Downlink Coverage Analysis in a Heterogeneous Cellular Network

In this paper, we consider the downlink signal-to-interference-plus-noise ratio (SINR) analysis in a heterogeneous cellular network with K tiers. Each tier is characterized by a base-station (BS) arrangement according to a homogeneous Poisson point process with certain BS density, transmission power, random shadow fading factors with arbitrary distribution, arbitrary path-loss exponent and a certain bias towards admitting the mobile-station (MS). The MS associates with the BS that has the maximum SINR under the open access cell association scheme. For such a general setting, we provide an analytical characterization of the coverage probability at the MS.Comment: 6 pages, 5 figures, submitted to IEEE Globecom 2012 - Wireless Communications Symposium on Apr 2, 201

Multi-tier Network Performance Analysis using a Shotgun Cellular System

This paper studies the carrier-to-interference ratio (CIR) and carrier-to-interference-plus-noise ratio (CINR) performance at the mobile station (MS) within a multi-tier network composed of M tiers of wireless networks, with each tier modeled as the homogeneous n-dimensional (n-D, n=1,2, and 3) shotgun cellular system, where the base station (BS) distribution is given by the homogeneous Poisson point process in n-D. The CIR and CINR at the MS in a single tier network are thoroughly analyzed to simplify the analysis of the multi-tier network. For the multi-tier network with given system parameters, the following are the main results of this paper: (1) semi-analytical expressions for the tail probabilities of CIR and CINR; (2) a closed form expression for the tail probability of CIR in the range [1,Infinity); (3) a closed form expression for the tail probability of an approximation to CIR in the entire range [0,Infinity); (4) a lookup table based approach for obtaining the tail probability of CINR, and (5) the study of the effect of shadow fading and BSs with ideal sectorized antennas on the CIR and CINR. Based on these results, it is shown that, in a practical cellular system, the installation of additional wireless networks (microcells, picocells and femtocells) with low power BSs over the already existing macrocell network will always improve the CINR performance at the MS.Comment: 6 pages, 3 figures, accepted at IEEE Globecom 201

Stochastic Ordering based Carrier-to-Interference Ratio Analysis for the Shotgun Cellular Systems

A simple analytical tool based on stochastic ordering is developed to compare the distributions of carrier-to-interference ratio at the mobile station of two cellular systems where the base stations are distributed randomly according to certain non-homogeneous Poisson point processes. The comparison is conveniently done by studying only the base station densities without having to solve for the distributions of the carrier-to-interference ratio, that are often hard to obtain.Comment: 10 pages, 0 figures, submitted for review to IEEE Wireless Communications Letters on October 11, 201

Stochastic Geometric Modeling and Analysis of Wireless Communications Systems

This thesis studies the interference performance of large-scale wireless communications systems. Mathematical models are developed for ad-hoc networks, cellular networks, multi-tier (heterogeneous cellular) networks, cognitive radio networks and the massive-MIMO networks based on stochastic geometry where the nodes of the network are distributed in a space according to a spatial stochastic (random) process. Analytical characterizations for important performance metrics such as the distribution of the signal to interference plus noise ratio, outage probability, average rate, etc. are obtained for the most general channel conditions and system scenarios. In the past the above mentioned wireless systems have been studied through large system simulations which suffer from computational infeasibilities and provide limited insights about the system. The mathematical models are shown to closely approximate the practical systems in scattering and fading rich environments. Using the tools in stochastic geometry and stochastic ordering, we demonstrate analytical tractability of these models and closed-form characterizations of important performance metrics of the systems. The tools developed in this work can be used to characterize the achievable performance gains with interference mitigation techniques employed in 4G LTE such as fractional frequency reuse, relays, multi-cell coordination and in the study of MIMO and secrecy networks

A Predator-Prey Model For Moon-Triggered Clumping In Saturn\u27S Rings

UVIS occultation data show clumping in Saturn\u27s F ring and at the B ring outer edge, indicating aggregation and disaggregation at these locations that are perturbed by Prometheus and by Mimas. The inferred timescales range from hours to months. Occultation profiles of the edge show wide variability, indicating perturbations by local mass aggregations. Structure near the B ring edge is seen in power spectral analysis at scales 200-2000. m. Similar structure is also seen at the strongest density waves, with significance increasing with resonance strength. For the B ring outer edge, the strongest structure is seen at longitudes 90° and 270° relative to Mimas. This indicates a direct relation between the moon and the ring clumping. We propose that the collective behavior of the ring particles resembles a predator-prey system: the mean aggregate size is the prey, which feeds the velocity dispersion; conversely, increasing dispersion breaks up the aggregates. Moons may trigger clumping by streamline crowding, which reduces the relative velocity, leading to more aggregation and more clumping. Disaggregation may follow from disruptive collisions or tidal shedding as the clumps stir the relative velocity. For realistic values of the parameters this yields a limit cycle behavior, as for the ecology of foxes and hares or the boom-bust economic cycle. Solving for the long-term behavior of this forced system gives a periodic response at the perturbing frequency, with a phase lag roughly consistent with the UVIS occultation measurements. We conclude that the agitation by the moons in the F ring and at the B ring outer edge drives aggregation and disaggregation in the forcing frame. This agitation of the ring material may also allow fortuitous formation of solid objects from the temporary clumps, via stochastic processes like compaction, adhesion, sintering or reorganization that drives the denser parts of the aggregate to the center or ejects the lighter elements. Any of these more persistent objects would then orbit at the Kepler rate. We would also expect the formation of clumps and some more permanent objects at the other perturbed regions in the rings... including satellite resonances, shepherded ring edges, and near embedded objects like Pan and Daphnis (where the aggregation/disaggregation cycles are forced similar to Prometheus forcing of the F ring). © 2011 Elsevier Inc