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

By Kaiming Shen, Wei Yu. IEEE Transactions on Signal Processing, 2018

1,851 citations recorded by the source corpus.

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.

Subfields: Aerospace Engineering, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/88ad983ffdc8bb6c2a88e6237ab875a6a494d62b

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Citations in the corpus

Applications of Deep Reinforcement Learning in Communications and Networking: A Survey (2018, methodology): “, the iterative algorithm based on closedform factional programming [155] can be used.”
User-Centric Cell-Free Massive MIMO Networks: A Survey of Opportunities, Challenges and Solutions (2021, background): “Problem Type Approach Reference”
Multi-Agent Deep Reinforcement Learning for Dynamic Power Allocation in Wireless Networks (2018, methodology): “In certain scenarios the proposed distributed algorithm even outperforms the centralized iterative algorithms introduced in [2], [3].”
Secure Radar-Communication Systems With Malicious Targets: Integrating Radar, Communications and Jamming Functionalities (2019, methodology): “According to [33], it is easy to prove the convergence of the algorithm given the non-increasing property of c during each iteration.”
Fractional Programming for Communication Systems—Part II: Uplink Scheduling via Matching (2018, methodology): “Theorem 1 (Quadratic Transform [3]):Given a nonempty constraint setX ⊆ Rd, a nonnegative functionA(x): Rd → R+, and a positive functionB(x): Rd → R++, whered ∈ N, a (single-ratio) FP problem is maximize x A(x) B(x) (1a) subject to x ∈ X .”
Large Language Model (LLM) for Telecommunications: A Comprehensive Survey on Principles, Key Techniques, and Opportunities (2024, background): “Meanwhile, fractional programming is a well-known convex optimization technique in wireless networks, e.g., decoupling signal strength with interference and noise to maximize the data rate [153].”
A Joint Precoding Framework for Wideband Reconfigurable Intelligent Surface-Aided Cell-Free Network (2020, methodology): “To tackle this issue, we fortunately notice a recently proposed method called multidimensional complex quadratic transform (MCQT) [34].”
Near-Field Communications: A Tutorial Review (2023, methodology): “It can be solved with existing methods [55]–[57].”
An Overview of Signal Processing Techniques for RIS/IRS-Aided Wireless Systems (2021, neutral): “Due to the usually complicated expressions for the data rate/SINR, advanced algorithms such as the weighted minimum mean-square error (WMMSE) algorithm [81] or fractional programming (FP) [82] are often used to convert the original intractable problem into a new tractable but approximated problem.”