On the Energy Efficiency-Spectral Efficiency Trade-Off in MIMO-OFDMA Broadcast Channels

This paper investigates the fundamental energy efficiency-spectral efficiency (EE-SE) relationship in a multipleinput multiple-output (MIMO)- orthogonal frequency division multiple access (OFDMA) broadcast channel (BC) 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 EESE trade-off optimization problem which jointly optimizes the transmit covariance matrices whilst determining the optimal admitted user set and active transmit antenna set is non-convex, and hence it is extremely difficult to solve directly. As a result, we propose an algorithm that decouples the multi-carrier 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 trade-off problem with 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 in order to tackle the comprehensive EE-SE trade-off problem. Meanwhile, since admitting more users and activating more transmit antennas can achieve higher sum-rate but at the cost of larger transmit-independent power consumption, there exists a trade-off between the sum-rate gain and the power consumption. We therefore study the user and antenna selection approach to further explore the optimal trade-off. 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 trade-off.