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

Outage Probability and Capacity for Two-Tier Femtocell Networks by Approximating Ratio of Rayleigh and Log Normal Random Variables