Weighted Sum Energy Efficiency Research Articles

Wireless Information and Power Transfer Enabled Massive MIMO Multi-Way Relaying

This work considers a multi-way massive multi-input multi-output (mMIMO) relaying system wherein several wireless information and power transfer capable users, first harvest energy, and then exchange information via a relay. The mMIMO relaying system is practically modelled by considering spatially-correlated relay-user channels, and by using a non-linear energy harvesting (EH) model. A closed-form spectral efficiency expression is derived for this system, which is then used to jointly allocate the relay and users transmit powers, and the charging time to optimize the weighted sum energy efficiency (WSEE) metric. The spatially-correlated channel and the non-linear EH model not only couple the optimization variables, but also introduce nested scalar fractional optimization functions. This makes the WSEE metric non-convex. The proposed solution first uses the existing quadratic transformation (QT) to decouple the scalar fractional forms. It then applies novel results, which are developed by extending the QT framework, to decouple the optimization variables. The proposed WSEE optimization algorithm is shown to provide close-to-optimal WSEE. It is also shown that channel spatial correlation increases the amount of energy harvested by the users, but reduces their WSEE.

Graph-Based Algorithm Unfolding for Energy-Aware Power Allocation in Wireless Networks

We develop a novel graph-based trainable framework to maximize the weighted sum energy efficiency (WSEE) for power allocation in wireless communication networks. To address the non-convex nature of the problem, the proposed method consists of modular structures inspired by a classical iterative suboptimal approach and enhanced with learnable components. More precisely, we propose a deep unfolding of the successive concave approximation (SCA) method. In our unfolded SCA (USCA) framework, the originally preset parameters are now learnable via graph convolutional neural networks (GCNs) that directly exploit multi-user channel state information as the underlying graph adjacency matrix. We show the permutation equivariance of the proposed architecture, which is a desirable property for models applied to wireless network data. The USCA framework is trained through a stochastic gradient descent approach using a progressive training strategy. The unsupervised loss is carefully devised to feature the monotonic property of the objective under maximum power constraints. Comprehensive numerical results demonstrate its generalizability across different network topologies of varying size, density, and channel distribution. Thorough comparisons illustrate the improved performance and robustness of USCA over state-of-the-art benchmarks.

WSEE Optimization of Cell-Free mMIMO Uplink Using Deep Deterministic Policy Gradient

Cell-free (CF) massive multiple-input multiple-output (mMIMO) systems are being actively investigated. We optimize the weighted sum energy efficiency (WSEE) for the uplink of a CF mMIMO system by using deep deterministic policy gradient (DDPG) technique, which does not require labeled data. We formulate the WSEE optimization as a reinforcement learning problem. We first show the limitations of the reward function and states being used in the baseline DDPG technique from the existing CF state of the art. We construct improved reward functions and states, and then propose two novel DDPG variants which have better sampling and exploration capabilities than the baseline DDPG technique. The proposed variants provide 4% WSEE gain, and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$5\times $ </tex-math></inline-formula> faster convergence.

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.

Full-Duplex Cell-Free Massive MIMO Systems: Analysis and Decentralized Optimization

Cell-free (CF) massive multiple-input-multiple-output (mMIMO) deployments are usually investigated with half-duplex nodes and high-capacity fronthaul links. To leverage the possible gains in throughput and energy efficiency (EE) of full-duplex (FD) communications, we consider a FD CF mMIMO system with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">practical limited-capacity fronthaul links</i> . We derive closed-form spectral efficiency (SE) lower bounds for this system with maximum-ratio combining/maximum-ratio transmission processing and optimal uniform quantization. We then optimize the weighted sum EE (WSEE) via downlink and uplink power control by using a two-layered approach: the first layer formulates the optimization as a generalized convex program, while the second layer solves the optimization decentrally using the alternating direction method of multipliers. We analytically show that the proposed two-layered formulation yields a Karush-Kuhn-Tucker point of the original WSEE optimization. We numerically show the influence of weights on the individual EE of the users, which demonstrates the utility of the WSEE metric to incorporate heterogeneous EE requirements of users. We show that low fronthaul capacity reduces the number of users each AP can support, and the cell-free system, consequently, becomes user-centric.

