Robust Rate-Maximization Game Under Bounded Channel Uncertainty

TL;DR

This paper develops a robust game-theoretic framework for decentralized power allocation in interference channels with uncertain channels, showing that increased uncertainty can improve overall system efficiency.

Contribution

It introduces a distribution-free robust rate-maximization game, deriving conditions for equilibrium existence, uniqueness, and convergence, and analyzes how uncertainty affects system performance.

Findings

Equilibrium converges under certain conditions.

Increased channel uncertainty can enhance sum rate.

Frequency-division solutions emerge with higher uncertainty.

Abstract

We consider the problem of decentralized power allocation for competitive rate-maximization in a frequency-selective Gaussian interference channel under bounded channel uncertainty. We formulate a distribution-free robust framework for the rate-maximization game. We present the robust-optimization equilibrium for this game and derive sufficient conditions for its existence and uniqueness. We show that an iterative waterfilling algorithm converges to this equilibrium under certain sufficient conditions. We analyse the social properties of the equilibrium under varying channel uncertainty bounds for the two-user case. We also observe an interesting phenomenon that the equilibrium moves towards a frequency-division multiple access solution for any set of channel coefficients under increasing channel uncertainty bounds. We further prove that increasing channel uncertainty can lead to a more efficient equilibrium, and hence, a better sum rate in certain two-user communication systems. Finally, we confirm, through simulations, this improvement in equilibrium efficiency is also observed in systems with a higher number of users.