Simple energy efficiency maximization methods for MU-MISO systems based on saturation power

In this paper, we investigate an energy efficiency (EE) maximization problem in multi-user multiple input single output downlink channels. In this system model, the optimization problem is difficult to solve since it is in a non-convex fractional form. Hence, conventional algorithms have addressed the problem in an iterative manner for each channel realization that leads to high computational complexity. To tackle this complexity issue, we propose a new simple method based on the fact that the EE maximization is identical to the spectral efficiency maximization for the region of power below the certain transmit power referred to as saturation power. In order to determine the saturation power, we introduce upper and lower bounds of the EE performance by adopting maximal ratio transmission beamforming strategy. Then, we propose an efficient way to compute the saturation power for the maximization problem in closed form. Based on the derived saturation power, we suggest a simplified scheme to calculate EE with low complexity. The saturation power is parameterized by employing random matrix theory, which relies only on the second order channel statistics. Numerical results validate that the proposed algorithm achieves near optimal EE performance with much reduced complexity.