On the Energy Efficiency of OFDMA Cellular Networks

In this article, we study the energy efficiency (EE) of orthogonal frequency-division multiple access (OFDMA) cellular networks under the 5 G requirement of EE enhancement. We aim to present a power allocation scheme maximizing the EE of downlink cellular communications while avoiding numerical methods such as fractional programming. We focus on two EE forms; global EE and weighted sum EE. Therefore, we propose a novel explicit expression of the optimal power allocation related to each subcarrier. We also present the power control with limited power budget or/and minimal transmission rate constraint in both base station and subcarrier perspectives. As a result, we notice the occurrence of some transmission outage events depending on the constraints’ parameters. From another side, we extend our study to analyze the effect of the channel state information (CSI) unavailability on our proposed power scheme. In the numerical results, we show that our proposed power control improves the EE, especially at high power budget regime and low minimal rate regime. We also show that having more subcarriers enhances the OFDMA EE. Finally, we show that EE degradation due to CSI unavailability is very small showing the robustness of the proposed scheme against CSI imperfectness. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>

Energy-Efficient Spatially-Correlated Hardware Impaired Massive MIMO FD Relaying

Most of the existing massive multi-input-multi-output (mMIMO) relaying works assume ideal transceiver hardware and spatially uncorrelated channels. A practical mMIMO relay, however, due to limited antenna spacing and the use of cost-effective equipment, usually experiences spatially-correlated channels and hardware impairments, respectively. We consider a hardware-impaired two-way full-duplex (FD) spatially-correlated mMIMO relaying with multiple MIMO FD user-pairs, and derive a closed-form spectral efficiency (SE) expression which is valid for a practical number of finite relay antennas. We use this expression to develop a quadratic transformation approach to optimize the non-convex global energy efficiency (GEE) and weighted sum energy efficiency (WSEE) metrics, which are fractional functions of optimization variables. The proposed approach first converts the fractional problem into its equivalent fraction-free counterpart, and then uses novel transformations to make the problem concave, and solve it using an iterative algorithm. We use this optimization to i) investigate the impact of spatial correlation and hardware impairments on GEE; ii) decide hardware impairment values for a tolerable reduction in GEE; and iii) investigate the impact of weights in WSEE on the users energy efficiency.

Joint Transmission Reception Point Selection and Resource Allocation for Energy-Efficient Millimeter-Wave Communications

In this paper, we study the joint transmission reception point (TRP) selection and resource allocation problem to maximize the weighted sum energy efficiency under imperfect channel state information (CSI) for an uplink mmWave network considering beam training overheads and delay constraints with and without inter-beam interference, respectively. First, to guarantee the delay constraints of all UEs, we use the worst-case approach to cast the considered problem to a deterministic optimization problem. Then, for the scenario without inter-beam interference, the product of transmitting and receiving beams and the power allocation scheme for each pair of UEs and TRPs are derived iteratively, where the former is obtained by some relaxation operations under given power allocation policy, and the latter is searched by bisection under given beamwidth selection policy. After that, Kuhn-Munkres algorithm is used to find the joint TRP selection and resource allocation policy. For the scenario with inter-beam interference, coalition game is proposed to solve the considered problem, where UEs form coalitions to select their respective serving TRPs. At each iteration of the coalition game, the beamwidth control and power allocation are performed successively, where the transmitting and receiving beamwidths are solved by particle swarm algorithm under given power allocation policy, and the power allocation strategy is designed by a novel cooperative cost mechanism under given beamwidth selection policy. Finally, extensive simulation results are provided to verify that the proposed schemes achieve better weighted sum energy efficiency than existing schemes.

