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Deep Unfolding of Fixed-Point Based Algorithm for Weighted Sum Rate Maximization

Jan Christian Hauffen, Chee Wei Tan, Giuseppe Caire

TL;DR

Given a Gaussian interference channel with $K$ links, the paper tackles non-convex Weighted Sum Rate (WSR) maximization under $\log$-concave interference by blending the standard interference function framework with Difference-of-Convex Programming (DCP). It develops a Primal-Dual Algorithm (PDA) to approximate the solution and then applies deep unfolding to distill a Learned Primal-Dual Algorithm (LPDA) whose inner ${\bf q}$-update is replaced by a trainable FCNN, reducing computational complexity. Theoretical guarantees are established for the $\log$-concave case, including a convergent fixed-point update in a special case and a PDA that converges to a stationary point. Numerical experiments on ITU outdoor scenarios show the learned algorithm is competitive with FPLinQ and achieves faster convergence, validating scalability for next-generation networks.

Abstract

In this paper, we propose a novel approach that harnesses the standard interference function, specifically tailored to address the unique challenges of non-convex optimization in wireless networks. We begin by establishing theoretical guarantees for our method under the assumption that the interference function exhibits log-concavity. Building on this foundation, we develop a Primal-Dual Algorithm (PDA) to approximate the solution to the Weighted Sum Rate (WSR) maximization problem. To further enhance computational efficiency, we leverage the deep unfolding technique, significantly reducing the complexity of the proposed algorithm. Through numerical experiments, we demonstrate the competitiveness of our method compared to the state-of-the-art fractional programming benchmark, commonly referred to as FPLinQ.

Deep Unfolding of Fixed-Point Based Algorithm for Weighted Sum Rate Maximization

TL;DR

Given a Gaussian interference channel with links, the paper tackles non-convex Weighted Sum Rate (WSR) maximization under -concave interference by blending the standard interference function framework with Difference-of-Convex Programming (DCP). It develops a Primal-Dual Algorithm (PDA) to approximate the solution and then applies deep unfolding to distill a Learned Primal-Dual Algorithm (LPDA) whose inner -update is replaced by a trainable FCNN, reducing computational complexity. Theoretical guarantees are established for the -concave case, including a convergent fixed-point update in a special case and a PDA that converges to a stationary point. Numerical experiments on ITU outdoor scenarios show the learned algorithm is competitive with FPLinQ and achieves faster convergence, validating scalability for next-generation networks.

Abstract

In this paper, we propose a novel approach that harnesses the standard interference function, specifically tailored to address the unique challenges of non-convex optimization in wireless networks. We begin by establishing theoretical guarantees for our method under the assumption that the interference function exhibits log-concavity. Building on this foundation, we develop a Primal-Dual Algorithm (PDA) to approximate the solution to the Weighted Sum Rate (WSR) maximization problem. To further enhance computational efficiency, we leverage the deep unfolding technique, significantly reducing the complexity of the proposed algorithm. Through numerical experiments, we demonstrate the competitiveness of our method compared to the state-of-the-art fractional programming benchmark, commonly referred to as FPLinQ.
Paper Structure (14 sections, 2 theorems, 30 equations, 1 figure, 2 tables, 1 algorithm)

This paper contains 14 sections, 2 theorems, 30 equations, 1 figure, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Mathematical Background and Problem Formulation
  3. Standard Interference Function Framework
  4. Difference-of-convex Programming
  5. System Model and Problem Formulation
  6. WSR-Maximization for $\log$-concave Interference Functions
  7. Special Case
  8. Weighted Sum Rate Maximization
  9. Deep Unfolding
  10. Learned Primal Dual Algorithm
  11. Training
  12. Numerical Experiments
  13. Conclusion
  14. Proof of Theorem 1

Key Result

Theorem 1

Let $\mathcal{I}$ be a standard and feasible interference function. eq:gen_alg converges to a fixed-point if $\mathcal{I}_i(\cdot)$ is $\log$-concave for all $i = 1,\dots, K$ and the gradient of $\mathcal{I}_i$ are scale invariant, i.e. $\nabla_{\bf p} \mathcal{I}_i(\alpha {\bf q}) = \nabla_{\bf p}

Figures (1)

  • Figure 1: Mean WSR versus iterations of the benchmark FPLinQ and the trained proposed LPDA \ref{['alg:PDA']} is evaluated across $500$ unseen D2D-networks with $K=10$ users and random uniform weights. LPDA is trained with $n_\text{train}=1000$, using random uniform weights and $N=8$ iterations, as indicated by the vertical black line in the figure.

Theorems & Definitions (6)

  • Definition 1
  • Theorem 1
  • proof
  • Lemma 1
  • proof
  • proof