Fundamentals of the Downlink Green Coverage and Energy Efficiency in   Heterogeneous Networks
  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. 
Chun-Hung Liu and Kok Leong Fong
cs.IT math.IT