analyzes the number of reflecting elements for guaranteed energy- and spectral-efficient intelligent reflecting surface (IRS)-assisted communication systems. As opposed to previous works where the energy efficiency (EE)/the spectral efficiency (SE) maximization or the EE-SE tradeoff was considered, our goal is to minimize the number of reflecting elements in the IRS-assisted system. Besides, both the EE and the SE constraints are considered in the number minimization problem, which has not been addressed in existing works. However, both the EE and the SE performance do not admit exact closed-form expressions due to the non-convexity incurred by joint beamforming and phase shift design. In order to make the optimization problem tractable, we resort to their performance bounds for problem reformulation. By decomposing the problem into two sub-problems, we are able to derive closed-form expressions for the minimum number of reflecting elements, and both the coherent phase shift (CPS)-oriented solution and the random phase shift (RPS)-oriented solution are proposed for comparison. In order to shed light on the practical design, the relationship between the derived number of reflecting elements is established for both schemes, and the upper bounds on both the EE and the SE thresholds and the placement of the IRS to achieve only one reflecting element are obtained. Simulation results confirm the validity of our analysis on the minimum number of reflecting elements and effectiveness of both schemes.

Energy Efficiency Trade-off with Spectral Efficiency in MIMO Systems

5G technology can greatly improve spectral efficiency (SE) and throughput of wireless communications. In this regard, multiple input multiple output (MIMO) technology has become the most influential technology using huge antennas and user equipment (UE). However, the use of MIMO in 5G wireless technology will increase circuit power consumption and reduce energy efficiency (EE). In this regard, this article proposes an optimal solution for weighing SE and throughput tradeoff with energy efficiency. The research work is based on the Wyner model of uplink (UL) and downlink (DL) transmission under the multi-cell model scenario. The SE-EE trade-off is carried out by optimizing the choice of antenna and UEs, while the approximation method based on the logarithmic function is used for optimization. In this paper, we analyzed the combination of UL and DL power consumption models and precoding schemes for all actual circuit power consumption models to optimize the trade-off between EE and throughput. The simulation results show that the SE-EE trade-off has been significantly improved by developing UL and DL transmission models with the approximation method based on logarithmic functions. It is also recognized that the throughput-EE trade-off can be improved by knowing the total actual power consumed by the entire network.

On the Comparison of Optimal NOMA and OMA in a Paradigm Shift of Emerging Technologies

Non-orthogonal multiple access (NOMA) is a better multiple access technique than orthogonal multiple access (OMA), precisely orthogonal frequency division multiple access (OFDMA) scheme, at the conceptual level for fifth-generation (5G) networks and beyond 5G (B5G) networks. We investigate the potentials of the schemes by comparing the proposed NOMA scheme with the traditional cooperative communication NOMA (CCNOMA) scheme, rather than the comparison between NOMA and OMA only. To probe the effectiveness of NOMA as a multiple access technique, we propose a novel NOMA scheme considering two adjacent BSs with a special design of the transceiver architecture. The proposed scheme provides a reasonable data rate to both near user (NU) and far user (FU) without compromising the quality of service (QoS) to anyone of them. The conclusive analyses on the optimization framework of multi-user sum rate, capacity, transmit power, spectral efficiency (SE), and energy efficiency (EE) trade-off for NOMA and OFDMA schemes have been established to a succession of derivations. Under the analytical optimization framework, we also prove quite a few properties for them. Simulation results confirm the theoretical findings and show that the two schemes can efficiently approach the optimal power allocation, minimization of power consumption, and optimal SE-EE trade-off, and the proposed NOMA scheme provides comparatively better data sum rates than the baseline OMA scheme.

