Optimization of Cellular Networks Capacity and Densification An Analytical approach Philippe Ezran Senior Industry Analyst Tel: 33 1 4323 6631 philippe.ezran@polytechnique.org Jean-Marc Kelif France Telecom R&D, 92794 Issy Moulineaux, France Tel: 33 1 4529 6179 jeanmarc.kelif@orange-ftgroup.com ABSTRACT We propose an analytical approach of cellular networks, which allows to optimize transmitting powers of base stations, and to maximize network capacity. In our framework, mobiles are considered as a continuum. Networks are often densified i.e. new base stations are added because of increasing traffic. Our approach enables to analyse the extra capacity offered by each new base station, according to its location. It can be performed without any simulation whatever the model used for the propagation. The continuous approach proposed in this paper can be applied to any frequency reuse 1 networks, such as OFDMA or CDMA ones. As an example, we calculate the maximum number of active mobiles per cell in a homogeneous network, considering different kinds of environments, and we show how to optimize the densification of a network. General Terms Performance, Theory Keywords analytical model, CDMA, OFDMA, densification, optimization. 1. INTRODUCTION In order to enable a frequency reuse 1 cellular network to support more traffic, a telecom provider can choose to densify the network, i.e to add new base stations (BS). In order to analyse the advantages and drawbacks of this solution, the provider generates simulations with relevant tools. These simulations do not give instantaneous results, may last a long time, and moreover, must be repeated many times by varying conditions. We develop thereafter an analytical approach. This approach can be applied to any frequency reuse 1 network, such as CDMA and OFDMA. It enables to analyse and compare instantly different solutions in the aim to adapt the network, or a given zone of the network, to an increasing traffic demand. For clarity of presentation, this paper is focused on CDMA networks. However, the analysis we develop can be used for other technologies such as OFDMA (see remark at the end of the section 2). Classical CDMA networks models [1-2] do not give explicit and simple analytical expressions due to the complexity of the analysis: for the downlink, the interferences received by a mobile are due to all the base stations of the network. They depend on their transmission powers, positions and numbers. We develop an analytical network's approach which does not need any simulation to obtain explicit expressions of some important characteristics of the network such as the possibility for a mobile to be admitted in the network. Our model is based on the assumption that mobiles are uniformly distributed in each cell, which enables the transformation of the discrete sum of constraints on a mobile to its mean value, expressed as an integral. The problem of CDMA capacity constraints has already been considered by several authors. Nettleton and Alavi [8] considered the power allocation problem in the cellular spread spectrum context. Considering each user has a required bit rate, Gilhousen et al [7] assumed a capacity of the network only interference-limited. In our paper, we propose an analytical method to calculate the maximum capacity of a cell or a network, using the minimum transmitting power. As a result of this approach, the maximum number of active mobiles supported in a network will only depend on the characteristics of the network: propagation conditions and positions of the base stations. The paper is organized as follows. Expressing the SIR target constraints for a mobile to be connected to a BS of a CDMA network, we establish the matricial inequality of any transmitted power to any active mobile of the network. Establishing the conditions under which the inequality has a solution, we propose afterwards a method to optimize these powers. We obtain the analytical expression of the capacity of a cell, and analyze the densification consequences. 2. Analysis of cellular networks We use the model similar to [4]. Let us consider a network of BS N base stations, each j BS defining a cell j. As an example, we develop our analysis considering a CDMA network. We assume that each mobile is active. We express that the Signal to Interference Ratio (SIR) received by a mobile has to be at least equal to a minimum threshold target value γ [4] [5]. The interferences are due to an intra-cell interference I own which represents the interferences due to the common channels and the traffic channels of the other mobiles located in the cell b,an inter- cell interference I other which represents the interferences due to the other base stations of the network, and the level of the thermal noise N th at the receiver of the mobile. Using the equation of the