Stochastic Geometry Modeling and Analysis of Single- and Multi-Cluster Wireless Networks

This paper develops a stochastic geometry-based approach for the modeling and analysis of single- and multi-cluster wireless networks. We first define finite homogeneous Poisson point processes to model the number and locations of the transmitters in a confined region as a single-cluster wireless network. We study the coverage probability for a reference receiver for two strategies; closest-selection, where the receiver is served by the closest transmitter among all transmitters, and uniform-selection, where the serving transmitter is selected randomly with uniform distribution. Second, using Matern cluster processes, we extend our model and analysis to multi-cluster wireless networks. Here, the receivers are modeled in two types, namely, closed- and open-access. Closed-access receivers are distributed around the cluster centers of the transmitters according to a symmetric normal distribution and can be served only by the transmitters of their corresponding clusters. Open-access receivers, on the other hand, are placed independently of the transmitters and can be served by all transmitters. In all cases, the link distance distribution and the Laplace transform (LT) of the interference are derived. We also derive closed-form lower bounds on the LT of the interference for single-cluster wireless networks. The impact of different parameters on the performance is also investigated

High-SIR Transmission Capacity of Wireless Networks with General Fading and Node Distribution

In many wireless systems, interference is the main performance-limiting factor, and is primarily dictated by the locations of concurrent transmitters. In many earlier works, the locations of the transmitters is often modeled as a Poisson point process for analytical tractability. While analytically convenient, the PPP only accurately models networks whose nodes are placed independently and use ALOHA as the channel access protocol, which preserves the independence. Correlations between transmitter locations in non-Poisson networks, which model intelligent access protocols, makes the outage analysis extremely difficult. In this paper, we take an alternative approach and focus on an asymptotic regime where the density of interferers $\eta$ goes to 0. We prove for general node distributions and fading statistics that the success probability \p \sim 1-\gamma \eta^{\kappa} for $\eta \rightarrow 0$, and provide values of $\gamma$ and $\kappa$ for a number of important special cases. We show that $\kappa$ is lower bounded by 1 and upper bounded by a value that depends on the path loss exponent and the fading. This new analytical framework is then used to characterize the transmission capacity of a very general class of networks, defined as the maximum spatial density of active links given an outage constraint.Comment: Submitted to IEEE Trans. Info Theory special issu

Variance Approximation Approaches For The Local Pivotal Method

The problem of estimating the variance of the Horvitz-Thompson estimator of the population total when selecting a sample with unequal inclusion probabilities using the local pivotal method is discussed and explored. Samples are selected using unequal inclusion probabilities so that the estimates using the Horvitz-Thompson estimator will have smaller variance than for simple random samples. The local pivotal method is one sampling method which can select samples with unequal inclusion probability without replacement. The local pivotal method also balances on other available auxiliary information so that the variability in estimates can be reduced further. A promising variance estimator, bootstrap subsampling, which combines bootstrapping with rescaling to produce estimates of the variance is described and developed. This new variance estimator is compared to other estimators such as naive bootstrapping, the jackknife, the local neighborhood variance estimator of Stevens and Olsen, and the nearest neighbor estimator proposed by Grafstrom. For five example populations, we compare the performance of the variance estimators. The local neighborhood variance estimator performs best where it is appropriate. The nearest neighbor estimator performs second best and is more widely applicable. The bootstrap subsample variance estimator tends to underestimate the variance

Uplink and Downlink Performance Bounds for Full Duplex Cellular Networks

With Full Duplex (FD), wireless terminal is capable of transmitting and receiving data simultaneously in the same frequency resources, however, it introduces self interference and co-channel interference. Even though various signal processing techniques are emerged to cancel the self interference, the bottleneck for FD performance in cellular systems is the co-channel interference from the other uplink and downlink signals. In this work we have studied both the uplink and downlink performances of a FD cellular network, where users employ fractional power control in uplink. We use Matern Cluster Process to model the network, which provides a tractable and realistic model to characterize the user-base station distances which are needed for uplink power control. Based on the obtained coverage probabilities, rates and their robust approximations, we show that while FD improves downlink performance, it severely hurts the uplink performance. Also, we provide a trade-off between uplink and downlink performances. Our study suggests dense deployment of low power base stations can improve the performance of FD system

Models and methods for computationally efficient analysis of large spatial and spatio-temporal data

