Radio frequency (RF) energy transfer and harvesting techniques have recently become alternative methods to power the next-generation wireless networks As this emerging technology enables proactive energy replenishment of wireless devices, it is advantageous in supporting applications with quality-of-service requirements In this paper, we present a comprehensive literature review on the research progresses in wireless networks with RF energy harvesting capability, which is referred to as RF energy harvesting networks (RF-EHNs) First, we present an overview of the RF-EHNs including system architecture, RF energy harvesting techniques, and existing applications Then, we present the background in circuit design as well as the state-of-the-art circuitry implementations and review the communication protocols specially designed for RF-EHNs We also explore various key design issues in the development of RF-EHNs according to the network types, ie, single-hop networks, multiantenna networks, relay networks, and cognitive radio networks Finally, we envision some open research directions

Wireless Networks With RF Energy Harvesting: A Contemporary Survey

We introduce several solution concepts for multicriteria optimization problems, give a characterization of approximately efficient elements and discuss a general scalarization procedure. Furthermore, we derive necessary and sufficient optimality conditions, a minimal point theorem, a vector-valued variational principle of Ekeland’s type, Lagrangean multiplier rules and duality statements. An overview on vector variational inequalities and vector equilibria is given. Moreover, we discuss the results for special classes of vector optimization problems (vector-valued location and approximation problems, multicriteria fractional programming and optimal control problems).

Theory of Vector Optimization

In this letter, we propose a practical non-linear energy harvesting model and design a resource allocation algorithm for simultaneous wireless information and power transfer (SWIPT) systems. The algorithm design is formulated as a non-convex optimization problem for the maximization of the total harvested power at energy harvesting receivers subject to minimum required signal-to-interference-plus-noise ratios (SINRs) at multiple information receivers. We transform the considered non-convex objective function from sum-of-ratios form into an equivalent objective function in subtractive form, which enables the derivation of an efficient iterative resource allocation algorithm. In each iteration, a rank-constrained semidefinite program (SDP) is solved optimally by SDP relaxation. Numerical results unveil a substantial performance gain that can be achieved if the resource allocation design is based on the proposed non-linear energy harvesting model instead of the traditional linear model.

Practical Non-Linear Energy Harvesting Model and Resource Allocation for SWIPT Systems

Fractional programming (FP) refers to a family of optimization problems that involve ratio term(s). This two-part paper explores the use of FP in the design and optimization of communication systems. Part I of this paper focuses on FP theory and on solving continuous problems. The main theoretical contribution is a novel quadratic transform technique for tackling the multiple-ratio concave–convex FP problem—in contrast to conventional FP techniques that mostly can only deal with the single-ratio or the max-min-ratio case. Multiple-ratio FP problems are important for the optimization of communication networks, because system-level design often involves multiple signal-to-interference-plus-noise ratio terms. This paper considers the applications of FP to solving continuous problems in communication system design, particularly for power control, beamforming, and energy efficiency maximization. These application cases illustrate that the proposed quadratic transform can greatly facilitate the optimization involving ratios by recasting the original nonconvex problem as a sequence of convex problems. This FP-based problem reformulation gives rise to an efficient iterative optimization algorithm with provable convergence to a stationary point. The paper further demonstrates close connections between the proposed FP approach and other well-known algorithms in the literature, such as the fixed-point iteration and the weighted minimum mean-square-error beamforming. The optimization of discrete problems is discussed in Part II of this paper.

Fractional Programming for Communication Systems—Part I: Power Control and Beamforming

The well-known EM algorithm is an optimization transfer algorithm that depends on the notion of incomplete or missing data By invoking convexity arguments, one can construct a variety of other optimization transfer algorithms that do not involve missing data These algorithms all rely on a majorizing or minorizing function that serves as a surrogate for the objective function Optimizing the surrogate function drives the objective function in the correct direction This article illustrates this general principle by a number of specific examples drawn from the statistical literature Because optimization transfer algorithms often exhibit the slow convergence of EM algorithms, two methods of accelerating optimization transfer are discussed and evaluated in the context of specific problems

http://lear.inrialpes.fr/people/oneata/reading_group/lange2000.pdf

Optimization Transfer Using Surrogate Objective Functions

The main purpose of this paper is to delineate an algorithm for fractional programming with nonlinear as well as linear terms in the numerator and denominator. The algorithm presented is based on a theorem by Jagannathan Jagannathan, R. 1966. On some properties of programming problems in parametric form pertaining to fractional programming. Management Sci.12 609--615. concerning the relationship between fractional and parametric programming. This theorem is restated and proved in a somewhat simpler way. Finally, it is shown how the given algorithm can be related to the method of Isbell and Marlow Isbell, J. R., W. H. Marlow. 1956. Attrition games. Naval Res. Logist. Quart.3 71--93. for linear fractional programming and to the quadratic parametric approach by Ritter Ritter, K. 1962. Ein Verfahren zur Losung parameterabhangiger, nichtlinearer Maximum-Probleme. Unternehmensforschung, Band 6, S. 149--166.. The Appendix contains a numerical example.

On Nonlinear Fractional Programming

Es wird einleitend herausgestellt, das die Beschrankungsungleichungen, wie sie bei normalen linearen Programmen auftreten, die einzelnen Variablen auf einen Losungsbereich, d. h. rein quantitativ beschranken. Daruber hinaus kann man auch Beschrankungen uber die Anzahl, der in der Endlosung auftauchenden Variablen, festsetzen. Solche Beschrankungen werden als Beschrankungen qualitativer Art bezeichnet. Im zweiten Abschnitt werden dann Modelle aufgestellt, die zusatzlich diese qualitativen Beschrankungen enthalten. Es handelt sich um gemischt ganzzahlige lineare Programme, deren Losungsmethode nach Gomory anschliesend dargestellt wird. Abschliesend wird ein numerisches Beispiel aus dem Bereich der Absatzplanung gebracht.

Werner Dinkelbach

Papers

On Nonlinear Fractional Programming

Gemischt ganzzahlige lineare Programme zur Lösung gewisser Entscheidungsprobleme