  This paper studies the proposed green (energy-efficient) coverage
probability, link and network energy efficiencies in the downlink of a
heterogeneous cellular network (HetNet) consisting of $K$ independent Poisson
point processes (PPPs) of base stations (BSs). The important statistical
properties of the universal (general) cell association functions are first
studied and the cell load statistics for power-law cell association functions,
which can characterize the accurate void cell probability of a BS in every
tier, is also derived. A simple and feasible green channel-aware cell
association (GCA) scheme is proposed and the green coverage probability is also
proposed for any particular cell association scheme, such as the maximum
received power association (MRPA) and nearest base station association (NBA)
schemes. Then the link and network energy efficiencies are proposed to
characterize the mean spectrum efficiency per unit power consumption for a BS
and the mean area spectrum efficiency for a HetNet, respectively. All the tight
bounds on the green coverage probability, link and network energy efficiencies
for the GCA, MRPA and NBA schemes are found. They are theoretically shown to
pose the fundamental maximum limits on the link and network energy efficiencies
achieved by any other cell association schemes and such a fact is validated by
numerical results as well.
