Learning to precode in outage minimization games over MIMO interference channels

In this paper, we consider a network composed of several interfering transmitter-receiver pairs where all the terminals are equipped with multiple antennas. The problem of finding the precoding matrices minimizing the outage probabilities is analyzed using a game theoretical framework under the assumption of slow fading links and non-cooperative transmissions. An analytical solution of this game is very difficult to be found in general. Even in the most simple case of single-user, the problem remains an open issue. However, the existence of a pure-strategy Nash equilibrium solution is proven in the extreme SNR regimes. Furthermore, we exploit a simple reinforcement algorithm and show that, based only on the knowledge of one ACK/NACK bit, the users may converge to an Nash equilibrium solution of the game under investigation.