We consider a two-hop cellular system in which the mobile nodes help the base
station by relaying information to the dead spots. While two-hop cellular
schemes have been analyzed previously, the distribution of the node locations
has not been explicitly taken into account. In this paper, we model the node
locations of the base stations and the mobile stations as a point process on
the plane and then analyze the performance of two different two-hop schemes in
the downlink. In one scheme the node nearest to the destination that has
decoded information from the base station in the first hop is used as the
relay. In the second scheme the node with the best channel to the relay that
received information in the first hop acts as a relay. In both these schemes we
obtain the success probability of the two hop scheme, accounting for the
interference from all other cells. We use tools from stochastic geometry and
point process theory to analyze the two hop schemes. Besides the results
obtained a main contribution of the paper is to introduce a mathematical
framework that can be used to analyze arbitrary relaying schemes. Some of the
main contributions of this paper are the analytical techniques introduced for
the inclusion of the spatial locations of the nodes into the mathematical
analysis.