Analytical Derivation of Downlink Data Rate Distribution for 5G HetNets with Cell-Edge Located Small Cells

In HetNets, time/frequency resources should be partitioned intelligently in order to minimize the interference among the users. In this paper, the probability distributions of per user downlink Data Rate, Spectral Efficiency (SE) and Energy Efficiency (EE) are analytically derived for a HetNet model with cell-edge located small cells. The high accuracy of analytically derived CDFs have been verified by the distributions obtained via simulations. CDF expressions have then been employed in order to optimize Key Parameter Indicators (KPI) which are selected here as $10^{th}$ percentile downlink user Data Rate ($R_{10}$), Spectral Efficiency ($SE_{10}$) and Energy Efficiency ($EE_{10}$). In addition to optimizing KPIs separately, employing the analytically derived distributions, we have also investigated the variation of the KPIs with respect to each other. The results have shown that the resource allocation parameter values maximizing $R_{10}$ is very close to the values that maximize $SE_{10}$. However, the values that are optimal for $SE_{10}$ and $R_{10}$, are not optimal for $EE_{10}$, which demonstrates the EE and SE trade-off in HetNets. We have also proposed a metric, $\theta$, aiming to jointly optimize SE and EE. The results have shown the value of resource sharing parameter optimizing $\theta$ is closer to the value that maximizes SE. This result shows that SE is more critical in SE-EE trade-off.