Network Formation Games in Cooperative MIMO Interference Systems

Abstract—This paper considers the cooperative optimization of mutual information in the MIMO Gaussian interference channel in a fully distributed manner via game theory. Null shaping constraints are enforced in the design of transmit covariance matrices to enable interference mitigation among links. The transmit covariance matrices leading to the Nash Equilibrium (NE) are derived, and the existence and uniqueness of the NE is analyzed. The formation of the cooperative sets, that represent the cooperation relationship among links, is considered as coalition games and network formation games. We prove that the proposed coalition formation (CF) and coalition graph formation (CGF) algorithms are Nash-stable, and the proposed network formation (NF) algorithm converges to a Nash Equilib-rium. Simulation results show that the proposed CF and CGF algorithms have significant advantages when the antennas at the transmitters is large, and the proposed NF algorithm enhances the sum rate of the system apparently even at low signal-to-noise ratio region and/or with small number of transmit antennas. Index Terms—Game theory, MIMO Interference channel, cooperative network, rate maximization. I