Optimizing Weighted-Sum Energy Efficiency in Downlink and Uplink NOMA Systems

In this paper, weighted sum energy efficiency (WSEE) in uplink and downlink of a multi-user non-orthogonal multiple access (NOMA) system is considered. we adopt a more realistic power consumption model where signal processing power is modeled as a linear function of transmit power. Rather than the well-known network-centric global energy efficiency (GEE) metric, which is a pseudo-concave (PC) function, the weighted sum energy efficiency metric is considered, which is not PC in general. To find the optimum user power allocation Dinkelbach-like algorithm is adopted, by which each individual fractional EE function is converted to a parametric function where under some conditions on the weights falls into a class of convex optimization problems and it is solved in the dual domain. The dual variables are updated using a sub-gradient and cutting plane-based algorithm, which here ellipsoid method is used. Since the optimum solution restricts user weights, a low complexity suboptimum algorithm that does not consider any condition on user's weights is proposed. The problem is non-convex in general; hence, epigraph form followed by successive convex approximation (SCA) is used to deal with that problem. Results demonstrate that with the user-oriented metric, one can provide different priorities to users, and by choosing proper weights entail fairness among users.

WSEE Optimization Using Asynchronous ADMM for Massive MIMO Two-Way Relaying

We decentrally optimize the weighted sum energy efficiency (WSEE) of a multi-pair two-way half-duplex massive multi-input multi-output relaying. We use asynchronous alternating direction method of multipliers (aADMM) optimization approach, which is robust to node delays and failures. We analytically prove its convergence under a bounded delay assumption. We numerically show that the proposed aADMM approach yields similar WSEE and improved computational efficiency than its synchronous counterpart.

Energy-Efficient Massive MIMO Multi-Relay NOMA Systems With CSI Errors

We consider a massive multi-input multi-output (mMIMO) system where in a base station (BS) serves its users via multiple relays by employing non-orthogonal multiple access (NOMA). We practically model this system by considering channel estimation errors both at the BS and at the users, which consequently perform imperfect successive interference cancellation. We consider these two artifacts, and derive a lower bound on the spectral efficiency (SE) of this multi-relay NOMA system, which is valid for arbitrary number of BS antennas. We then jointly allocate the BS and relay powers to optimize non-convex global energy efficiency (GEE) and the weighted sum energy efficiency (WSEE) metrics, which are fractional functions of sum-of-products/ratios of optimization variables. These two optimizations require extension of an existing fractional programming framework, which we do by proposing two novel transformations. We analytically prove the monotonic convergence of the transformed problems to a stationary point of their respective original counterparts. We numerically show that i) a multi-relay mMIMO NOMA system outperforms its orthogonal counterpart only with accurate channel information; and ii) the proposed GEE and WSEE algorithms significantly improve the energy efficiency by avoiding additional power use, after attaining optimal value.

Energy Efficiency Optimization of Massive MIMO FD Relay With Quadratic Transform

We optimize the weighted sum energy efficiency (WSEE) of two-way amplify and forward relaying, where multiple full-duplex (FD) user-pairs exchange information via a shared FD massive multiple-input multiple-output (MIMO) relay. Optimization of user-centric WSEE metric, which prioritizes links of users with high energy efficiency (EE) requirements by suitably choosing their weights, is a non-convex problem due to its sum-of-ratio form. We optimize it by first approximating WSEE as a concave-convex fractional function, and then by using the quadratic transform. We then use Karush-Kuhn-Tucker (KKT) conditions to derive a closed-form solution to optimize WSEE. We numerically show that the i) proposed solutions achieve significant WSEE gains; and ii) suitable choice of weights can help prioritize EE requirements of different users.

