"Written by the pioneers of the concept, this is the first complete guide to the physical and engineering principles of Massive MIMO. Assuming only a basic background in communications and statisti ...

Fundamentals of Massive MIMO

Intelligent reflecting surfaces (IRSs) constitute a disruptive wireless communication technique capable of creating a controllable propagation environment. In this paper, we propose to invoke an IRS at the cell boundary of multiple cells to assist the downlink transmission to cell-edge users, whilst mitigating the inter-cell interference, which is a crucial issue in multicell communication systems. We aim for maximizing the weighted sum rate (WSR) of all users through jointly optimizing the active precoding matrices at the base stations (BSs) and the phase shifts at the IRS subject to each BS’s power constraint and unit modulus constraint. Both the BSs and the users are equipped with multiple antennas, which enhances the spectral efficiency by exploiting the spatial multiplexing gain. Due to the non-convexity of the problem, we first reformulate it into an equivalent one, which is solved by using the block coordinate descent (BCD) algorithm, where the precoding matrices and phase shifts are alternately optimized. The optimal precoding matrices can be obtained in closed form, when fixing the phase shifts. A pair of efficient algorithms are proposed for solving the phase shift optimization problem, namely the Majorization-Minimization (MM) Algorithm and the Complex Circle Manifold (CCM) Method. Both algorithms are guaranteed to converge to at least locally optimal solutions. We also extend the proposed algorithms to the more general multiple-IRS and network MIMO scenarios. Finally, our simulation results confirm the advantages of introducing IRSs in enhancing the cell-edge user performance.

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Multicell MIMO Communications Relying on Intelligent Reflecting Surfaces

After about a decade of intense research, spurred by both economic and operational considerations, and by environmental concerns, energy efficiency has now become a key pillar in the design of communication networks. With the advent of the fifth generation of wireless networks, with millions more base stations and billions of connected devices, the need for energy-efficient system design and operation will be even more compelling. This survey provides an overview of energy-efficient wireless communications, reviews seminal and recent contribution to the state-of-the-art, including the papers published in this special issue, and discusses the most relevant research challenges to be addressed in the future.

A Survey of Energy-Efficient Techniques for 5G Networks and Challenges Ahead

This monograph presents a unified framework for energy efficiency maximization in wireless networks via fractional programming theory. The definition of energy efficiency is introduced, with reference to single-user and multi-user wireless networks, and it is observed how the problem of resource allocation for energy efficiency optimization is naturally cast as a fractional program. An extensive review of the state-of-the-art in energy efficiency optimization by fractional programming is provided, with reference to centralized and distributed resource allocation schemes. A solid background on fractional programming theory is provided. The key-notion of generalized concavity is presented and its strong connection with fractional functions described. A taxonomy of fractional problems is introduced, and for each class of fractional problem, general solution algorithms are described, discussing their complexity and convergence properties. The described theoretical and algorithmic framework is applied to solve energy efficiency maximization problems in practical wireless networks. A general system and signal model is developed which encompasses many relevant special cases, such as one-hop and two-hop heterogeneous networks, multi-cell networks, small-cell networks, device-to-device systems, cognitive radio systems, and hardware-impaired networks, wherein multiple-antennas and multiple subcarriers are possibly employed. Energy-efficient resource allocation algorithms are developed, considering both centralized, cooperative schemes, as well as distributed approaches for self-organizing networks. Finally, some remarks on future lines of research are given, stating some open problems that remain to be studied. It is shown how the described framework is general enough to be extended in these directions, proving useful in tackling future challenges that may arise in the design of energy-efficient future wireless networks.

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Energy Efficiency in Wireless Networks via Fractional Programming Theory

This paper develops power control algorithms for energy efficiency (EE) maximization (measured in bit/Joule) in wireless networks. Unlike previous related works, minimum-rate constraints are imposed and the signal-to-interference-plus-noise ratio takes a more general expression, which allows one to encompass some of the most promising 5G candidate technologies. Both network-centric and user-centric EE maximizations are considered. In the network-centric scenario, the maximization of the global EE and the minimum EE of the network is performed. Unlike previous contributions, we develop centralized algorithms that are guaranteed to converge, with affordable computational complexity, to a Karush–Kuhn–Tucker point of the considered non-convex optimization problems. Moreover, closed-form feasibility conditions are derived. In the user-centric scenario, game theory is used to study the equilibria of the network and to derive convergent power control algorithms, which can be implemented in a fully decentralized fashion. Both scenarios above are studied under the assumption that single or multiple resource blocks are employed for data transmission. Numerical results assess the performance of the proposed solutions, analyzing the impact of minimum-rate constraints, and comparing the network-centric and user-centric approaches.

