Abstract-An almost ubiquitous assumption made in the stochastic-analytic approach to study of the quality of user-service in cellular networks is Poisson distribution of base stations, often completed by some specific assumption regarding the distribution of the fading (e.g. Rayleigh). The former (Poisson) assumption is usually (vaguely) justified in the context of cellular networks, by various irregularities in the real placement of base stations, which ideally should form a lattice (e.g. hexagonal) pattern. In the first part of this paper we provide a different and rigorous argument justifying the Poisson assumption under sufficiently strong lognormal shadowing observed in the network, in the evaluation of a natural class of the typical-user service-characteristics (including path-loss, interference, signal-to-interference ratio, spectral efficiency). Namely, we present a Poisson-convergence result for a broad range of stationary (including lattice) networks subject to log-normal shadowing of increasing variance. We show also for the Poisson model that the distribution of all these typical-user service characteristics does not depend on the particular form of the additional fading distribution. Our approach involves a mapping of 2D network model to 1D image of it "perceived" by the typical user. For this image we prove our Poisson convergence result and the invariance of the Poisson limit with respect to the distribution of the additional shadowing or fading. Moreover, in the second part of the paper we present some new results for Poisson model allowing one to calculate the distribution function of the SINR in its whole domain. We use them to study and optimize the mean energy efficiency in cellular networks.

International audienceWe give numerically tractable, explicit integral expressions for the distribution of the signal-to-interference-and-noise-ratio (SINR) experienced by a typical user in the down-link channel from the k-th strongest base stations of a cellular network modelled by Poisson point process on the plane. Our signal propagation-loss model comprises of a power-law path-loss function with arbitrarily distributed shadowing, independent across all base stations, with and without Rayleigh fading. Our results are valid in the whole domain of SINR, in particular for SINR<1, where one observes multiple coverage. In this latter aspect our paper complements previous studies reported in [Dhillon et al. JSAC 2012]

Geographic locations of cellular base stations sometimes can be well fitted with spatial homogeneous Poisson point processes. In this paper, we make a complementary observation. In the presence of the log-normal shadowing of sufficiently high variance, the statistics of the propagation loss of a single user with respect to different network stations are invariant with respect to their geographic positioning, whether regular or not, for a wide class of empirically homogeneous networks. Even in a perfectly hexagonal case they appear as though they were realized in a Poisson network model, i.e., form an inhomogeneous Poisson point process on the positive half-line with a power-law density characterized by the path-loss exponent. At the same time, the conditional distances to the corresponding base stations, given their observed propagation losses, become independent and log-normally distributed, which can be seen as a decoupling between the real and model geometry. The result applies also to the Suzuki (Rayleigh-log-normal) propagation model. We use the Kolmogorov-Smirnov test to empirically study the quality of the Poisson approximation and use it to build a linear-regression method for the statistical estimation of the value of the path-loss exponent.

This paper proposes scalable admission and congestion control schemes that allow each base station to decide independently of the others what set of voice users to serve and/or what bit rates to offer to elastic traffic users competing for bandwidth. These algorithms are primarily meant for large CDMA networks with a random but homogeneous user distribution. They take into account in an exact way the influence of geometry on the combination of inter-cell and intra-cell interferences as well as the existence of maximal power constraints of the base stations and users. We also study the load allowed by these schemes when the size of the network tends to infinity and the mean bit rate offered to elastic traffic users. By load, we mean here the number of voice users that each base station can serve.

The objective of the present paper is to build analytical methods for the evaluation of the quality of service (QoS) perceived by the users in the downlink of OFDMA wireless cellular networks serving streaming and elastic traffic.To do so, we first describe the resource (power and bandwidth) allocation problem and characterize its feasibility by some reference feasibility condition (FC). The QoS for FC may only by evaluated by simulations. To cope with this difficulty, we propose some sufficient feasibility condition (SFC) having the multi-Erlang form which permits analytical evaluation of the QoS. In particular, the blocking probability for streaming users can be calculated using Kaufman-Roberts algorithm. For elastic users, explicit expressions of the throughputs are obtained by using a multi-class processor sharing model. Moreover, we study the QoS in a network serving simultaneously streaming and elastic traffic.We validate this approach by comparing SFC's blocking probabilities to these simulated for FC. Moreover, we illustrate the proposed approach by solving the dimensioning problem; i.e., evaluating the minimal density of base stations assuring acceptable QoS of a given traffic demand per surface unit.