Equilibrium Outcomes of Dynamic Games in MIMO Channels with Active Eavesdroppers

This paper investigates transmission strategies in a MIMO wiretap channel with a transmitter, receiver and wiretapper, each equipped with multiple antennas. The secrecy rate between the transmitter and the legitimate receiver is chosen as the performance metric. In a departure from existing work, the wiretapper is able to act either as a passive eavesdropper or as an active jammer, under a half-duplex constraint. The transmitter therefore faces a choice between allocating all of its power for data; or broadcasting artificial noise along with the information signal in order to selectively degrade the eavesdropper's channel. We model the network as a dynamic zero-sum game in extensive form with the secrecy rate as the payoff function. We first examine subgame-perfect equilibrium strategies in the extensive form of the game with perfect information. We then discuss sequential and trembling hand perfect equilibria for the case of imperfect information. Finally, numerical simulations are presented to corroborate the analytical results.