Millimeter Wave MIMO-OFDM With Index Modulation: A Pareto Paradigm on Spectral- Energy Efficiency Trade-Off

Multiple-input multiple-output orthogonal frequency division multiplexing with index modulation (MIMO-OFDM-IM) has recently received increased attention, due to the potential advantage to balance the trade-off between spectral efficiency (SE) and energy efficiency (EE). In this paper, we investigate the application of MIMO-OFDM-IM to millimeter wave (mmWave) communication systems, where a hybrid analogy-digital (HAD) beamforming architecture is employed. Taking advantage of the Pareto-optimal beam design, we propose a feasible solution to approximately achieve a globally Pareto-optimal trade-off between SE and EE, and the collision constraints of the multi-objective optimization problem (MOP) can be solved efficiently. Correspondingly, the MOP of SE-EE trade-off can be converted into a feasible solution for energy-efficient resource usage, by finding the Pareto-optimal set (POS) towards the Pareto front. This combinatorial-oriented resource allocation approach on the SE-EE relation considers the optimal beam design and power control strategies for downlink multi-user mmWave transmission. To ease the system performance evaluation, we adopt the Poisson point process (PPP) to model the mobile data traffic, and the evolutionary algorithm is applied to speed up the search efficiency of the Pareto front. Compared with benchmarks, the experimental results collected from extensive simulations demonstrate that the proposed optimization approach is vastly superior to existing algorithms.

Non-linear biobjective EE-SE optimization for NOMA-MIMO systems under user-rate fairness and variable number of users per cluster

The trade-off between energy efficiency (EE) and spectrum efficiency (SE) in downlink (DL) multiple-input and multiple-output (MIMO) non-orthogonal multiple access (NOMA) systems under equal-rate constraint has been investigated. The maximum fairness of the NOMA-MIMO system is attained when it is assured the same data rate for all active users in the system. The SE-EE trade-off was formulated as a multi-objective (MOO) problem. The optimization problem was solved by using primarily ∊-Constraint (∊-C) scalarization method combined with nonlinear programming (NLP) techniques, as sequential quadratic programming (SQP) and Dinkelback method (DK). The proposed iterative-analytical ∊-C-DK and ∊-C-SQP methods were able to achieve optimal EE-SE solutions at the Pareto frontier. Besides, both proposed iterative-analytical optimization methods are compared with a greedy local search heuristic method, by combining the ∊-C with the Hill Climbing (HC) heuristic and weighted sum (WS) scalarization method. Numerical results have demonstrated the ability of the ∊-C method in finding a diversity of EE-SE NOMA-MIMO solutions in the Pareto frontier. Furthermore, the proposed ∊-C-SQP method is able to attain a much more variety of solutions in the Pareto frontier in a remarkably reduced computational time.

A Trade-Off Between Energy Efficiency and Spectral Efficiency in Macro-Femtocell Networks

Obtaining large spectral efficiency (SE) and energy efficiency (EE) subject to quality of experience (QoE) is one of the prime concerns for the wireless next generation networks, however a major confrontation with its trade-off which is becoming apparent while optimizing both SE and EE parameters concurrently. In this work, an analytical framework for a cognitive-femtocell network is proposed to be dealt with and overcome the situations regarded as unwelcome. Here, the conflict of SE-EE trade-off in downlink (DL) transmission is expressed methodically by Pareto Optimal Set (POS) based on a multi-empirical most effective use of a resource scheme as a function of femto base station (FBS) and macro base station (MBS) transmit power and base station (BS) density, respectively. Then, SE and EE are formulated in a utility function by applying Cobb-Douglas production function to transform the multi-empirical difficulty into the single-empirical optimization case. Besides, it is analytically shown that the SE-EE trade-off can be optimize through a distinctive universal optimum among the Pareto optimal by fine-tuning the weighting metric other than BS transmit power and density, respectively. Simulation results validate that it is possible to obtain the EE-SE trade-off with SINR threshold at different weighting factor.

Genetic algorithm-based joint Spectral-Energy efficiency optimisation for 5G heterogeneous network

ABSTRACT Carrier Aggregation (CA) technology, introduced in 3GPP release 10, aims at increasing Spectral Efficiency (SE) only, which may lead to huge undesirable circuit power consumption. Hence, not only SE, but also Energy Efficiency (EE), particularly the tradeoff between both the parameters, is crucial in the design of CA systems. In this work, a novel approach, using Genetic Algorithm (GA) is proposed to solve the SE-EE tradeoff problem for a 5 G heterogeneous network with intra-band contiguous Carrier Aggregation (CA). Complete physical layer simulation is performed for generating the CA waveform, with parameters set in accordance with practical deployment scenarios, as specified in 3GPP TS 38.104. Carrier aggregated waveform is generated in 5 G New Radio (NR) frequency band FR1, using frequency bands in India which are currently not allocated for licenced usage. From simulations, it is observed that the proposed technique ensures that neither SE nor EE is seriously degraded for improving the other, for any given value of transmit power. The proposed technique, which performs Multi Objective Optimisation (MOO) using SPEA-2 GA outperforms Single Objective Optimisation (SOO) methods providing a maximum of 37% improvement in SE and 43% improvement in EE.

