Game Theoretical Power Control for Open-Loop Overlaid Network MIMO Systems with Partial Cooperation

In this paper, we consider an open-loop network MIMO system with K BSs serving K private MSs and M
^c
common MS based on a novel partial cooperation overlaying scheme. Exploiting the heterogeneous path gains between the private MSs and the common MSs, each of the K BSs serves a private MS non-cooperatively and the K BSs also serve the M
^c
common MSs cooperatively. The proposed scheme does not require closed loop instantaneous channel state information feedback, which is highly desirable for high mobility users. Furthermore, we formulate the long-term distributive power allocation problem between the private MSs and the common MSs at each of the K BSs using a partial cooperative game. We show that the long-term power allocation game has a unique Nash Equilibrium (NE) but standard best response update may not always converge to the NE. As a result, we propose a low-complexity distributive long-term power allocation algorithm which only relies on the local long-term channel statistics and has provable convergence property.