Outage Probability and Capacity for Two-Tier Femtocell Networks by   Approximating Ratio of Rayleigh and Log Normal Random Variables
  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. 
Sumudu Samarakoon and Nandana Rajatheva and Mehdi Bennis and Matti   Latva-aho
cs.IT cs.PF cs.SY math.IT