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

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 c...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 66; no. 10; pp. 2616 - 2630
Main Authors: Shen, Kaiming, Yu, Wei
Format: Journal Article
Language:English
Published: IEEE 15.05.2018
Subjects:
Array signal processing
beamforming
Communication systems
energy efficiency
Fractional programming (FP)
Interference
Linear programming
Optimization
power control
quadratic transform
Signal to noise ratio
Transforms
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2018.2812733