Robust Spectrum Sharing via Worst Case Approach

TL;DR

This paper develops a distributed power-allocation method for spectrum sharing that accounts for uncertainties in interference, ensuring convergence to a robust equilibrium and analyzing its impact on overall network throughput.

Contribution

It introduces a robust Nash equilibrium framework for spectrum sharing under interference uncertainty, with conditions for uniqueness and convergence, and explores social utility outcomes.

Findings

Power allocation converges to a robust Nash equilibrium under uncertainty.

Distributed algorithm simplifies power control with symmetric uncertainty sets.

Social utility can be higher at a robust equilibrium than at a standard Nash equilibrium.

Abstract

This paper considers non-cooperative and fully-distributed power-allocation for secondary-users (SUs) in spectrum-sharing environments when normalized-interference to each secondary-user is uncertain. We model each uncertain parameter by the sum of its nominal (estimated) value and a bounded additive error in a convex set, and show that the allocated power always converges to its equilibrium, called robust Nash equilibrium (RNE). In the case of a bounded and symmetric uncertainty set, we show that the power allocation problem for each SU is simplified, and can be solved in a distributed manner. We derive the conditions for RNE's uniqueness and for convergence of the distributed algorithm; and show that the total throughput (social utility) is less than that at NE when RNE is unique. We also show that for multiple RNEs, the the social utility may be higher at a RNE as compared to that at the corresponding NE, and demonstrate that this is caused by SUs' orthogonal utilization of bandwidth for increasing the social utility. Simulations confirm our analysis.