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In this paper, we investigate an energy efficiency (EE) maximization problemin multi-user multiple input single output downlink channels. The optimizationproblem in this system model is difficult to solve in general, since it is innon-convex fractional form. Hence, conventional algorithms have addressed theproblem in an iterative manner for each channel realization, which leads tohigh computational complexity. To tackle this complexity issue, we propose anew simple method by utilizing the fact that the EE maximization is identicalto the spectral efficiency (SE) maximization for the region of the power belowa certain transmit power referred to as saturation power. In order to calculatethe saturation power, we first introduce upper and lower bounds of the EEperformance by adopting a maximal ratio transmission beamforming strategy.Then, we propose an efficient way to compute the saturation power for the EEmaximization problem. Once we determine the saturation power corresponding tothe maximum EE in advance, we can solve the EE maximization problem with SEmaximization schemes with low complexity. The derived saturation power isparameterized by employing random matrix theory, which relies only on thesecond order channel statistics. Hence, this approach requires much lowercomputational complexity compared to a conventional scheme which exploitsinstantaneous channel state information, and provides insight on the saturationpower. Numerical results validate that the proposed algorithm achieves nearoptimal EE performance with significantly reduced complexity.

Saturation Power based Simple Energy Efficiency Maximization Schemes for MU-MISO Systems