  In this work, we assess the viability of heterogeneous networks composed of
legacy macrocells which are underlaid with self-organizing picocells. Aiming to
improve coverage, cell-edge throughput and overall system capacity,
self-organizing solutions, such as range expansion bias, almost blank subframe
and distributed antenna systems are considered. Herein, stochastic geometry is
used to model network deployments, while higher-order statistics through the
cumulants concept is utilized to characterize the probability distribution of
the received power and aggregate interference at the user of interest. A
compre- hensive analytical framework is introduced to evaluate the performance
of such self-organizing networks in terms of outage probability and average
channel capacity with respect to the tagged receiver. To conduct our studies,
we consider a shadowed fading channel model incorporating log-normal shadowing
and Nakagami-m fading. Results show that the analytical framework matches well
with numerical results obtained from Monte Carlo simulations. We also observed
that by simply using almost blank subframes the aggregate interference at the
tagged receiver is reduced by about 12dB. Although more elaborated interference
control techniques such as, downlink bitmap and distributed antennas systems
become needed, when the density of picocells in the underlaid tier gets high.
