Analyzing Dependent Placements of Small Cells in a Two-Layer   Heterogeneous Network with a Rate Coverage Constraint
  We consider the downlink of a two-layer heterogeneous network, comprising macro cells (MCs) and small cells (SCs). The existing literature generally assumes independent placements of the access points (APs) in different layers; in contrast, we analyze a dependent placement where SC APs are placed at locations with poor service from the MC layer. Our goal is to obtain an estimate of the number of SCs required to maintain a target outage rate. Such an analysis is trivial if the MCs are located according to a Poisson point process (PPP), which provides a lower bound on performance. Here, we consider MCs placed on a hexagonal grid, which complements the PPP model by providing an upper bound on performance. We first provide accurate bounds for the average interference within a MC when SCs are not used. Then, by obtaining the outage areas, we estimate the number of SCs required within an MC to overcome outage. If resource allocation amongst SCs is not used, we show that the problem of outage is not solved completely, and the residual outage area depends on whether co-channel or orthogonal SCs are used. Simulations show that a much smaller residual outage area is obtained with orthogonal SCs. 
S. Alireza Banani, Andrew W. Eckford, and Raviraj S. Adve
cs.IT cs.NI math.IT