Optimum number of gateways for cluster-based two-hop cellular networks

An ever increasing number of mobile users combined with an increase in the demand for data rates has led researchers to explore the feasibility of multihop cellular networks. However, due to the NP-hard complexity in resource allocation and scheduling techniques in a multihop cellular network, the focus of multihop cellular design is mostly restricted to two-hop. In this work, we analyze the capacity of a cluster-based hierarchical two-hop multi-cellular network, with a frequency reuse of one. We prove mathematically that when there are six cells surrounding the center cell, and the number of simultaneous communicating pairs in all the six cells are same, there are six distinct locations in any cell where the link capacity reaches its maximum and six distinct locations where the link capacity reaches its minimum. Significantly, all these twelve points are equidistant. Similarly, we observe that if a cell is surrounded by four cells such that all the base stations (BSs) of the adjacent cells are equidistant from the BS of the center cell, then the number of locations where the capacity is maximum or minimum is found to be exactly four each. This provides an insight on the exact number and the location where the gateways should be placed in a hierarchical cellular architecture in order to maximize the system capacity in a multi-cellular environment.In addition, for a hexagonal geometry, when the number of simultaneously communicating pairs are different in different adjacent cells, the optimum number of gateways per cell that maximizes the system capacity for all the cases is not a fixed number, but varies between a minimum value of one and a maximum value of six, depending on the number of cells which has two simultaneously communication pairs.