Non-cooperative feedback control game under a sum feedback-rate constraint in MIMO broadcast channels

Channel state information (CSI) is known to play crucial role in multiple-input multiple-output (MIMO) broadcast channels. To acquire CSI at the base station, feedback from users is necessary. Since the optimal feedback-rate to maximize the total system throughput is possibly changed by the channel condition, the conventional equal-sized feedback can be inefficient in multi-user MIMO system. Therefore, in this paper, we investigate the effect of different-sized feedback-rate and propose the non-cooperative feedback-rate control game in multi-user MIMO system with multiple frequency bands. Based on the game theory, the utility function of each user is defined as the downlink throughput minus a linear price function of the CSI feedback-rate. Moreover, we suggest a simple algorithm to find the proper pricing factors for the proposed game considering multiple users and multiple frequency bands. Simulation results show that the sum-rate of the proposed game yields better performance than that of the conventional equal-sized feedback-rate scheme.