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We propose a new framework to study the performance of cellular networks using a fluid model and we derive from this model analytical formulas for interference, outage probability, and spatial outage probability. The key idea of the fluid model is to consider the discrete base station (BS) entities as a continuum of transmitters that are spatially distributed in the network. This model allows us to obtain simple analytical expressions to reveal main characteristics of the network. In this paper, we focus on the downlink other-cell interference factor (OCIF), which is defined for a given user as the ratio of its outer cell received power to its inner cell received power. A closed-form formula of the OCIF is provided in this paper. From this formula, we are able to obtain the global outage probability as well as the spatial outage probability, which depends on the location of a mobile station (MS) initiating a new call. Our analytical results are compared to Monte Carlo simulations performed in a traditional hexagonal network. Furthermore, we demonstrate an application of the outage probability related to cell breathing and densification of cellular networks.

Abstract-The uplink power control procedure in Long Term Evolution (LTE) cellular networks is made of an open-loop part and a closed loop part. In this paper, we focus on the former and study the compensation factor of the related Fractional Power Control (FPC) scheme. In particular, we propose a first analytical approach in order to derive approximate equations for the Signal to Interference plus Noise Ratio (SINR) at a given distance of the eNode-B, the average SINR, and the average cell spectral efficiency. This method avoids extensive and timeconsuming simulations. From derived expressions, we are able to find the optimal compensation factor, and to study the impact of various network and environment parameters on the system performance.

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