  This paper presents the derivation for per-tier outage probability of a
randomly deployed femtocell network over an existing macrocell network. The
channel characteristics of macro user and femto user are addressed by
considering different propagation modeling for outdoor and indoor links.
Location based outage probability analysis and capacity of the system with
outage constraints are used to analyze the system performance. To obtain the
simplified expressions, approximations of ratios of Rayleigh random variables
(RVs), Rayleigh to log normal RVs and their weighted summations, are derived
with the verifications using simulations.
