Coalitional Games for Transmitter Cooperation in MIMO Multiple Access Channels

TL;DR

This paper uses cooperative game theory to analyze the stability and benefits of transmitter cooperation in MIMO multiple access channels, showing conditions under which cooperation is stable and optimal.

Contribution

It models transmitter cooperation as a partition form game, analyzes stability conditions, and demonstrates stability and sum-rate optimality in various decoding strategies and SNR regimes.

Findings

Grand coalition is sum-rate optimal without coordination costs.

Cooperation is stable if the core of the game is nonempty.

Stability varies with decoding strategy and SNR, being stable at high and low SNRs under certain conditions.

Abstract

Cooperation between nodes sharing a wireless channel is becoming increasingly necessary to achieve performance goals in a wireless network. The problem of determining the feasibility and stability of cooperation between rational nodes in a wireless network is of great importance in understanding cooperative behavior. This paper addresses the stability of the grand coalition of transmitters signaling over a multiple access channel using the framework of cooperative game theory. The external interference experienced by each TX is represented accurately by modeling the cooperation game between the TXs in \emph{partition form}. Single user decoding and successive interference cancelling strategies are examined at the receiver. In the absence of coordination costs, the grand coalition is shown to be \emph{sum-rate optimal} for both strategies. Transmitter cooperation is \emph{stable}, if and only if the core of the game (the set of all divisions of grand coalition utility such that no coalition deviates) is nonempty. Determining the stability of cooperation is a co-NP-complete problem in general. For a single user decoding receiver, transmitter cooperation is shown to be \emph{stable} at both high and low SNRs, while for an interference cancelling receiver with a fixed decoding order, cooperation is stable only at low SNRs and unstable at high SNR. When time sharing is allowed between decoding orders, it is shown using an approximate lower bound to the utility function that TX cooperation is also stable at high SNRs. Thus, this paper demonstrates that ideal zero cost TX cooperation over a MAC is stable and improves achievable rates for each individual user.