Area Spectral Efficiency for Cellular Networks with Small Reuse Distance: An Algebraic Approach

In this paper we present an algebraic analytical approach to estimate area spectrum efficiency (ASE) of interference-limited cellular mobile systems with small reuse distance ratio. In an ultra-dense network (UDN), the co-channel inter-site distance is very small (e.g. 2 times of cell radius). However, to the best of our knowledge, an accurate performance framework for cellular mobile network with small number of co-channel inter-site distance ratio is rarely seen in the literature. To improve the accuracy of expression, we take interference signals from the all interfering BSs on two-dimension and area spectral efficiency (ASE) into account, and derive the close-form expression for the downlink signal-to-interference plus noise ratio (SINR) by Newton's generalized binomial equation and triangle identities of a base station (BS) geometry model. Based on the SINR expression, we further derive tight approximation formulas of downlink spectral efficiency (SE)s and ASE. Moreover, the SINR close-form expression and the tight approximation for SE and ASE with small reuse distance ratio are also presented and validated.