SINR-based k-coverage probability in cellular networks with arbitrary shadowing

We 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]

Wireless networks appear Poissonian due to strong shadowing

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 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 Suzuki (Rayleigh-log-normal) propagation model. We use 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

A Tractable Approach to Coverage and Rate in Cellular Networks

Cellular networks are usually modeled by placing the base stations on a grid, with mobile users either randomly scattered or placed deterministically. These models have been used extensively but suffer from being both highly idealized and not very tractable, so complex system-level simulations are used to evaluate coverage/outage probability and rate. More tractable models have long been desirable. We develop new general models for the multi-cell signal-to-interference-plus-noise ratio (SINR) using stochastic geometry. Under very general assumptions, the resulting expressions for the downlink SINR CCDF (equivalent to the coverage probability) involve quickly computable integrals, and in some practical special cases can be simplified to common integrals (e.g., the Q-function) or even to simple closed-form expressions. We also derive the mean rate, and then the coverage gain (and mean rate loss) from static frequency reuse. We compare our coverage predictions to the grid model and an actual base station deployment, and observe that the proposed model is pessimistic (a lower bound on coverage) whereas the grid model is optimistic, and that both are about equally accurate. In addition to being more tractable, the proposed model may better capture the increasingly opportunistic and dense placement of base stations in future networks.Comment: Submitted to IEEE Transactions on Communication

Role of Interference and Computational Complexity in Modern Wireless Networks: Analysis, Optimization, and Design

Owing to the popularity of smartphones, the recent widespread adoption of wireless broadband has resulted in a tremendous growth in the volume of mobile data traffic, and this growth is projected to continue unabated. In order to meet the needs of future systems, several novel technologies have been proposed, including cooperative communications, cloud radio access networks (RANs) and very densely deployed small-cell networks. For these novel networks, both interference and the limited availability of computational resources play a very important role. Therefore, the accurate modeling and analysis of interference and computation is essential to the understanding of these networks, and an enabler for more efficient design.;This dissertation focuses on four aspects of modern wireless networks: (1) Modeling and analysis of interference in single-hop wireless networks, (2) Characterizing the tradeoffs between the communication performance of wireless transmission and the computational load on the systems used to process such transmissions, (3) The optimization of wireless multiple-access networks when using cost functions that are based on the analytical findings in this dissertation, and (4) The analysis and optimization of multi-hop networks, which may optionally employ forms of cooperative communication.;The study of interference in single-hop wireless networks proceeds by assuming that the random locations of the interferers are drawn from a point process and possibly constrained to a finite area. Both the information-bearing and interfering signals propagate over channels that are subject to path loss, shadowing, and fading. A flexible model for fading, based on the Nakagami distribution, is used, though specific examples are provided for Rayleigh fading. The analysis is broken down into multiple steps, involving subsequent averaging of the performance metrics over the fading, the shadowing, and the location of the interferers with the aim to distinguish the effect of these mechanisms that operate over different time scales. The analysis is extended to accommodate diversity reception, which is important for the understanding of cooperative systems that combine transmissions that originate from different locations. Furthermore, the role of spatial correlation is considered, which provides insight into how the performance in one location is related to the performance in another location.;While it is now generally understood how to communicate close to the fundamental limits implied by information theory, operating close to the fundamental performance bounds is costly in terms of the computational complexity required to receive the signal. This dissertation provides a framework for understanding the tradeoffs between communication performance and the imposed complexity based on how close a system operates to the performance bounds, and it allows to accurately estimate the required data processing resources of a network under a given performance constraint. The framework is applied to Cloud-RAN, which is a new cellular architecture that moves the bulk of the signal processing away from the base stations (BSs) and towards a centralized computing cloud. The analysis developed in this part of the dissertation helps to illuminate the benefits of pooling computing assets when decoding multiple uplink signals in the cloud. Building upon these results, new approaches for wireless resource allocation are proposed, which unlike previous approaches, are aware of the computing limitations of the network.;By leveraging the accurate expressions that characterize performance in the presence of interference and fading, a methodology is described for optimizing wireless multiple-access networks. The focus is on frequency hopping (FH) systems, which are already widely used in military systems, and are becoming more common in commercial systems. The optimization determines the best combination of modulation parameters (such as the modulation index for continuous-phase frequency-shift keying), number of hopping channels, and code rate. In addition, it accounts for the adjacent-channel interference (ACI) and determines how much of the signal spectrum should lie within the operating band of each channel, and how much can be allowed to splatter into adjacent channels.;The last part of this dissertation contemplates networks that involve multi-hop communications. Building on the analytical framework developed in early parts of this dissertation, the performance of such networks is analyzed in the presence of interference and fading, and it is introduced a novel paradigm for a rapid performance assessment of routing protocols. Such networks may involve cooperative communications, and the particular cooperative protocol studied here allows the same packet to be transmitted simultaneously by multiple transmitters and diversity combined at the receiver. The dynamics of how the cooperative protocol evolves over time is described through an absorbing Markov chain, and the analysis is able to efficiently capture the interference that arises as packets are periodically injected into the network by a common source, the temporal correlation among these packets and their interdependence