Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Percentile Optimization in Wireless Networks- Part I: Power Control for Max-Min-Rate to Sum-Rate Maximization (and Everything in Between)

Ahmad Ali Khan, Raviraj Adve

TL;DR

This paper proposes cyclic maximization algorithms that transform the original problems into equivalent block-concave forms, thereby enabling guaranteed convergence to stationary points and revealing that the proposed algorithms achieve superior performance while computing solutions orders of magnitude faster.

Abstract

Improving throughput for cell-edge users through coordinated resource allocation has been a long-standing driver of research in wireless cellular networks. While a variety of wireless resource management problems focus on sum utility, max-min utility and proportional fair utility, these formulations do not explicitly cater to cell-edge users and can, in fact, be disadvantageous to them. In this two-part paper series, we introduce a new class of optimization problems called percentile programs, which allow us to explicitly formulate problems that target lower-percentile throughput optimization for cell-edge users. Part I focuses on the class of least-percentile throughput maximization through power control. This class subsumes the well-known max-min and max-sum-rate optimization problems as special cases. Apart from these two extremes, we show that least-percentile rate programs are non-convex, non-smooth and strongly NP-hard in general for multiuser interference networks, making optimization extremely challenging. We propose cyclic maximization algorithms that transform the original problems into equivalent block-concave forms, thereby enabling guaranteed convergence to stationary points. Comparisons with state-of-the-art optimization algorithms such as successive convex approximation and sequential quadratic programming reveal that our proposed algorithms achieve superior performance while computing solutions orders of magnitude faster.

Percentile Optimization in Wireless Networks- Part I: Power Control for Max-Min-Rate to Sum-Rate Maximization (and Everything in Between)

TL;DR

This paper proposes cyclic maximization algorithms that transform the original problems into equivalent block-concave forms, thereby enabling guaranteed convergence to stationary points and revealing that the proposed algorithms achieve superior performance while computing solutions orders of magnitude faster.

Abstract

Improving throughput for cell-edge users through coordinated resource allocation has been a long-standing driver of research in wireless cellular networks. While a variety of wireless resource management problems focus on sum utility, max-min utility and proportional fair utility, these formulations do not explicitly cater to cell-edge users and can, in fact, be disadvantageous to them. In this two-part paper series, we introduce a new class of optimization problems called percentile programs, which allow us to explicitly formulate problems that target lower-percentile throughput optimization for cell-edge users. Part I focuses on the class of least-percentile throughput maximization through power control. This class subsumes the well-known max-min and max-sum-rate optimization problems as special cases. Apart from these two extremes, we show that least-percentile rate programs are non-convex, non-smooth and strongly NP-hard in general for multiuser interference networks, making optimization extremely challenging. We propose cyclic maximization algorithms that transform the original problems into equivalent block-concave forms, thereby enabling guaranteed convergence to stationary points. Comparisons with state-of-the-art optimization algorithms such as successive convex approximation and sequential quadratic programming reveal that our proposed algorithms achieve superior performance while computing solutions orders of magnitude faster.
Paper Structure (23 sections, 8 theorems, 58 equations, 8 figures, 1 table, 2 algorithms)

This paper contains 23 sections, 8 theorems, 58 equations, 8 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Overview
  3. Contributions of Part I
  4. Notation
  5. Organization
  6. Sum-Percentile Functions and Their Properties
  7. Definitions
  8. Properties
  9. Optimization for Parallel Gaussian Channels
  10. Problem Formulation
  11. Solution Techniques and Implementation
  12. Numerical Results
  13. Least-$q^\mathrm{th}$-Percentile (LqP) Rate Optimization
  14. Short-Term Sum-Percentile Rate Optimization
  15. Problem Formulation
  16. ...and 8 more sections

Key Result

Theorem 1

For a fixed value of $q$ such that $K_q>1$, the percentile program in (SPR_problem_shortterm) is strongly NP-hard in the number of users $K$.

Figures (8)

  • Figure 1: A typical cell-edge user in a wireless cellular network.
  • Figure 2: Achieved rates for optimal solutions to the parallel channel SLqP rate optimization problem for different values of $q$.
  • Figure 3: Convergence of proposed algorithms for $25^\mathrm{th}$-percentile SLqP rate maximization problem, $K=56$, $K_q=14$.
  • Figure 4: User and BS locations for a single realization in a network with $K=70$ users.
  • Figure 5: Convergence of SLqP utility for $K=14$ and $K_q=7$.
  • ...and 3 more figures

Theorems & Definitions (37)

  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • proof
  • Remark 1
  • proof
  • Remark 2
  • ...and 27 more