Performance analysis for heterogeneous cellular networks based on Matern-like point process model

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.

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.

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.

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.

During the last decades the Mediterranean zone in Europe has experienced an increment in the incidence of forest wildfires. This increase is partly explained by higher mean temperature and lower relative humidity, while socioeconomic change has lead to the abandonment of farms, resulting in an increase in an unusual accumulation of forest fuels, increasing the risk of wildfires. Mapping wildfire risk is highly important because wildfires are known to potentially lead to landscape changes and to modify fire regime by inducing potential changes in vegetation composition. Also, they pose a hazard to human property and life. Maps of wildfire risk based on statistical models provide a measure of uncertainty for the inferences derived from such risk maps, leaving a quantitative error margin for managers and decision takers. Further, some of the model parameters often have a physical or a biological interpretation which can give ecologists and forest engineers answers about scientific questions of interest. In this paper, we analyze the incidence of wildfires in the province of Castellón in Spain in order to identify risk factors associated with wildfire incidences during the years 2001–2006. We used the discrete nature of wildfire events to build such models using point process theory and methods and included information about elevation, slope, aspect, land use and distance to nearest road as covariates in our modeling process. Our results show that wildfire risk in Castellón is associated with all the covariates considered and that three land-use categories have the highest risk of wildfire incidence. Also, wildfire incidences are not independent and some degree of interaction exists, which indicates that the commonly used Poisson point process models are not applicable in this case, but instead area-interaction models should be considered.

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.

How many small cell (SC) access points (APs) are required to guarantee a chosen quality of service in a heterogeneous network? In this chapter, we answer this question considering two different network models. The first is the downlink of a finite-area SC network where the locations of APs within the chosen area are uniformly distributed. A key step in obtaining the closed-form expressions is to generalize the well-accepted moment matching approximation for the linear combination of lognormal random variables. For the second model, we focus on a two-layer downlink heterogeneous network with frequency reuse-1 hexagonal macro cells (MCs), and SC APs that are placed at locations that do not meet a chosen quality of service from macro base stations (BSs). An important property of this model is that the SC AP locations are coupled with the MC coverage. Here, simple bounds for the average total interference within an MC makes the formulation possible for the percentage of MC area in outage, as well as the required average number of SCs (per MC) to overcome outage, assuming isolated SCs. Introduction Heterogeneous cellular networks (HCNs) are being considered as an efficient way to improve system capacity as well as effectively enhance network coverage [1, 2]. Comprising multiple layers of access points (APs), HCNs encompass a conventional macro cellular network (first layer) overlaid with a diverse set of small cells (SCs) (higher layers). Cell deployment is an important problem in heterogeneous networks, both in terms of the number and positioning of the SCs. Traditional network models are either impractically simple (such as the Wyner model [3]) or excessively complex (e.g., the general case of random user locations in a hexagonal lattice network [4]) to accurately model SC networks. A useful mathematical model that accounts for the randomness in SC locations and irregularity in the cells uses spatial point processes, such as Poisson point process (PPP), to model the location of SCs in the network [5–10]. The independent placement of SCs from the MC layer, has the advantage of analytical tractability and leads to many useful SINR and/or rate expressions. However, even assuming that wireless providers would deploy SCs to support mobile broadband services, the dominant assumption remains that SCs are deployed randomly and independent of the MC layer [11].

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.

This paper introduces Stochastic Compressive Data Aggregation (S-CDA) for wireless sensor networks (WSN) under random deployments. The Poisson point process (PPP) models the random deployment, and at the same time, allows the efficient implementation of an adequate sparsifying matrix, the random discrete Fourier transform (RDFT). The signal recovery is based on the RDFT which reveals the frequency content of smooth signals, such as temperature or humidity maps, which consist of few frequency components. The recovery methods are based on the accelerated iterative hard thresholding (AIHT) which sets all but the largest (in magnitude) frequency components to zero. The adoption of the PPP allows to analyze the communication and compression aspects of S-CDA using previous results from stochastic geometry and compressed sensing, respectively.

Assuming a connected base station at the point of reference (or origin) in the tier of interest, we derive an expression for the downlink probability of coverage over a heterogeneous network, wherein the base station locations result from different point processes, such as Poisson point and Poisson cluster processes. Numerical results show increasing the base station density in each tier lowers the coverage probability, but not as much as increasing the coverage threshold does. We also provide lower and upper bounds for the coverage probability in a two-tier heterogeneous network modeled with Poisson point and cluster processes, and evaluate the effect on those bounds when changing the various parameter values. These results are of potential use for future cellular heterogeneous network designs.