With the development of technology, massive amounts of data are often observed at a large number of spatial locations (n). However, statistical analysis is usually not feasible or not computationally efficient for such large dataset. This is the so-called big n problem . The goal of this dissertation is to contribute solutions to the big n problem . The dissertation is devoted to computationally efficient methods and models for large spatial and spatio-temporal data. Several approximation methods to the big n problem are reviewed, and an extended autoregressive model, called the EAR model, is proposed as a parsimonious model that accounts for smoothness of a process collected over space. It is an extension of the Pettitt et a1. as well as Czado and Prokopenko parameterizations of the spatial conditional autoregressive (CAR) model. To complement the computational advantage, a structure removing orthonormal transformation named pre-whitening is described. This transformation is based on a singular value decomposition and results in the removal of spatial structure from the data. Circulant embedding technique further simplifies the calculation of eigenvalues and eigenvectors for the pre-whitening procedure. The EAR model is studied to have connections to the Matern class covariance structure in geostatistics as well as the integrated nested Laplace approximation (INLA) approach that is based on a stochastic partial differential equation (SPDE) framework. To model geostatistical data, a latent spatial Gaussian Markov random field (GMRF) with an EAR model prior is applied. The GMRF is defined on a fine grid and thus enables the posterior precision matrix to be diagonal through introducing a missing data scheme. This results in parameter estimation and spatial interpolation simultaneously under the Bayesian Markov chain Monte Carlo (MCMC) framework. The EAR model is naturally extended to spatio-temporal models. In particular, a spatio-temporal model with spatially varying temporal trend parameters is discussed

CHARACTERIZING FORAGING PATTERNS AMONG CATTLE AND BONDED AND NON-BONDED SMALL RUMINANTS USING SPATIAL POINT PROCESS TECHNIQUES

This paper uses the technique of spatial point processes to describe the spatial patterns of freeranging cattle and small ruminants. Two mixed-species livestock groups were monitored while foraging on 410 ha of brush-infested Southern New Mexico rangeland during July and August 1988. The groups consisted of crossbred Bos taurus and Bos indicus beef cattle with white-faced sheep (Ovis aries) and mohair goats (Capra hircus). The bonded group consisted of small ruminants that had their behaviours modified through socialization with cattle to form a ‘flerd’ in which small ruminants consistently remained near cattle. Small ruminants in the non-bonded group had not been socialized with cattle. A subset of animal location data measured during the morning and afternoon over five days for both the bonded and non-bonded groups was analyzed for spatial patterns. Only data for five morning periods (7:00-8:00 a.m.) are reported because morning and afternoon spatial patterns were similar. Observed nearest neighbor distances, mean number of small ruminant near an arbitrary cow, and point-to-animal distances were compared to Monte Carlo simulations of independently and uniformly distributed animal locations. Bonded and non-bonded groups were also compared. Results suggested bonded and non-bonded groups were similar in spatial patterns of intra-specific distances for both cattle and small ruminants. However, bonding changed the repulsive relationship observed between cattle and non-bonded small ruminants stocked together to one of inter-specific attraction. Bonded small ruminants remained close to and formed inter-specific clusters with cattle. In addition, the mean number of bonded small ruminants near an arbitrary cow was consistently higher than for non-bonded small ruminants. Finally, the spatial pattern of cattle across the paddock did not differ between bonded and non-bonded groups, while bonded small ruminants tended to disperse slightly more uniformly across the paddock than did non-bonded small ruminants. These findings indicate the usefulness of spatial point processes techniques to analyze such animal location data, substantiate on a larger scale conclusions of previous, replicated studies about the effect of bonding small ruminants to cattle, and suggest utilization of paddock landscapes may be positively influenced using flerds compared to flocks and herds

Co-localization Analysis of Bivariate Spatial Point Pattern

Spatial point pattern analysis investigates the localizations of random events in a defined spatial space usually conveyed in the form of images. Spatial distribution of two types of events observed in these images reflects their underlying interactions, which is the focus of co-localization analysis in spatial statistics. Malkusch et al. (Malkusch, et al., 2012) recently proposed the Coordinate-based Co-localization (CBC) method for co-localization analysis. However, the method did not incorporate edge corrections for point proportions and ignored their correlations over nested incremental observational regions. Hence, it yields false positive results for even complete spatial random distributions. In this research, we propose the new K(r) function Coordinate-based Colocalization (KCBC) method to quantify co-localization of two species by utilizing local bivariate Ripley\u27s K and Pearson’s Correlation Coefficient. Simulation studies are conducted to demonstrate the unbiasedness of the new method. An application to real life data was provided to illustrate its applicability