On the Energy Efficiency–Spectral Efficiency Tradeoff in Random Beamforming

Energy efficiency (EE) and spectral efficiency (SE) are among the most important metrics in wireless systems. The relationship between EE and SE has attracted more attention recently. In this letter, we derive a closed-form approximation of the EE-SE tradeoff in a multi-antenna random beamforming system under a realistic power consumption model. Based on the approximate EE-SE tradeoff, the EE-maximum SE and the corresponding transmit power are obtained in closed form with the help of Lambert W function. We also derive the optimal number of transmit antennas to maximize the EE when the value of SE is given. These results are helpful to gain analytical insights on choosing proper system parameters, e.g., the transmit power and the number of transmit antennas, to meet the demand of green communication. Simulation results validate the accuracy of our proposed closed-form approximation.