Compressive Data Aggregation from Poisson point process observations

Cellular networks have a great transformation during the last decade. The traditional cellular network system is often overlaid with well-deployed BSs of proper power. However, more and more complex elements such as picocells, femtocells and relays have been introduced to cellular network system. BSs in these elements are unplanned, user-installed and randomly deployed. All of these things compose heterogeneous cellular networks (HCNs). In order to evaluate the performance of HCNs, people usually model the distribution of BSs in HCNs as spatial stochastic point process model. One of the most popular spatial models for these HCNs is Poisson Point Process (PPP) model. However the PPP model is not exact for some cases where BSs in PPP model may be too close to each other. In this paper, we propose a more reasonable and practical model called Matern-like point process (MLPP) model which imposes a certain minimal distance between any two BSs to overcome this problem. Simulations show that the coverage probability of the proposed model noticeably outperforms the PPP model. This improvement depends on the value of minimal distance. We also evaluate the system efficiency defined by the ratio of coverage probability and total power. The results show that the MLPP model has a significant improvement compared to PPP model.

We develop a new class of event detection algorithms in Wireless Sensor Networks where the sensors are randomly deployed spatially. We formulate the detection problem as a binary hypothesis testing problem and design the optimal decision rules for two scenarios, namely the Poisson Point Process and Binomial Point Process random deployments. To calculate the intractable marginal likelihood density, we develop three types of series expansion methods which are based on an Askey-orthogonal polynomials. In addition, we develop a novel framework to provide guidance on which series expansion is most suitable (i.e., most accurate) to use for different system parameters. Extensive Monte Carlo simulations are carried out to illustrate the benefits of this framework as well as the quality of the series expansion methods, and the impacts that different parameters have on detection performance via the Receiver Operating Curves (ROC).

In this paper, we analyze the performance of a cloud radio access network (CRAN), consisting of multiple randomly distributed remote radio heads (RRHs) and a macro base station (MBS), each equipped with multiple antennas. To model the spatial distribution of RRHs and analyze its performance, we use stochastic geometry tools. In contrast to previous works on CRAN that consider Poisson Point Process (PPP) model for the spatial distribution of RRHs, we consider a more realistic Matern hard-core point process (MHCPP) model that imposes a certain minimal distance (referred to as hard-core distance) between the two RRHs so that the RRHs are not too close to each other. To compare system performance of CRAN when different transmission strategies are used, three RRH selection schemes are adopted including 1) the best RRH selection (BRS); 2) all RRHs participation (ARP); and 3) nearest RRH selection (NRS). Considering downlink transmission, the ergodic capacity, outage probability, and system throughput of CRAN are analytically characterized for different RRH selection schemes. The presented results demonstrate that compared to PPP model, the increase in hard-core distance will result in a higher outage probability and cause a negative impact on ergodic capacity. Furthermore, when the same total transmit power is consumed, BRS scheme provides the best outage performance while ARP scheme is the best RRH selection scheme when the same transmit SNR at each RRH is assumed. Moreover, it is shown that the hard-core distance has a more significant impact on systems with higher intensity of PPP distributed candidate points and in large hard-core distance regime increasing the intensity of candidate points can only provide a small improvement in outage performance. We extend our work to multiuser case with zero-forcing (ZF) precoding where it is proven that the results in multiuser case reduce to the derived results in this work by substituting K=1 for single-user.

Base station (BS) locations are usually modelled using one of two extremes: at one end is a deterministic, hexagonal, location model; while at the other is a random deployment following a Poisson point process (PPP). However, real-world networks follow neither extreme; as such, in this paper, we focus on a modified perturbed hexagonal lattice model that, in terms of regularity, lies in between the PPP and the perfect hexagonal lattice models. In our modified perturbed hexagonal lattice, the location of all interfering BSs, except for the serving BS under consideration, are perturbed. We provide a simple and tight upper bound on the average total interference in an interference-limited reuse-1 network. The bound is presented in the form of a polynomial in the distance from the serving BS and another polynomial in the normalized perturbation. The presented formulation is useful in obtaining simple analytical expressions for various network parameters such as SIR and/or coverage probability. As an added benefit, the formulations here quantify the loss in the coverage probability in moving from the perfect lattice model to a random BS deployment. We use simulations to illustrate the accuracy of the theory developed.

