A Game Theoretic Approach to Uplink Pilot and Data Power Control in Multi-Cell Multi-User MIMO Systems

In multi-user multiple-input-multiple-output (MU-MIMO) systems that employ pilot-symbol aided channel estimation, the pilot-to-data power ratio (PDPR) has a large impact on the system performance. In this paper, we consider the problem of setting the PDPR in multi-cell MU-MIMO systems in the presence of channel estimation errors, intercell interference and pilot contamination. To analyze and address this problem, we first develop a model of the multi-cell MU-MIMO system and derive a closed-form expression for the mean squared error of the uplink received data symbols. Building on this result, we then propose two decentralized PDPR-setting algorithms based on game theoretic approaches that are applicable in multi-cell systems. We find that both algorithms converge to a Nash equilibrium and provide performance improvements over systems that do not properly set the PDPR, while they maintain different levels of fairness.