Decentralized WSEE Optimization for Massive MIMO Two-Way Half-Duplex AF Relaying

Design of energy-efficient wireless systems has recently attracted attention to reduce their carbon footprint. This paper optimizes non-convex weighted sum energy efficiency (WSEE) of a multi-pair two-way amplify-and-forward half-duplex massive multiple-input multiple output relay system. We optimize it by developing a two-layer decentralized successive convex approximation optimization framework. The first layer approximates the non-convex WSEE either as a generic convex program (GCP) or as a second order cone program (SOCP). The second layer decentrally solves the approximated problem using alternating direction method of multipliers. We show that the proposed iterative algorithm yields a Karush-Kuhn-Tucker point of the original WSEE problem. We numerically analyze the effect of weights on the energy efficiency (EE) of individual users, and show that the proposed framework enable us to meet the heterogeneous EE requirements. We also analytically and numerically show that the decentralized algorithm has lesser complexity than its centralized counterpart, but yields the same WSEE.

WSEE Maximization of mmWave NOMA Systems

We maximize the weighted sum energy efficiency (WSEE) of millimeter-wave hybrid massive multiple-input multiple-output systems, employing non-orthogonal multiple access. The WSEE is a non-convex metric, and we maximize it by approximating it either as a generalized convex program (GCP) or as a second-order conic program, which requires lesser computation time than the GCP. We further reduce the computation time by proposing a low-complexity iterative algorithm that yields a Karush–Kuhn–Tucker point of the WSEE maximization problem. We show that the proposed algorithms yield equal WSEE and outperform two other baseline schemes.

Weighted Sum Energy Efficiency Maximization of Device-to-Device groups underlaying NOMA cellular network

The problem of Weighted Sum Energy Efficiency (WSEE) Maximization of Device-to-Device (D2D) groups with underlaid Non-Orthogonal Multiple Access (NOMA) cellular network is investigated in this paper. In the novel network model, transmitters in each of the D2D groups will be able to communicate with multiple D2D receivers in the same spectral sub-band via NOMA protocol. Similarly, Base Station (BS) also communicates with multiple Cellular Users (CUs) via NOMA strategy. Power allocation for this hybrid network is presented in this paper. Optimization problem is formulated as WSEE Maximization of the D2D groups. This framework is suitable for energy-crunch devices, where the nodes can have different energy efficiency requirements. Further, to meet Quality of Service (QoS), rate constraints are imposed on all the receivers in the network. The optimization problem is challenging because of its non-convex sum-of-ratios form. So, it is first converted into an equivalent convex form. Subsequently, a successive convex approximation based algorithm is used to obtain optimal power distribution. The proposed power allocation algorithm is shown to be convergent and the simulation results closely match with the optimal values at all Signal-to-Noise Ratio (SNR) values.

Optimal Energy-Efficient Beamforming Designs for Cloud-RANs With Rate-Dependent Fronthaul Power

We study the downlink of a limited fronthaul capacity cloud-radio access networks (C-RANs). Three energy efficiency metrics, namely, global energy efficiency (GEE), weighted sum energy efficiency (WSEE), and energy efficiency fairness (EEF) are maximized by jointly designing transmit beamforming, remote radio head (RRH) selection, and RRH-user association. Furthermore, we incorporate a rate-dependent fronthaul power model, in which the fronthaul power consumption is proportional to the user sum rate. The formulated problems are difficult to solve. Our first contribution is to customize a branch and reduce and bound (BRB) method based on monotonic optimization to find globally optimal solutions for the three energy efficiency maximization problems. Subsequently, for a more practical approach, we propose a unified framework based on successive convex approximation (SCA) method that can be applied to all the considered problems. Our novelty lies in the equivalent transformations leading to more tractable problems that are amenable to the SCA. Specifically, appropriate continuous relaxation and convex approximation techniques are employed to arrive at a sequence of second-order cone programs (SOCPs) for which dedicated solvers are available. Then, a post-processing algorithm is devised to obtain a high-performance feasible solution from the continuous relaxation. The numerical results demonstrate that the proposed SCA-based algorithms converge rapidly and achieve near-optimal performance as well as outperform the known methods. They also highlight the importance of the rate dependent fronthaul power model in designing the energy efficient C-RANs.