A novel method for the optimization of Spectral -Energy efficiency tradeoff in 5 G heterogeneous Cognitive Radio Network

Cognitve Radio (CR) technology has recently become popular for future communication networks since it allows co-existence of Secondary User (SU) and Primary User (PU) networks. Compared to interweave and overlay, underlay mode of operation is best suited for practical scenarios since it facilitates PU-SU co-existence with minimum overhead. Aiming to enhance Spectral Efficiency (SE) alone using CR may lead to huge power consumption and thus increase the overall cost of network operation. Hence, effort must be taken to maintain a tradeoff between SE and Energy Efficiency (EE). In this work, a novel technique, called Superior Population Generation Algorithm (SPGA), is developed to solve the crucial problem of SE-EE tradeoff for a Fifth generation (5 G) heterogeneous network which uses key future technologies such as CR and Carrier Aggregation (CA). The proposed technique performs optimum resource allocation, by modifying regular Genetic Algorithm (GA) to incorporate the capabilities of conventional techniques. SPGA follows a multi objective optimization approach towards obtaining SE-EE tradeoff, rather than focusing on SE alone. Simulation results show that SPGA outperforms conventional methods and regular GA in terms of SE-EE tradeoff with about 5% and 10% better EE for the same SE respectively. It is also observed that SPGA converges to the Pareto optimal solutions, much faster using only 25% of iterations required for regular GA. All simulations in this work are performed according to 3GPP specifications for 5 G communication networks. Also, power consumption of various base station components is also considered in addition to the transmit power to make the EE calculations further close to reality.

Resource Allocation and EE-SE Tradeoff for H-CRAN with NOMA-Based D2D Communications

We propose a general framework for studying resource allocation problem and the tradeoff between spectral efficiency (SE) and energy efficiency (EE) for downlink traffic in power domain―non-orthogonal multiple access (PD-NOMA) and device to device (D2D) based heterogeneous cloud radio access networks (H-CRANs) under imperfect channel state information (CSI). The aim is jointly optimize radio remote head (RRH) selection, spectrum allocation and power control, which is formulated as a multi-objective optimization (MOO) problem that can be solved with weighted Tchebycheff method. We propose a low-complexity algorithm to solve user association, spectrum allocation and power coordination separately. We first compute the CSI for RRHs. Then we study allocating the cell users (CUs) and D2D groups to different subchannels by constructing a bipartite graph and Hungrarian algorithm. To solve the power control and EE-SE tradeoff problems, we decompose the target function into two subproblems. Then, we utilize successive convex program approach to lower the computational complexity. Moreover, we use Lagrangian method and KKT conditions to find the global optimum with low complexity, and get a fast convergence by subgradient method. Numerical simulation results demonstrate that by using PD-NOMA technique and H-CRAN with D2D communications, the system gets good EE-SE tradeoff performance.

Spectral‐Energy Efficiency Tradeoff in Mixed‐ADC Massive MIMO Uplink with Imperfect CSI

An uplink multi-user massive Multi-input multi-output (MIMO) system is considered with a mixed Analog-to-digital converter (ADC) architecture under imperfect Channel state information (CSI). A closed-form approximation for the Spectral efficiency (SE) is derived for a general mixed ADC structure with any resolution profile. To achieve a balance between the SE and receive Energy efficiency (EE) of the system, the ADC resolution profile optimization problem that maximizes a linear combination of the SE and the Base station (BS) receive power consumption is formulated. An algorithm based on gradient search is proposed whose complexity is linear in the number of BS antennas. Numerical results verify that the proposed ADC resolution design largely outperforms the two-level structure especially in the lower SE region and provides more choices than the uniform-ADC architecture for resolving the SE-EE tradeoff.

