Saturation Power-Based Simple Energy Efficiency Maximization Schemes for MISO Broadcast Channel Systems

In this paper, we investigate an energy efficiency (EE) maximization problem in multiple input single output broadcast channels. The optimization problem in this system model is difficult to solve in general, since it is in non-convex fractional form. Hence, conventional algorithms have addressed the problem in an iterative manner for each channel realization, which leads to high computational complexity. To tackle this complexity issue, we propose a new simple method by utilizing the fact that EE maximization becomes identical to spectral efficiency (SE) maximization for the region of the power below a certain transmit power termed as saturation power. In order to calculate the saturation power, we first introduce upper and lower bounds of the EE performance by adopting a maximal ratio transmission beamforming strategy. Then, we propose an efficient way to compute the saturation power for the EE maximization problem. Once we determine the saturation power in advance, we can transform the EE maximization problem into a simplified sub-optimal EE problem, which can be solved by the SE maximization schemes with low complexity. The derived saturation power is parameterized by employing random matrix theory, which relies only on the second-order channel statistics. Hence, this approach needs much lower computational complexity compared with a conventional scheme, which requires instantaneous channel state information. Numerical results validate that the proposed algorithm achieves near optimal EE performance with significantly reduced complexity.