  The problem of base station cooperation has recently been set within the
framework of Stochastic Geometry. Existing works consider that a user
dynamically chooses the set of stations that cooperate for his/her service.
However, this assumption often does not hold. Cooperation groups could be
predefined and static, with nodes connected by fixed infrastructure. To analyse
such a potential network, in this work we propose a grouping method based on
proximity. It is a variation of the so called Nearest Neighbour Model. We
restrict ourselves to the simplest case where only singles and pairs of base
stations are allowed to be formed. For this, two new point processes are
defined from the dependent thinning of a Poisson Point Process, one for the
singles and one for the pairs. Structural characteristics for the two are
provided, including their density, Voronoi surface, nearest neighbour, empty
space and J-function. We further make use of these results to analyse their
interference fields and give explicit formulas to their expected value and
their Laplace transform. The results constitute a novel toolbox towards the
performance evaluation of networks with static cooperation.
