  Interference field in wireless networks is often modeled by a homogeneous
Poisson Point Process (PPP). While it is realistic in modeling the inherent
node irregularity and provides meaningful first-order results, it falls short
in modeling the effect of interference management techniques, which typically
introduce some form of spatial interaction among active transmitters. In some
applications, such as cognitive radio and device-to-device networks, this
interaction may result in the formation of holes in an otherwise homogeneous
interference field. The resulting interference field can be accurately modeled
as a Poisson Hole Process (PHP). Despite the importance of PHP in many
applications, the exact characterization of interference experienced by a
typical node in a PHP is not known. In this paper, we derive several tight
upper and lower bounds on the Laplace transform of this interference. Numerical
comparisons reveal that the new bounds outperform all known bounds and
approximations, and are remarkably tight in all operational regimes of
interest. The key in deriving these tight and yet simple bounds is to capture
the local neighborhood around the typical point accurately while simplifying
the far field to attain tractability. Ideas for tightening these bounds further
by incorporating the effect of overlaps in the holes are also discussed. These
results immediately lead to an accurate characterization of the coverage
probability of the typical node in a PHP under Rayleigh fading.