Modeling the spatial distribution of a species is a fundamental problem in ecology. A number of modeling methods have been developed, an extremely popular one being MAXENT, a maximum entropy modeling approach. In this article, we show that MAXENT is equivalent to a Poisson regression model and hence is related to a Poisson point process model, differing only in the intercept term, which is scale-dependent in MAXENT. We illustrate a number of improvements to MAXENT that follow from these relations. In particular, a point process model approach facilitates methods for choosing the appropriate spatial resolution, assessing model adequacy, and choosing the LASSO penalty parameter, all currently unavailable to MAXENT. The equivalence result represents a significant step in the unification of the species distribution modeling literature.

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 better utilize TV white space, the paper considers deploying secondary users (SUs) on vacant channels inside TV coverage. In this heterogeneous case, TV and SU receivers suffer not only mutual adjacent channel interference (ACI) from each other, but also co-channel interference (CCI) from cellular network (CN) outside TV coverage. Therefore SU access opportunity is formulated as the maximal capacity of available SU channels under both TV and SU receiver outage probability constraints. To facilitate the maximization, the analytical interference from both CN and SUs is deduced using Poisson Point Process model. Since the exact interference distribution is too complex to analyze, we approximate it as Gaussian and prove the accuracy of our approximation with Kolmogorov-Smirnov test. Main results include that SU access opportunity follows a volcano-shaped distribution geographically and optimal network-status-aware SU transmit power exists to maximize the access opportunity, which can contribute to the practical deployment of secondary system and the utilization improvement of white space.

Due to its mathematical tractability, the homogeneous Poisson point process (PPP) has been employed to model wireless networks and analyze their performance widely. PPP falls short in modeling the effect of interference management techniques, which typically introduces some form of spatial mutual exclusion among base stations (BSs). Considering the spatial mutual exclusion between macro BSs s (BSs), in this paper, we studies the coverage performance of a two-tier heterogeneous cellular network (HCN) modeled by Poisson hard-core process (PHCP) and PPP. We first provide the approximate expression of coverage probability of the two-tier PHCP-PPP HCN with the use of PT-ASAPPP method, which stands for “per tier approximate signal to interference ratio (SIR) analysis based on PPP. In this method, each tier is approximated to PPP by using SIR gain. The concrete expression of the SIR gain G PHCP for PHCP model is derived through simulation and data fitting. Simulation results verify the correctness of theoretical analysis and the effectiveness of PT-ASAPPP method.

Heterogeneous Networks (HetNets) have gained the attraction of the communication industry recently, due to their promising ability to enhance the performance of future broadband Fifth Generation (5G) networks and are integral parts of 5G systems. They can be viewed in multi-dimensional space where, each slice represents a unique tier that has its own Base Station (BS)s and User Equipment (UE)s. Different tiers cooperate with each other for their mutual benefit. Data can be interactively exchanged among the tiers, and UEs have the flexibility to switch between the tiers. The cells in such a heterogeneous cellular networks have variable sizes, shapes, and coverage regions. However, in HetNets with ultra dense BSs, the distance between them gets very small and, they suffer from very high levels of mutual interference. To improve the performance of HetNets, we have done multiple contributions in this dissertation. First, we have developed analytical derivations for optimizing pilot sequence length which is a very crucial factor in acquiring the Channel State Information (CSI) and the channel estimation process in general. Poisson Point Process (PPP) has been widely used to allocate BSs among various tiers so far. However, BS locations obtained using PPP approach may not be optimum to reduce interference. Therefore, in this dissertation, BSs locations are optimized to reduce the interference and improve the coverage and received signal power. Also, we have derived expressions for static UEs coverage probability and network energy efficiency in HetNets. A proper UE association algorithm for HetNets is a great challenge. The classic max-Signal to Interference and Noise Ratio (SINR) or max-received signal strength (RSS) user association algorithms are inappropriate solutions for HetNets as UEs in this context will tend to connect to the Macro BS, which is the one with the highest signal power. A severe load imbalance and significant inefficiency arises and impacts the performance. The aforementioned algorithms tend to associate UEs to BSs with the best received signal power or signal quality. In HetNets, usually Macro BSs are the ones transmitting the strongest signals; hence most UEs tend to associate with the Macro BS leaving Micro BSs with less load. Also, the conventional max-SINR and max-RSS algorithms do not provide adequate results in multi-tier systems. We suggest two centralized algorithms, LSTD and RTLB, for an even UE association to provide fair load distribution. However RTLB outperforms LSTD in real time scenarios as it easily and quickly adapts to rapid network changes. Furthermore, we consider the mobility of nodes. We derive coverage probability for moving UEs considering both handover and no handover scenarios. Proposed algorithms are fast enough to associate the moving users to different Micro and Macro BSs appropriately in real time. Our algorithms are proved to be feasible and provide a path towards attainable future communication systems.