Weighted Sum Energy Efficiency Optimization for Massive MIMO Two-Way Half-Duplex AF Relaying

We consider two-way amplitude and forward half-duplex massive multiple-input multiple output (MIMO) relaying with multiple user-pairs. Most of the existing massive MIMO relaying literature has optimized the network-centric global energy efficiency metric, which is a pseudo-concave (PC) function, and can be optimized using well-known Dinkelbach algorithm. We optimize the user-centric weighted sum energy efficiency (WSEE), which is defined as the weighted sum of energy efficiencies of all the users, and is not a PC function. We propose a successive convex approximation approach to optimize it, and analytically show that this approach yields a Karush–Kuhn–Tucker point of the original WSEE problem. We also reduce the computational complexity of the above approach by approximating it as a second order cone program. We numerically demonstrate the WSEE improvement achieved by the proposed algorithms over baseline equal- and random-power allocation algorithms.

A Framework for Weighted-Sum Energy Efficiency Maximization in Wireless Networks

Weighted-sum energy efficiency (WSEE) is a key performance metric in heterogeneous networks, where the nodes may have different energy efficiency (EE) requirements. Nevertheless, WSEE maximization is a challenging problem due to its nonconvex sum-of-ratios form. Unlike previous work, this paper presents a systematic approach to WSEE maximization under not only power constraints, but also data rate constraints, using a general SINR expression. In particular, the original problem is transformed into an equivalent form, and then a sequential convex optimization (SCO) algorithm is proposed. This algorithm is theoretically guaranteed to converge for any initial feasible point, and, under suitable constraint qualifications, achieves a Karush-Kuhn-Tucker (KKT) solution. Furthermore, we provide remarkable extensions to the proposed methodology, including systems with multiple resource blocks as well as a more general power consumption model which is not necessarily a convex function of the transmit powers. Finally, numerical analysis reveals that the proposed algorithm exhibits fast convergence, low complexity, and robustness (insensitivity to initial points).

User Association With Maximizing Weighted Sum Energy Efficiency for Massive MIMO-Enabled Heterogeneous Cellular Networks

In this letter, we design an association strategy to maximize the weighted sum energy efficiency (EE) for massive multiple-input and multiple-output (MIMO)-enabled heterogeneous cellular networks. Considering that the final formulated problem is in a sum-of-ratio form, we first need to transform it into a parametric nonfractional form, by which we can achieve its solution through a two-layer iterative algorithm. The outer layer searches the EE parameters and the multipliers associated with signal-interference-plus-noise ratio constraints using Newton-like method, and the inner layer optimizes the association indices using Lagrange multiplier method. Then, we give some convergence and complexity analyses for the proposed algorithm. Numerical results show that the proposed scheme significantly outperforms the existing one on the system throughput and network EE under a certain condition. In addition, we also investigate the impacts of the number of massive antennas and the transmit power of each pico base station on the association performance.

Energy-Efficient Beam Coordination Strategies With Rate-Dependent Processing Power

This paper proposes energy-efficient coordinated beamforming strategies for multi-cell multi-user multiple-input single-output system. We consider a practical power consumption model, where part of the consumed power depends on the base station or user specific data rates due to coding, decoding and backhaul. This is different from the existing approaches where the base station power consumption has been assumed to be a convex or linear function of the transmit powers. Two optimization criteria are considered, namely network energy efficiency maximization and weighted sum energy efficiency maximization. We develop successive convex approximation based algorithms to tackle these difficult nonconvex problems. We further propose decentralized implementations for the considered problems, in which base stations perform parallel and distributed computation based on local channel state information and limited backhaul information exchange. The decentralized approaches admit closed-form solutions and can be implemented without invoking a generic external convex solver. We also show an example of the pilot contamination effect on the energy efficiency using a heuristic pilot allocation strategy. The numerical results are provided to demonstrate that the rate dependent power consumption has a large impact on the system energy efficiency, and, thus, has to be taken into account when devising energy-efficient transmission strategies. The significant gains of the proposed algorithms over the conventional low-complexity beamforming algorithms are also illustrated.