Game Theoretic Approaches To Communication Over MIMO Interference Channels In The Presence Of A Malicious Jammer

Abstract

This dissertation considers a system consisting of self-interested users of a common multiple-input multiple-output (MIMO) channel and a jammer wishing to reduce the total capacity of the channel. In this setting, two games are constructed that model different system-level objectives. In the first—called “utility games”—the users maximize the mutual information between their transmitter and their receiver subject to a power constraint. In the other (termed “cost games”), the users minimize power subject to an information rate floor. A duality is established between the equilibrium strategies in these two games, and it is shown that Nash equilibria always exist in utility games. Via an exact penalty approach, a modified version of the cost game also possesses an equilibrium. Additionally, multiple equilibria may exist in utility games, but with mild assumptions on users’ own channels and the jammer-user channels, systems with no user-user interference, there can be at most one Nash equilibrium where a user transmits on all of its subchannels. A similar but weaker result is also found for channels with limited amounts of user-user interference. Two distributed update processes are proposed: gradient-play and best-response. The performance of these algorithms are compared via software simulation. Finally, previous results on network-level improvement via stream control are shown to carry over when a jammer is introduced.