On the Performance of Cell-Free Massive MIMO With Low-Resolution ADCs

This paper considers an uplink cell-free massive multi-input multi-output (mMIMO) system with multi-antenna access points (APs) and users, assuming low-resolution analog-to-digital converter (ADC) architecture is employed at the APs. Leveraging on the additive quantization noise model (AQNM), we derive a tight approximate expression for uplink spectral efficiency (SE). This trackable finding provides us with a tool for easily quantifying the impacts of the number of antenna arrays and the number of quantization bit of low-resolution ADCs. We find 5-bit is required in a cell-free mMIMO with low-resolution ADCs to achieve the same SE as a cell-free mMIMO with full-precision ADCs. Besides, when the number of antennas of the user is small, deploying more antennas at the users can boost the sum SE. Then, to further highlight the potential of low-resolution ADCs architecture, we also investigate the tradeoff between the SE and energy efficiency (EE) with design issues surrounding the quantization bit of low-resolution ADCs and the number of antenna arrays. The resulting observations reveal that by choosing a proper quantization bit, the cell-free mMIMO with low-resolution ADCs has the capability to enjoy a better SE-EE tradeoff compared to the perfect ADCs counterpart.

SE and EE Optimization for Cognitive UAV Network Based on Location Information

Unmanned Aerial Vehicle (UAV) aided communication has the potential to provide on-demand wireless services and improve the outdoor link throughput. Applications for UAVs are rapidly growing with the development of Internet of Things. Because of limited battery energy, the UAVs need time-limited spectrum access to complete data transmission. Hence there are two challenges for the UAV-based communication: 1) Spectrum-efficient design; 2) Energy-efficient design. In this paper, we investigate the optimization of spectrum efficiency (SE) and energy efficiency (EE) for cognitive UAV network based on location information. Because of high mobility, the cognitive radio (CR) based UAVs operate on different frequency bands that vary with time and space. Thus, one spectrum band that is available in one region may not be necessarily available in another region. Based on location information of the primary transmitter and the UAV, we propose a hybrid mode in which the sensing performance and UAV’s transmit power can be adjusted simultaneously to satisfy the outage constraint of the primary user. The multi-objective optimization theory is used to solve the tradeoff between SE and EE. The UAV’s transmit power, sensing time and sensing threshold are optimized jointly to solve the tradeoff problem. To further improve the SE and EE performance, we propose a multi-frame combined sensing scheme, in which multiple frames are bundled together. Simulation results are provided to show the SE-EE tradeoff design, to validate the effectiveness of the proposed hybrid mode, and to show the advantages of the multi-frame combined sensing scheme in EE performance.

Offloading Design for Energy and Spectral Efficiencies Tradeoff in Massive MIMO Enabled Heterogeneous Cellular Networks

To fully utilize the system resources and enhance the user experience, two types of offloading mechanisms are designed for massive MIMO (multiple-input-multiple-out) enabled heterogeneous cellular networks (HCNs). Such mechanisms can achieve a tradeoff between energy efficiency (EE) and spectral efficiency (SE) experiences, but also have a difference on whether or not a power coordination measure is mentioned. At last, they are mathematically written as the network-wide utility maximization problems that are closely related to the SEs and EEs of associated users. In them, we introduce a crucial parameter α to adjust the EE-SE preference. It is noteworthy that the finally formulated problems are in some relatively complicated forms. To solve them, some necessary changes should be made at first, and then we can design some feasible algorithms. Specifically, we try to design a distributed algorithm for a mere offloading problem using dual decomposition (DD), and develop a two-layer iterative algorithm for the joint power coordination and offloading problem using DD and two-sided scalable (2.s.s.) function update. Regarding such these algorithms, we show the corresponding computation complexity and convergence analyses. In the simulation, we mainly investigate different network parameters on an EE-SE tradeoff for our advocated mechanisms and another existing mechanism.

Energy- and Spectral-Efficiency Trade-Off for D2D-Multicasts in Underlay Cellular Networks

Underlay in-band device-to-device (D2D) multicast communication, where the same content is disseminated via direct links in a group, has the potential to improve the spectral and energy efficiencies of cellular networks. However, most of the existing approaches for this problem only address either spectral efficiency (SE) or energy efficiency (EE). We study the tradeoff between SE and EE in a single cell D2D integrated cellular network, where multiple D2D multicast groups (MGs) may share the uplink channel with multiple cellular users. We explore SE-EE tradeoff for this problem by formulating the EE maximization problem with constraint on SE and maximum available transmission power. A power allocation algorithm is proposed to solve this problem and its efficacy is demonstrated via extensive numerical simulations. The tradeoff between SE and EE as a function of density of D2D MGs, and maximum transmission power of an MG is characterized.