Poisson Point Process (PPP) models provide important insights for the analysis of heterogeneous networks (HetNets). Recently, several theoretical results which investigate the outage and the capacity of HetNets have been developed based on PPPs. The goal of the present paper is to provide exact analytical expressions for the capacity of range expanded and interference coordinated HetNets, and validate these theoretical analysis through well-documented computer simulations. Both analytical and simulated capacity results are obtained for various range expansion and interference coordination scenarios, and are shown to have good agreement.

We propose and investigate dynamic spatial-temporal point process models for independent and interacting events. The models for independent events are dynamic spatial-temporal Poisson point process (DSTPPP) model that account for temporal and spatial clustering. The models proposed for events with interaction are Markov (Gibbs) space-time point process models. We model the intensity function of a DSTPPP via conditioning arguments that allow for additional interpretations and inclusion of well-known point process models as special cases. Depending on the nature of the questions to be answered, the in- tensity function of a DSTPPP can be modeled in several ways. First, we develop models via conditioning on the time component of the events and then consider conditioning on the location component of the events. Modeling, simulation and computation are accomplished in a fully hierarchical Bayesian framework. Finally, we focus on dynamic marked Markov space-time point processes, where the events are allowed to interact with each other across time and space. Once again the hierarchical Bayesian framework is invaluable in this case, since it allows us to introduce dynamic process models via conditioning. The methodolo- gies are illustrated using simulated data, and several applications, including modeling and inference for earthquake events in California, and tornado events in Missouri.

This paper analyzes the performance of a vehicular ad hoc network (VANET) modeled as a Cox process, where the spatial layout of the roads is modeled by a Poisson line process (PLP) and the locations of nodes on each line are modeled as a 1D Poisson point process (PPP). For this setup, we characterize the success probability of a typical link and the area spectral efficiency (ASE) of the network assuming slotted ALOHA as the channel access scheme. We then concretely establish that the success probability of a typical link in a VANET modeled using a Cox process converges to that of a 1D and 2D PPP for some extreme values of the line and node densities. We also study the trends in success probability as a function of the system parameters and show that the optimum transmission probability that maximizes the ASE for this Cox process model differs significantly from those of the relatively-simpler 1D and 2D PPP models used commonly in the literature to model vehicular networks.

This paper provides a tractable framework to understand the performance of Device-to-device (D2D) underlay cellular networks. D2D communication can improve range, data rates and energy efficiency of cellular networks. However, analyzing performance of D2D techniques is non-trivial. In this paper, ergodic capacity of D2D underlay cellular networks is investigated using Poisson point process (PPP) models. Line-of-sight (LoS) components in D2D direct links are characterized via a Rician fading model. In addition, locations of D2D receiving users (DRUs) are assumed to be random with varying distribution. Specifically, we investigate two different cases of DRUs: (1) distance between a D2D user (DU) pair follows a uniform distribution and (2) a DRU is distributed uniformly in the circular area around its serving D2D transmit user (DTU). We derive, for the first time, closed-form results for ergodic capacity of D2D communications for a practical case with path loss exponent of 4. We demonstrate that our new analytical results better approximate the actual capacity relative to prior approaches.

This article performs a unified analysis of three coordinated multipoint (CoMP) transmission strategies in the downlink of mmWave cellular networks, including the fixed-number base station (BS) cooperation (FNC), the fixed-region BS cooperation (FRC), and the interference-aware BS cooperation (IAC). We first develop a comprehensive framework for CoMP operation in cellular networks, and investigate the network performance under a Poisson point process (PPP) model together with mmWave spectrum. To show what fraction of users in the network achieve target reliability for a given signal to interference-plus-noise ratio (SINR)/signal-to-interference ratio (SIR), we derive the SINR/SIR meta distributions, and further obtain the coverage probability as well as mean local delay for the three cooperation strategies. A pivotal intermediate step to compute the performance metrics is the derivation of joint distributions of distances between a typical user and cooperative BSs. Our analysis demonstrates that parameters of blockage have a significant influence on the network performance for the three CoMP schemes. We find that the FRC scheme makes more users achieve the given link reliability for the scenario with a low density of BSs, while the IAC scheme provides better performance for the network with a high density of BSs. Moreover, the optimal CoMP scheme can be approximately selected by considering the nearest distance from the serving BS to user and the radius of the approximate line-of-sight (LoS) region in the cellular networks.

