Sharp approximation for transcendental equation in optimising energy efficiency

Improving energy efficiency of high-speed broad-band radios by optimally allocating wireless resources is a crucial topic in green communication systems. Although the numerous and valuable efforts on this topic, a key challenge remains on how to effectively track and resolve the energy efficiency maximization problem, which is transcendental in nature. This paper introduces a new approximation technique to represent the convex optimization-based solution of such problem by a cubic polynomial that can be robustly solved using the Karush-Kuhn-Tucker conditions for optimality. The idea is to correlate the optimization operands with known system parameters (channel gain, noise spectral density etc.) in a simple equation, which can be described by a power series with guaranteed region of convergence. We show that our approximation results similar accuracy to the actual transcendental solution with particularly lower implementation complexity. The step-by-step analysis included in this work is also novel and can be revealed as a useful tool for future studies in and beyond the wireless radio research field.