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

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

Periodic and Localized Solutions of the Long Wave-Short Wave Resonance Interaction Equation

In this paper, we investigate the (2+1) dimensional long wave-short wave resonance interaction (LSRI) equation and show that it possess the Painlev\'e property. We then solve the LSRI equation using Painlev\'e truncation approach through which we are able to construct solution in terms of three arbitrary functions. Utilizing the arbitrary functions present in the solution, we have generated a wide class of elliptic function periodic wave solutions and exponentially localized solutions such as dromions, multidromions, instantons, multi-instantons and bounded solitary wave solutions.Comment: 13 pages, 6 figure

Miura Transformation between two Non-Linear Equations in 2+1 dimensions

A Dispersive Wave Equation in 2+1 dimensions (2LDW) widely discussed by different authors is shown to be nothing but the modified version of the Generalized Dispersive Wave Equation (GLDW). Using Singularity Analysis and techniques based upon the Painleve Property leading to the Double Singular Manifold Expansion we shall find the Miura Transformation which converts the 2LDW Equation into the GLDW Equation. Through this Miura Transformation we shall also present the Lax pair of the 2LDW Equation as well as some interesting reductions to several already known integrable systems in 1+1 dimensions.Comment: 14 pages, latex. Journal of Mathematical Physics (to appear

On the Throughput Cost of Physical Layer Security in Decentralized Wireless Networks

This paper studies the throughput of large-scale decentralized wireless networks with physical layer security constraints. In particular, we are interested in the question of how much throughput needs to be sacrificed for achieving a certain level of security. We consider random networks where the legitimate nodes and the eavesdroppers are distributed according to independent two-dimensional Poisson point processes. The transmission capacity framework is used to characterize the area spectral efficiency of secure transmissions with constraints on both the quality of service (QoS) and the level of security. This framework illustrates the dependence of the network throughput on key system parameters, such as the densities of legitimate nodes and eavesdroppers, as well as the QoS and security constraints. One important finding is that the throughput cost of achieving a moderate level of security is quite low, while throughput must be significantly sacrificed to realize a highly secure network. We also study the use of a secrecy guard zone, which is shown to give a significant improvement on the throughput of networks with high security requirements.Comment: Accepted for publication in IEEE Transactions on Wireless Communication

PAPADAKIS NEAREST NEIGHBOR ANALYSIS OF YIELD IN AGRICULTURAL EXPERIMENTS

Papadakis analysis, originally proposed by Papadakis in 1937 belongs to a larger class of methodologies called the nearest neighbor analysis which is primarily based on the fact that plots in close proximity ( neighbors ) are exposed to similar environmental conditions and therefore, for a given plot, information from its neighboring plots could be used for adjustment of its response for spatial variability. The basic theory behind the application of Papadakis methodology to field trials is relatively simple. It is based on an analysis of covariance where the covariate is an index of fertility environment), and the response is some observable trait (e.g., grain yield), which is adjusted up or down to reflect the effect due to spatial variability. There have been several references in the literature to application of Papadakis methodology to field trials where the analysis is routinely carried out on data coming from a replicated design within a testing location. The application that is presented here is an exception to the rule in that the analysis is conducted on multi-location data with single replication per location. In plant breeding industry, a recent trend has been to move towards one-replicate testing system to maximize the coverage of the testing environments. Note that for a one-replicate test, no design such as a Lattice, can be used for adjustment of the observations for spatial variability. We start with describing the theory and methodology behind the proposed Papadakis analysis for multilocation data. Several practical problems such as impact of missing values on Papadakis covariate, choice of homogeneous vs. heterogeneous slope coefficient, and effect of influential observations, etc. are discussed and solutions are proposed. Finally, results from several validation studies on com yield data, including comparison to lattice adjusted plot values and ANOV A on adjusted vs. unadjusted data are presented to demonstrate the benefit from the proposed procedure

Load-Aware Modeling and Analysis of Heterogeneous Cellular Networks

Random spatial models are attractive for modeling heterogeneous cellular networks (HCNs) due to their realism, tractability, and scalability. A major limitation of such models to date in the context of HCNs is the neglect of network traffic and load: all base stations (BSs) have typically been assumed to always be transmitting. Small cells in particular will have a lighter load than macrocells, and so their contribution to the network interference may be significantly overstated in a fully loaded model. This paper incorporates a flexible notion of BS load by introducing a new idea of conditionally thinning the interference field. For a K-tier HCN where BSs across tiers differ in terms of transmit power, supported data rate, deployment density, and now load, we derive the coverage probability for a typical mobile, which connects to the strongest BS signal. Conditioned on this connection, the interfering BSs of the $i^{th}$ tier are assumed to transmit independently with probability $p_i$, which models the load. Assuming - reasonably - that smaller cells are more lightly loaded than macrocells, the analysis shows that adding such access points to the network always increases the coverage probability. We also observe that fully loaded models are quite pessimistic in terms of coverage.Comment: to appear, IEEE Transactions on Wireless Communication

Prevalence of root caries among elders living in residential homes of Bengaluru city, India

Background: Among the various oral ailments which have been observed in elderly, root caries is a significant one. Tooth loss is chief oral health-related negative variable to the quality of life in elderly and root caries is the major cause of tooth loss in them. It has been reported about a third of older population bears most of the root caries burden, so the present study aimed to assess the prevalence of root caries among older individuals residing in residential homes of Bengaluru city India. Material and Methods: Elderly individuals aged 60 and above, residing in residential homes of Bangalore city, were included in the study. The study participants filled a questionnaire regarding their demographic details and oral health habits. Root surface caries was recorded according to criteria described by Banting et al. and root caries was expressed in terms of the root caries index (RCI). The statistical analysis was performed using descriptive statistics and chi-square test. P < 0.05 was considered as statistically significant. Results: The prevalence of root caries was 46.4%. The root caries index was 15%. Statistically significant differences (P < 0.05) observed across gender, marital status, diet, socio-economic status, medication, method of cleaning and frequency of cleaning and were identified as significant predictors of root caries. Conclusions: The prevalence of root caries among institutionalized older people was high. Oral health policies and preventive measures are needed focusing on the special needs of this neglected and socioeconomically deprived population to improve their quality of life