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Energy-Efficient Power Control: A Look at 5G Wireless Technologies

This paper studies the impact of hardware mismatch (HM) between the base station (BS) and the user equipment (UE) in the downlink (DL) of large-scale antenna systems. Analytical expressions to predict the achievable rates are derived for different precoding methods, i.e., matched filter (MF) and regularized zero-forcing (RZF), using large system analysis techniques. Furthermore, the upper bounds on achievable rates of MF and RZF with HM are investigated, which are related to the statistics of the circuit gains of the mismatched hardware. Moreover, we present a study of HM calibration, where we take zero-forcing (ZF) precoding as an example to compare two HM calibration schemes, i.e., Pre-precoding Calibration (Pre-Cal) and Post-precoding Calibration (Post-Cal). The analysis shows that Pre-Cal outperforms Post-Cal schemes. Monte-Carlo simulations are carried out, and numerical results demonstrate the correctness of the analysis.

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Large-Scale Antenna Systems With UL/DL Hardware Mismatch: Achievable Rates Analysis and Calibration

This letter considers the power optimization problem for downlink transmission in coordinated multi-point (CoMP) systems. We aim to maximize the minimum weighted energy efficiency (EE) with QoS constraint and limited intercell coordination. The established optimization problem is converted to the standard form of max-min fractional programming problem first. Then we discuss feasibility of the Dual Dinkelbach-type Algorithm (DDA). A distributed algorithm is proposed to solve the subproblem in DDA with limited intercell coordination, where only a small number of positive scalars are shared between base stations. Simulation results show that the proposed algorithm outperforms previous schemes in terms of both the minimum EE of all the BSs' EE and fairness.

Distributed Energy-Efficient Power Optimization for CoMP Systems With Max-Min Fairness

This paper aims to design an optimal set of beam-vectors for multi-band multi-antenna cognitive radio networks that jointly allocate power over both space and frequency, so that the sum power of secondary users (SUs) is minimized, subject to rate demands at the SUs, as well as the interference constraints imposed by primary users. Unlike the rate maximization problems, which are always feasible, this power minimization (PM) problem may be infeasible due to the rate constraints. Therefore, we provide a complete analysis of the PM problem by splitting the solution into two separate phases. In phase I, a novel method is developed to check the feasibility of the PM problem by considering an alternative problem, where one additional variable is introduced. This alternative problem is always feasible and one algorithm based on network duality and geometric programs is developed to solve it. In phase II, a novel algorithm is developed to solve the PM problem. This algorithm can be implemented in an online fashion. Furthermore, this algorithm is proved to converge to a Karush-Kuhn-Tucker point of the PM problem. Simulation results show that the proposed algorithms converge in only a few iterations and significantly outperform the existing single-band method in terms of both the feasibility probabilities and power savings.

Power Minimization in Multi-Band Multi-Antenna Cognitive Radio Networks

In this paper, a novel optimization objective namely weighted sum rate is proposed for beamformer design in single group multicast systems. As an upper bound and special case of maximizing minimum rate, it can overcome previous disadvantages of computation complexity and sensitivity to channel state when the weights are chosen properly. Although the corresponding optimization problem is nonconvex, some properties of the optimal solution and closed-form solutions under some usual special cases are derived. In addition, an iterative algorithm with low computation complexity for general case is proposed. Simulation results show that the beamformer obtained by the iterative algorithm not only improves the minimum rate and average rate, but also gets better fairness and overall performance compared with previous schemes.

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Optimal beamforming for single group multicast systems based on weighted sum rate

The problem of energy-efficient joint beamforming and antenna selection for multicast systems is consider in this paper. Under the performance objective of maximizing the number of bits per joule of energy consumed, beamformer design, optimal transmit power and antenna selection is discussed respectively. The beamforming problem is converted to an equivalent form of the max-min problem and we propose a suboptimal solution with low complexity whose validity is verified by the numerical results. The existence and uniqueness of the optimal transmit power is proved. Then, a simple antenna selection scheme is presented. In the end, we combine the above algorithms into a joint beamforming and antenna selection algorithm. Simulation results show the performance gain of the proposed scheme. A great deal of energy can be saved at the expense of acceptable throughput loss especially with low number of users or short distance. In addition, antenna selection is necessary for energy-efficient design in multi-antenna systems through the performance comparison.

Bo Du

Papers

Large-Scale Antenna Systems With UL/DL Hardware Mismatch: Achievable Rates Analysis and Calibration

Distributed Energy-Efficient Power Optimization for CoMP Systems With Max-Min Fairness

Power Minimization in Multi-Band Multi-Antenna Cognitive Radio Networks

Optimal beamforming for single group multicast systems based on weighted sum rate

Energy-efficient joint beamforming and antenna selection for multicast systems