On the Energy Efficiency–Spectral Efficiency Tradeoff in MIMO-OFDMA Broadcast Channels

This paper investigates the fundamental energy efficiency-spectral efficiency (EE-SE) relationship in a multiple-input-multiple-output (MIMO) orthogonal frequency-division multiple-access (OFDMA) broadcast channel with a practical power model considering the power consumption due to the number of admitted users, as well as the number of active transmit antennas. However, with this power model, the EE-SE tradeoff optimization problem, which jointly optimizes the transmit covariance matrices while determining the optimal admitted user set and the active transmit antenna set, is nonconvex, and hence, it is extremely difficult to solve directly. As a result, we propose an algorithm that decouples the multicarrier EE optimization problem to a set of single-carrier EE optimization problems. For the single-carrier EE optimization problem, we first investigate the EE-SE tradeoff problem with a fixed admitted user set and transmit antenna set. Under this setup, we prove that the EE-SE relationship is a quasiconcave function. Furthermore, EE is proved to be either strictly decreasing with SE or first strictly increasing and then strictly decreasing with SE. Based on these findings, we propose a two-layer resource allocation algorithm to tackle the comprehensive EE-SE tradeoff problem. Meanwhile, since admitting more users and activating more transmit antennas can achieve a higher sum rate at the cost of larger transmit-independent power consumption, there exists a tradeoff between sum-rate gain and power consumption. We therefore study the user and antenna selection approach to further explore the optimal tradeoff. Both the optimal exhaustive search and the Frobenius-norm-based dynamic selection schemes are developed to further improve the achievable EE. To further reduce the computational complexity, a strategy that chooses a fixed admitted user set for all the subcarriers is developed. Simulation results confirm the theoretical findings and demonstrate that the proposed resource allocation algorithm can efficiently approach the optimal EE-SE tradeoff.