Energy- and Spectral-Efficiency Tradeoff with $\alpha$-Fairness in Downlink OFDMA Systems

In this letter, we adopt multi-objective optimization to investigate the tradeoff between energy efficiency (EE) and spectral efficiency (SE) in downlink orthogonal frequency division multiple access (OFDMA) systems. In the proposed model, α-fair utility function is applied to take account of the rate fairness among users. We then transfer the original multi-objective optimization into a single objective optimization employing the weighted sum method to obtain the solution set characterized as a Pareto set. The obtained Pareto set demonstrates the tradeoff between EE and SE while α-fairness guarantee is in place. We further consider price of fairness, as a metric to quantify the loss of EE due to enforcing fairness requirements. Such a metric enables the network operators to determine an acceptable operation point in terms of EE-SE tradeoff when certain level of fairness is required. Simulation results indicate that higher fairness results in lower system EE, and the price of fairness is significantly raised with the increase of overall SE.