Exchange Economy in Two-User Multiple-Input Single-Output Interference Channels

TL;DR

This paper models a two-user MISO interference channel as a competitive market, using general equilibrium theory to find Pareto optimal beamforming solutions and proposing a distributed algorithm for implementation.

Contribution

It introduces a market-based approach to beamforming in interference channels, providing closed-form Pareto optimal solutions and a decentralized algorithm based on Walrasian equilibrium.

Findings

Closed-form Pareto optimal outcomes using Edgeworth box

Unique Walrasian equilibrium prices calculated

Distributed algorithm achieves Pareto optimal beamforming

Abstract

We study the conflict between two links in a multiple-input single-output interference channel. This setting is strictly competitive and can be related to perfectly competitive market models. In such models, general equilibrium theory is used to determine equilibrium measures that are Pareto optimal. First, we consider the links to be consumers that can trade goods within themselves. The goods in our setting correspond to beamforming vectors. We utilize the conflict representation of the consumers in the Edgeworth box, a graphical tool that depicts the allocation of the goods for the two consumers, to provide closed-form solution to all Pareto optimal outcomes. Afterwards, we model the situation between the links as a competitive market which additionally defines prices for the goods. The equilibrium in this economy is called Walrasian and corresponds to the prices that equate the demand to the supply of goods. We calculate the unique Walrasian equilibrium and propose a coordination process that is realized by an arbitrator which distributes the Walrasian prices to the consumers. The consumers then calculate in a decentralized manner their optimal demand corresponding to beamforming vectors that achieve the Walrasian equilibrium. This outcome is Pareto optimal and dominates the noncooperative outcome of the systems. Thus, based on the game theoretic model and solution concept, an algorithm for a distributed implementation of the beamforming problem in multiple-input single-output interference channels is provided.