23 research outputs found
Tight Lower Bounds on the Contact Distance Distribution in Poisson Hole Process
In this letter, we derive new lower bounds on the cumulative distribution
function (CDF) of the contact distance in the Poisson Hole Process (PHP) for
two cases: (i) reference point is selected uniformly at random from
independently of the PHP, and (ii) reference point is located at
the center of a hole selected uniformly at random from the PHP. While one can
derive upper bounds on the CDF of contact distance by simply ignoring the
effect of holes, deriving lower bounds is known to be relatively more
challenging. As a part of our proof, we introduce a tractable way of bounding
the effect of all the holes in a PHP, which can be used to study other
properties of a PHP as well.Comment: To appear in IEEE Wireless Communications Letter