The split control and user plane is key to the future heterogeneous cellular network (HCN), where the small cells are dedicated for the most data transmission while the macrocells are mainly responsible for the control signaling. Adapting to this technology, we propose a general and tractable framework of extra cell range expansion (CRE) by introducing an additional bias factor to enlarge the range of small cells flexibly for the extra offloaded macrousers in a two-tier HCN, where the macrocell and small cell users have different required data rates. Using stochastic geometry, we analyze the energy efficiency (EE) of the extra CRE with joint low power transmission and resource partitioning, where the coverages of EE and data rate are formulated theoretically. Numerical simulations verify that the proposed extra CRE can improve the EE performance of HCN, and also show that deploying more small cells can provide benefits for EE coverage, but the EE improvement becomes saturated if the sm查看全文