Energy-Efficient HARQ-IR for Massive MIMO Systems

In this paper, an optimization problem to maximize the energy efficiency of a hybrid automatic repeat request with incremental redundancy (HARQ-IR) is considered for massive multiple-input multiple-output (MIMO) systems. Because a sum rate for multiple HARQ-IR rounds is approximated by a Gaussian distribution, a problem maximizing energy efficiency becomes tractable. In particular, a simplified form of energy efficiency for massive MIMO transmissions with an HARQ-IR protocol is derived using an outage probability, which is given by a tail probability of the Gaussian distribution. By exploiting the proposed simplified form, we show that the energy efficiency of the system is approximated by a piecewise quasi-concave function. Using these properties, an algorithm finding the optimal transmission power and number of transmission rounds for maximizing energy efficiency is proposed. Moreover, we show that the optimal number of HARQ transmission rounds can be less than the maximum allowable retransmissions when considering the constant power consumption of the massive MIMO system with an HARQ-IR protocol. Simulation results verify the theoretical analysis and show the performance of the proposed algorithm.