  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 small cell density exceeds a threshold. Instead of
establishing the detail configuration, this paper can provide some valuable
insights and guidelines to the practical design of future networks, especially
for the traffic offloading in HCN.
