  Heterogeneous cellular networks (HetNets) are to be deployed for future
wireless communication to meet the ever-increasing mobile traffic demand.
However, the dense and random deployment of small cells and their uncoordinated
operation raise important concerns about energy efficiency. Base station (BS)
cooperation is set to play a key role in managing interference in the HetNets.
In this paper, we consider BS cooperation in the downlink HetNets where BSs
from different tiers within the respective cooperative clusters jointly
transmit the same data to a typical user, and further optimize the energy
efficiency performance. First, based on the proposed clustering model, we
derive the spatial average rate using tools from stochastic geometry.
Furthermore, we formulate a power minimization problem with a minimum spatial
average rate constraint and derive an approximate result of the optimal
received signal strength (RSS) thresholds. Building upon these results, we
effectively address the problem of how to design appropriate RSS thresholds,
taking into account the trade-off between spatial average rate and energy
efficiency. Simulations show that our proposed clustering model is more
energy-saving than the geometric clustering model, and under our proposed
clustering model, deploying a two-tier HetNet is significantly more
energy-saving compared to a macro-only network.
