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

TL;DR

This paper introduces a novel quadratic transform technique for fractional programming in communication systems, enabling efficient optimization of power control and beamforming problems with multiple ratios, and demonstrating convergence and connections to existing algorithms.

Contribution

A new quadratic transform method for multi-ratio fractional programming problems in communication system optimization is proposed, extending FP theory beyond single-ratio cases.

Findings

The quadratic transform simplifies multi-ratio FP problems into convex subproblems.

The proposed method converges to a stationary point with provable guarantees.

Connections to fixed-point and MMSE algorithms are established.

Abstract

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.