Matern Hard-core Point Process Research Articles

Performance of Indoor VLC System Under Random Placement of LEDs With Nonimaging and Imaging Receiver

This article analyzes the performance of multiple-input-multiple-output indoor visible light communication (VLC) system by randomly deploying the light-emitting-diodes (LEDs) using Matern hardcore point process (MHCP). Furthermore, photodetectors (PDs) with two different field of view (FOVs) have been utilized for an imaging as well as nonimaging receiver structures. It is a widely known fact that in a conventional VLC system, signal-to-noise ratio (SNR) profile inside the room varies with respect to the LED placement and the PDs position. Consequently, the proposed work attempts to achieve uniform SNR across the room, by utilizing MHCP based LED placement at the transmitter, and a nonimaging receiver with four PDs using 1-FOV, 2-FOV, and imaging receiver configurations. Simulation results show that random deployment of LED using MHCP configuration results in a more uniform SNR profile inside the room as compared to regular LED deployment schemes. Furthermore, three different power allocation schemes for LEDs namely equal power, distance-based power, and an optimal power allocation are proposed. For the different power allocation schemes, the average SNR and the variance of the received optical power (OP) inside the room are derived and compared. In addition, the closed-form expression for the bit-error-rate (BER) probability is derived for the proposed MHCP configuration using <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">on</small> - <sc xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">off</small> keying as a modulation scheme. Results show improvement in BER performance with the OP allocation in comparison to other power allocation schemes both for imaging and nonimaging receiver configuration.

Energy efficiency optimization for heterogeneous cellular networks modeled by Matérn hard-core point process

The Poisson point process (PPP) has been widely used in wireless network modeling and performance analysis due to the independence between its nodes. Therefore, it may not be a suitable model for many of the exclusive networks between the nodes. This paper analyzes the energy efficiency (EE) and optimizes the two-tier heterogeneous cellular networks (HetNets). Considering the mutual exclusion between macro base stations (MBSs) distribution, the deployment of MBSs is modeled by the Matern hard-core point process (MHCPP), and the deployment of pico base stations (PBSs) is modeled by the PPP. We adopt a simple approximation method to study the signal to interference ratio (SIR) distribution in two-tier MHCPP-PPP networks and then derive the coverage probabilities, the average data rates and the energy efficiency of HetNets. Finally, an optimization algorithm is proposed to improve the EE of HetNets by controlling the transmit power of PBSs. The simulation results show that the EE of a system can be effectively improved by selecting the appropriate transmit power for the PBSs. In addition, two-tier MHCPP-PPP HetNets have higher energy efficiency than two-tier PPP-PPP HetNets.

Performance Analysis of C-RAN with Different Deployment Distributions

In cloud radio access networks (C-RAN) for 5G and beyond, the user-centric system model has gained popularity during downlink performance analysis for various reasons like tractability of stochastic geometric approach and distributed beamforming methods. In this paper, the coverage analysis of C-RAN with different distributions of BSs, e.g. uniform, PPP, Matern hard-core point process (MHCPP) of types I, II, and III are studied. We present the coverage analysis with the uniform distribution of BSs and compare it with other deployment distributions of BSs. The effect of threshold distance on the performance of MHCPP distributions is explored. The Monte Carlo simulation of heterogeneous C-RAN with different cluster point processes is observed and compared with the PPP model. The effect of the range of child clusters on the performance analysis is observed in the cluster point processes. To avoid the complexity in the study, interference is not considered in the analysis, and its counterpart simulations are also not considered while performing the comparison.

Performance of Next-Generation Cellular Networks Guarded With Frequency Reuse Distance

In this paper, we lay an analytic framework for computing the downlink success probability of cellular networks, taking into account a frequency reuse distance as an interference mitigation scheme. We model the frequency reuse distance using tools from stochastic geometry, namely, we utilize the Matern hard-core (MHC) point process to capture the effect of interference protection zones created around base stations. To model the overall cellular network, we introduce a new point process composed of $N$ superimposed MHC processes, where each individual MHC process corresponds to a co-channel base station group; this new point process is called the union-MHC (UMHC) process. We further investigate the resulting performance of the UMHC process and present the link success probability in integral form. The success probability can be evaluated for an arbitrary fading model and an arbitrary number of orthogonal resource groups. We test the newly proposed model against the practical data sets from a network operator and observe a good match of the results.