Spectrum and Energy Efficient Resource Allocation With QoS Requirements for Hybrid MC-NOMA 5G Systems

In this paper, we investigate the resource allocation problem for achieving spectral efficiency (SE) and energy efficiency (EE) tradeoff with users’ minimum rate requirements in hybrid multi-carrier non-orthogonal multiple access (MC-NOMA) systems which incorporate both NOMA and orthogonal multiple access (OMA) modes into one unified framework. All the degrees of freedom involved in resource allocation, including the choice of multiple access (MA) modes, user clustering, subcarrier assignment, and power allocation, are jointly considered. We first formulate the SE-EE tradeoff as a multi-objective optimization (MOO) problem with minimum rate requirement constraints. Then, considering the non-convexity of the MOO problem, it is converted into a single-objective optimization (SOO) problem by utilizing weighted Tchebycheff method. Lagrangian dual decomposition and sequential convex programming are applied to solve the SOO problem. We propose a joint resource allocation algorithm which is applicable to the general case, where an arbitrary number of users can be multiplexed on the same subcarrier. Simulation results demonstrate that users’ minimum rate requirements and channel conditions have great impact on the selection of MA modes. The proposed hybrid MC-NOMA mode significantly outperforms MC-NOMA and OMA in terms of SE-EE tradeoff, and the performance gain brought by four or more users sharing the same subcarrier is minimal. Meanwhile, the hybrid MC-NOMA also shows great potential to improve the tradeoff between fairness and system efficiency.

Secure spectral-energy efficiency tradeoff in random cognitive relay networks

Spectral efficiency (SE) and energy efficiency (EE) in secure communications is of primary importance due to the fact that 5G wireless networks aim to achieve high throughput, low power consumption and high level of security. Nevertheless, maximizing SE and EE are not achievable simultaneously. In this paper, we investigate the SE and EE tradeoff for secure transmission in cognitive relay networks where all nodes are randomly distributed. We first introduce the opportunistic relay selection policy, where each primary transmitter communicates with the primary receiver with the help of a secondary user as a relay. Then, we evaluate the secure SE and secure EE of the primary network based on the outage probabilities analysis. Thirdly, by applying a unified SE-EE tradeoff metric, the secure SE and EE tradeoff problem is formulated as the joint secure SE and EE maximization problem. Considering the non-concave feature of the objective function, an iterative algorithm is proposed to improve secure SE and EE tradeoff. Numerical results show that the opportunistic relay selection policy is always superior to random relay selection policy. Furthermore, the opportunistic relay selection policy outperforms conventional direct transmission policy when faced with small security threat (i.e., for smaller eavesdropper density).

Results on Energy- and Spectral-Efficiency Tradeoff in Cellular Networks With Full-Duplex Enabled Base Stations

In this paper, we address the tradeoff between energy efficiency (EE) and spectral efficiency (SE) for cellular networks with full-duplex (FD) communications enabled base stations. To be backward compatible with legacy LTE systems, it is assumed that user devices still work in the conventional half-duplex (HD) mode. There usually exists residual self-interference (RSI) in FD communications after advanced interference suppression techniques are applied. In this paper, we consider two different RSI models: constant RSI model and linear RSI model. First, the necessary conditions for an FD transceiver to achieve better EE-SE tradeoff than an HD one are derived for both the RSI models. Then, for the constant RSI model, a closed-form EE-SE expression is obtained in the scenario of single pair of users. We further extend our result and prove that EE is a quasi-concave function of SE in the scenario of multiple user pairs. Accordingly, an optimal algorithm to achieve the maximum EE based on the Lagrange dual decomposition technique is developed. For the linear RSI model, the EE-SE relation is difficult to deal with and we develop a heuristic algorithm by decoupling the problem into two sub-problems: power control and resource allocation. Our analysis and algorithms are finally verified by comprehensive numerical results.