A Game Theoretic Approach to Setting the Pilot Power Ratio in Multi-User MIMO Systems

Abstract

We consider the uplink of a single cell multi-user multiple input multiple output (MU-MIMO) system, in which the base station acquires channel state information at the receiver by means of uplink pilot signals. Since each mobile station has a sum power budget that is used to transmit pilot and data symbols, the pilot power ratio (PPR) has a large impact on the system performance in terms of spectral and energy efficiency. We formulate the problem of PPR setting as a non-cooperative game, in which each mobile station aims at minimizing the mean squared error of the uplink received data symbols at the base station. We show that in this game a unique Nash equilibrium exists, and propose an iterative decentralized algorithm—termed best PPR algorithm (BPA)—that is guaranteed to converge to that Nash equilibrium. Since BPA dynamically responds to the measured interference, it outperforms widely used schemes that use a predetermined PPR. BPA also performs close to the global optimum, especially when mobile stations with similar path loss values are co-scheduled in the MU-MIMO system. Based on these insights, we propose a practical signaling mechanism for implementing BPA in MU-MIMO systems.