MAPEL: Achieving Global Optimality for a Non-convex Wireless Power Control Problem

TL;DR

This paper introduces MAPEL, a novel algorithm that guarantees global optimality for weighted throughput maximization in interference-limited wireless networks across all SINR regimes, overcoming previous limitations.

Contribution

The paper presents MAPEL, the first algorithm to globally solve the non-convex WTM problem in general SINR conditions, using polyblock approximation of the feasible SINR region.

Findings

MAPEL achieves global optimality in weighted throughput maximization.

The algorithm effectively balances optimality and convergence time.

MAPEL serves as a benchmark for evaluating heuristic algorithms.

Abstract

Achieving weighted throughput maximization (WTM) through power control has been a long standing open problem in interference-limited wireless networks. The complicated coupling between the mutual interferences of links gives rise to a non-convex optimization problem. Previous work has considered the WTM problem in the high signal to interference-and-noise ratio (SINR) regime, where the problem can be approximated and transformed into a convex optimization problem through proper change of variables. In the general SINR regime, however, the approximation and transformation approach does not work. This paper proposes an algorithm, MAPEL, which globally converges to a global optimal solution of the WTM problem in the general SINR regime. The MAPEL algorithm is designed based on three key observations of the WTM problem: (1) the objective function is monotonically increasing in SINR, (2) the objective function can be transformed into a product of exponentiated linear fraction functions, and (3) the feasible set of the equivalent transformed problem is always normal although not necessarily convex. The MAPLE algorithm finds the desired optimal power control solution by constructing a series of polyblocks that approximate the feasible SINR region in increasing precision. Furthermore, by tuning the approximation factor in MAPEL, we could engineer a desirable tradeoff between optimality and convergence time. MAPEL provides an important benchmark for performance evaluation of other heuristic algorithms targeting the same problem. With the help of MAPEL, we evaluate the performance of several respective algorithms through extensive simulations.