Spatial Poisson process models are popular partly because of their mathematical tractability based on a simple and powerful calculus whose main ingredients, besides Campbell’s formula, are the covariance formula and the exponential formula (also know as Campbell’s second formula). These formulas extend immediately to marked Poisson processes with independent (or location dependent) IID marks as a consequence of the fact that such marked Poisson processes can be described as unmarked Poisson processes in a higher-dimensional space. This slight modification of point of view will be applied to the study of the point processes obtained by meas of elementary transformations of a basic Poisson process, such as thinning, translation or clustering. All the results concerning Poisson processes find straightforward extensions concerning Cox processes. The calculus of spatial marked Poisson or Cox processes will be applied to a particular type of stochastic geometry (featuring the Boolean model) and to the exact sampling of cluster point processes.

In this paper models and algorithms are presented for transcription of pitch and timings in polyphonic music extracts. The data are decomposed framewise into the frequency domain, where a Poisson point process model is used to write a polyphonic pitch likelihood function. From here Bayesian priors are incorporated both over time (to link successive frames) and also within frames (to model the number of notes present, their pitches, the number of harmonics for each note, and inharmonicity parameters for each note). Inference in the model is carried out via Bayesian filtering using a powerful Sequential Markov chain Monte Carlo (MCMC) algorithm that is an MCMC extension of particle filtering. Initial results with guitar music, both laboratory test data and commercial extracts, show promising levels of performance.KeywordsAutomated music transcriptionmulti-pitch estimationBayesian filteringPoisson point processMarkov chain Monte Carloparticle filterspatio-temporal dynamical model

To provide proper coverage of their random deployment regions, wireless sensor networks (WSN) should employ abundant nodes. In this paper we correct such situations by employing some mobile robots as mobile nodes in WSN which can actively move to desired locations for repairing the broken networks. According to the pre-research work we know that the number of nodes employed by WSN is closely relevant to quality of service (QoS) in sensing coverage when the nodes are randomly deployed in the target region. A modified particle swarm optimization (PSO) named particle swarm genetic optimization (PSGO), which imports selection and mutation operators in PSO to overcome the premature fault of classical PSO, is proposed to redeploy the mobile robots according to the node density for repairing the sensing coverage hole after their initial random deployment. It is suggested by the simulated experiment results that the WSN employing the mobile robots can improve the QoS in sensing coverage than the stationary WSN by redeploying mobile robots according to the node density.

To satisfy the requirement of increasing mobile traffic, heterogeneous networks (HetNets) will be deployed for the fifth generation (5G) mobile communications systems. Since the deployment of base stations (BSs) in HetNets is generally dense and random, stochastic geometry has increasingly been used to analyze the performance of HetNets. Most of the existing work is based on Poisson point processes (PPPs), which lead to some closed-form expressions for local delay and energy efficiency. Considering the geographical distribution of BSs, PPP may not be accurate enough. In contrast, a Poisson cluster process (PCP) proves more realistic for the deployment of BSs. In this paper, by using the discontinuous transmission (DTX) mode, the local delay and energy efficiency based on PCP have been analyzed. It is found that the local delay is larger and the energy efficiency is lower under PCP because of the strong intra-cluster interference. However, the local delay under PCP becomes similar to that under PPP if the radii of clusters are sufficiently large.

Heterogeneous cellular networks (HCNs) constitute a necessary step in the evolution of cellular networks. In this paper, we apply the signal-to-interference ratio (SIR) meta distribution framework for a refined SIR performance analysis of HCNs, focusing on K-tier heterogeneous cellular networks based on the homogeneous independent Poisson point process (HIP) model, with range expansion bias (offloading bias) in each tier. Expressions for the b-th moment of the conditional success probability for both the entire network and each tier are derived, based on which the exact meta distributions and the beta approximations are evaluated and compared. Key performance metrics including the mean success probability, the variance of the conditional success probability, the mean local delay and the asymptotic SIR gains of each tier are obtained. The results show that the biases are detrimental to the overall mean success probability of the whole network and that the b-th moment curve (versus the SIR threshold) of the conditional success probability of each tier can be excellently approximated by the horizontal shifted versions of the first moment curve of the single-tier PPP network. We also provide lower bounds for the region of the active probabilities of the base stations to keep the mean local delay of each tier finite.

In this paper we analysed a special kind of wireless ad hoc networks. The elements of this network are distributed according to marked Poisson point processes in the plan so as to derive the characteristics of this network we use stochastic geometry. We assume that the channel between receivers and transmitters varies according to a gamma distribution and based on this assumption we model our network. The main topic of study in this issue is transmission capacity so we focus on it as well using some other related terms we try to find some bounds for it. Our work shows that different assumptions of channel variation in wireless ad hoc networks must be carried by precise calculation because of the complication of transmission capacity.