Optimal Combination of Base Station Densities for Energy-Efficient Two-Tier Heterogeneous Cellular Networks

In this paper, the optimal BS (Base Station) density for both homogeneous and heterogeneous cellular networks to minimize network energy cost is analyzed with stochastic geometry theory. For homogeneous cellular networks, both upper and lower bounds of the optimal BS density are derived. For heterogeneous cellular networks, our analysis reveals the best type of BSs to be deployed for capacity extension, or to be switched off for energy saving. Specifically, if the ratio between the micro BS cost and the macro BS cost is lower than a threshold, which is a function of path loss and their transmit power, then the optimal strategy is to deploy micro BSs for capacity extension or to switch off macro BSs (if possible) for energy saving with higher priority. Otherwise, the optimal strategy is the opposite. The optimal combination of macro and micro BS densities can be calculated numerically through our analysis, or alternatively be conservatively approximated with a closed-form solution. Based on the parameters from EARTH, numerical results show that in the dense urban scenario, compared to the traditional macro-only homogeneous cellular network with no BS sleeping, deploying micro BSs can reduce about 40% of the total energy cost, and further reduce up to 35% with BS sleeping capability.