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In this paper, the probability distributions of per user downlink data rate, spectral efficiency (SE) and energy efficiency (EE) are analytically derived for a heterogeneous network model with cell-edge located small cells. The high accuracies of analytically derived cumulative distribution functions (CDF) are verified using distributions obtained via simulations. CDF expressions are then used in order to optimize key performance indicators (KPI) which are selected here as 10th percentile downlink data rate ( $$R_{10}$$ R 10 ), spectral efficiency ( $$SE_{10}$$ S E 10 ) and energy efficiency ( $$EE_{10}$$ E E 10 ). In addition to optimizing KPIs separately, we also investigate the variation of the KPIs with respect to each other employing the analytically derived distributions. The results show that the resource allocation parameter values maximizing $$R_{10}$$ R 10 are very close to the values that maximize $$EE_{10}$$ E E 10 . However, the values that are optimal for $$EE_{10}$$ E E 10 and $$R_{10}$$ R 10 are not optimal for $$SE_{10}$$ S E 10 , which demonstrates the EE and SE trade-off in HetNets.

Downlink data rate, energy and spectral efficiency distribution in heterogeneous networks with cell-edge located small cells