Wireless Capacity With Arbitrary Gain Matrix

TL;DR

This paper addresses the problem of maximizing simultaneous wireless transmissions under arbitrary gain matrices and fixed powers, proposing a semi-definite programming approach that guarantees a constant factor approximation under certain conditions.

Contribution

It introduces a novel semi-definite programming method for a complex wireless capacity problem with arbitrary gains and fixed powers, extending existing approaches.

Findings

Provides a constant factor approximation algorithm.

Addresses a problem generalizing the max independent set.

Works effectively when the optimal solution exceeds half the input size.

Abstract

Given a set of wireless links, a fundamental problem is to find the largest subset that can transmit simultaneously, within the SINR model of interference. Significant progress on this problem has been made in recent years. In this note, we study the problem in the setting where we are given a fixed set of arbitrary powers each sender must use, and an arbitrary gain matrix defining how signals fade. This variation of the problem appears immune to most algorithmic approaches studied in the literature. Indeed it is very hard to approximate since it generalizes the max independent set problem. Here, we propose a simple semi-definite programming approach to the problem that yields constant factor approximation, if the optimal solution is strictly larger than half of the input size.