Fractional Power Control for Decentralized Wireless Networks

TL;DR

This paper introduces fractional power control (FPC) in decentralized wireless networks, deriving formulas for outage probability and capacity, and finds that using an exponent of 1/2 optimally balances interference and user fairness.

Contribution

It proposes a new fractional power control scheme with a closed-form analysis and identifies the optimal exponent s=1/2 for minimizing outage probability in low-density networks.

Findings

s=1/2 minimizes outage probability

FPC with s=1/2 balances interference and fairness

Approximations are accurate over typical parameters

Abstract

We consider a new approach to power control in decentralized wireless networks, termed fractional power control (FPC). Transmission power is chosen as the current channel quality raised to an exponent -s, where s is a constant between 0 and 1. The choices s = 1 and s = 0 correspond to the familiar cases of channel inversion and constant power transmission, respectively. Choosing s in (0,1) allows all intermediate policies between these two extremes to be evaluated, and we see that usually neither extreme is ideal. We derive closed-form approximations for the outage probability relative to a target SINR in a decentralized (ad hoc or unlicensed) network as well as for the resulting transmission capacity, which is the number of users/m^2 that can achieve this SINR on average. Using these approximations, which are quite accurate over typical system parameter values, we prove that using an exponent of 1/2 minimizes the outage probability, meaning that the inverse square root of the channel strength is a sensible transmit power scaling for networks with a relatively low density of interferers. We also show numerically that this choice of s is robust to a wide range of variations in the network parameters. Intuitively, s=1/2 balances between helping disadvantaged users while making sure they do not flood the network with interference.