Obtaining large spectral efficiency (SE) and energy efficiency (EE) subject to quality of experience (QoE) is one of the prime concerns for the wireless next generation networks, however a major confrontation with its trade-off which is becoming apparent while optimizing both SE and EE parameters concurrently. In this work, an analytical framework for a cognitive-femtocell network is proposed to be dealt with and overcome the situations regarded as unwelcome. Here, the conflict of SE-EE trade-off in downlink (DL) transmission is expressed methodically by Pareto Optimal Set (POS) based on a multi-empirical most effective use of a resource scheme as a function of femto base station (FBS) and macro base station (MBS) transmit power and base station (BS) density, respectively. Then, SE and EE are formulated in a utility function by applying Cobb-Douglas production function to transform the multi-empirical difficulty into the single-empirical optimization case. Besides, it is analytically shown that the SE-EE trade-off can be optimize through a distinctive universal optimum among the Pareto optimal by fine-tuning the weighting metric other than BS transmit power and density, respectively. Simulation results validate that it is possible to obtain the EE-SE trade-off with SINR threshold at different weighting factor.
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