Abstract: Based on Poisson point process(PPP) theory in stochastic geometry,the base station(BS) deployment problem in ultra-dense heterogeneous cellular networks,especially the influence of the distribution density of small cells on network energy efficiency is studied,and a method to maximize network energy efficiency(EE) through optimizing the density of small cells is proposed. Firstly,the coverage probability of each tier BS and the BS load oriented minimum achievable rate are derived through the PPP theory. Secondly,according to the definition of network EE and base station energy consumption model,the closed expression of network EE related to BS density is derived. Finally,the influence of the distribution density of the small cells on the network EE is analyzed,and an optimization algorithm of the small cell density based on Newton search method is proposed to maximize the network EE. Simulations verify the correctness of the theoretical analysis;and show that the network EE can be maximized through optimizing the deployment density of small cells.

Key words: energy efficiency, ultra-dense heterogeneous networks, stochastic geometry, Newton iteration method