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

TLDR

Part I focuses on fractional‑programming theory and solving continuous problems, emphasizing that multiple‑ratio FP problems are crucial for communication‑network optimization due to the prevalence of multiple SIR terms. The paper investigates how fractional programming can be applied to design and optimize communication systems, especially for power control, beamforming, and energy‑efficiency maximization. A novel quadratic transform technique is introduced to handle multiple‑ratio concave‑convex FP problems, enabling continuous‑problem optimization for power control, beamforming, and energy‑efficiency maximization. The quadratic transform reformulates ratio‑based nonconvex problems into a sequence of convex subproblems, yielding an efficient iterative algorithm that provably converges to a stationary point and aligns closely with fixed‑point and weighted‑MMSE beamforming methods. The optimization of discrete problems is discussed in Part II of this paper.

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.