Energy Efficiency and Spectral Efficiency Trade-Off in MIMO Broadcast Channels

Spectral efficiency (SE) and energy efficiency (EE) are the main performance metrics for designing green radio (GR) networks; however they are conflicting criteria. Consequently, instead of separately focusing on either SE or EE, characterizing the fundamental trade-off between EE and SE of MIMO broadcast channels (BC) is significant for the development of green wireless communications. This paper investigates the fundamental EE-SE relationship in a multiple-input multiple-output (MIMO) broadcast channel, which is important for facilitating a desirable balance between energy savings and spectrum utilization. Through our investigation, we prove that EE-SE relationship for MIMO-BC 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-offs problem. The key of the proposed method lies in the inner-layer algorithm which is solved by applying the principle of multiple access channel - broadcast channel (MAC-BC) duality. The algorithm in its dual form is solved using sub-gradient method and bisection searching scheme. Simulation results confirm the theoretical findings and demonstrate that the proposed resource allocation algorithm can efficiently approach the optimal EE-SE trade-off for MIMO-BC.