Recent studies have set the problem of base station cooperation within the framework of stochastic geometry and point processes. In this way, the irregularity of the base station positions and the randomness of other network parameters can be considered. Existing works study the case when the user can dynamically choose the set of stations cooperating for its service. This assumption, besides being not realistic, saturates the backhaul with intensive communication between the stations. To confront this problem, other authors propose to form the cooperative groups in a static way. These methodologies are, however, not optimal. Instead, static groups must be defined by means of proximity, with nodes linked by fixed infrastructure. To analyze such a potential work, we propose a grouping method based on node proximity. Actually, it is a variation of the so-called nearest neighbor model. With the mutually nearest neighbor relation, we allow the formation of singles and pairs of nodes. In this way, for a given topology of atoms, two point processes are created: the process of singles and the process of cooperative pairs. We derive structural characteristics for these and analyze the resulting interference fields. The results constitute a novel toolbox towards the performance evaluation of networks with static cooperation. When the node positions are modeled by a Poisson point process, the processes of singles and pairs are not Poisson, complicating the corresponding analysis. The performance of the original model can be approximated by the superposition of two Poisson point processes. This allows the derivation of exact expressions for the coverage probability. Numerical evaluation shows coverage gains from different signal cooperation that can reach up to 15%, compared with the standard noncooperative case. The analysis is general and can be applied to any type of cooperation in pairs of transmitting nodes.