Optimal Deployment for Maximizing Average Sum Rate of Small Cells in Ultra-dense Networks

In future 5G communication system, demands of high data rate can be effectively met by ultra-dense networks (UDN), where a lot of small cells are locally deployed and share the frequency resources in the cellular networks. In this paper, we analyzed the optimal deployment of small cells in UDN, which the average sum rate (ASR) of small cells can be maximized. Based on the stochastic geometry, we firstly use the homogeneous Poisson point process (PPP) to characterize the random distribution of both macro cell user equipments (UEs) and small cells. Then, the successful transmission probabilities of both uplink and downlink transmissions in small cells are derived with closed forms. Further, we get the average sum rate (ASR) of small cells and the ASR maximization problem is analyzed under the outage probability constraints. With the help of convex optimization, the interval of small cell BS density which contain maximum ASR value is obtained. Finally the optimal small cell BS density for maximizing ASR of small cells is evaluated in closed form. Simulation results demonstrate the impact of system parameters on the optimal small cell BS density as well as the influence of interference to the maximum ASR of small cells.