Resource allocation is a major concern in wireless communication systems. The main aim of allocation of limited resources is to increase the total capacity as much as possible. Fair or demand-based resource allocation approaches can be applied for different scenarios. Stable matching algorithm lets us to consider both quality of service (QoS)-sensitive or fair allocation for an efficent usage of the scarce bandwidth. In this paper, we analyse the stable matching algorithm and its applications on wireless communications are considered. As a realistic approach, stable matching algorithm is applied to heterogeneous networks (HetNets) for resource allocations. The fairness and capacity performances of stable matching algorithm are studied on both one-to-one systems and systems that maximize the number of users.