We propose a distance-based inter-cell interference coordination (ICIC) scheme in small cell networks (SCNs). While most of the previous works focus on a randomly selected user called a typical user, we focus on an edge user because the main purpose of ICIC is to improve the performance of an edge user. Since there are many inactive small cell base stations (SBSs) in SCNs, a simple criterion for an edge user such as being located near a cell boundary is not appropriate for SCNs. To accurately detect edge users experiencing severe performance degradation, we newly define an edge user in SCNs based on the nearest active neighbor SBS. We then apply our scheme only to edge users where SBSs within so-called the cooperation radius from each edge user cooperate. With the help of the stochastic geometry we obtain a semi-closed expression for the coverage probability of an edge user with our scheme. We investigate two tradeoffs on the resource efficiency of a network and the coverage probability of an interior user. We then determine the optimal cooperation radius that maximizes the coverage probability of an edge user considering the two tradeoffs. Our analytical results are validated through simulations.