Performance analysis of cache‐enabled wireless networks considering stochastic geometry approach

Caching of the popular content in the storages of local nodes near to the users has been proposed as a promising approach to handle the network data traffic and the backhaul constraint of access points in the cellular networks. These local storages, also called caches or helpers nodes, are the nodes with the limited communication range but with considerable storage capacities which are generally established condensed to realise the above goals. This dense distribution makes possible the collaboration among the helper nodes for exchanging their embedded files and delivery of the requested files to the users. In this study, to manage the traffic in smaller areas and also to establish more users' accesses to their requested files, clustered dense helper scenario is considered. More precisely, the helper nodes are grouped in disjoint clusters, through the clustering strategy induced by Matern hard core point process. Then the closed-form expressions based on stochastic geometry are derived for some performance metrics of the network. The analytical derivations are validated with Monte Carlo simulations which also compare two cases of clustered dense helper nodes and fewer helper nodes without clustering scenarios. The results show the advantage of the former from the outage probability perspective.

Uplink Power Control and Ergodic Rate Characterization in FD Cellular Networks: A Stochastic Geometry Approach

Simultaneous co-channel transmission and reception, denoted as in-band full-duplex (FD) communications, has been promoted as a solution to improve the spectral efficiency in wireless networks. For cellular networks, in addition to the existing aggregate interference in half-duplex transmission, the residual self-interference and cross-mode interference [i.e., between uplink (UL) and downlink (DL)] impose major obstacles for FD communications’ deployment. Although the FD communication’s promising impact on the overall network data rate has been established in the literature, the rate gains are achieved in the DL transmissions at the expense of marginal gain, or even degradation, for the UL transmissions. This paper, therefore, focuses on the analysis of UL ergodic rate in FD cellular networks where a minimum distance between BSs using the same time-frequency resource block is imposed. Hence, the mutually interfering BSs’ locations are modeled by Matern hard core point process. The distribution of the aggregate interference and the channel-to-interference-plus-noise ratio at the UL of a typical user are characterized using a stochastic geometry analysis. Several UL power control techniques are presented and their resulting ergodic rates are derived and compared. The simulation results suggest that the UL performance highly depends on the network parameters and the UL power control techniques.

Secrecy Rate Analysis of UAV-Enabled mmWave Networks Using Matérn Hardcore Point Processes

Communications aided by low-altitude unmanned aerial vehicles (UAVs) have emerged as an effective solution to provide large coverage and dynamic capacity for both military and civilian applications, especially in unexpected scenarios. However, because of their broad coverage, UAV communications are prone to passive eavesdropping attacks. This paper analyzes the secrecy performance of UAVs networks at the millimeter wave band and takes into account unique features of air-to-ground channels and practical constraints of UAV deployment. To be specific, it explores the 3-D antenna gain in the air-to-ground links and uses the Matern hardcore point process to guarantee the safety distance between the randomly deployed UAV base stations. In addition, we propose the transmit jamming strategy to improve the secrecy performance in which part of UAVs send jamming signals to confound the eavesdroppers. Simulation results verify our analysis and demonstrate the impact of different system parameters on the achievable secrecy rate. It is also revealed that optimizing the density of jamming UAVs will significantly improve security of UAV-enabled networks.

Spatially Correlated Content Caching for Device-to-Device Communications

We study optimal geographic content placement for device-to-device ( ${\mathsf {D2D}}$ ) networks in which each file’s popularity follows the Zipf distribution. The locations of the ${\mathsf {D2D}}$ users (caches) are modeled by a Poisson point process and have limited communication range and finite storage. Inspired by the Matern hard-core (type II) point process that captures pairwise interactions between nodes, we devise a novel spatially correlated caching strategy called hard-core placement ( ${\mathsf {HCP}}$ ) such that the ${\mathsf {D2D}}$ nodes caching the same file are never closer to each other than the exclusion radius . The exclusion radius plays the role of a substitute for caching probability. We derive and optimize the exclusion radii to maximize the hit probability , which is the probability that a given ${\mathsf {D2D}}$ node can find a desired file at another node’s cache within its communication range. Contrasting it with independent content placement, which is used in most prior work, our ${\mathsf {HCP}}$ strategy often yields a significantly higher cache hit probability. We further demonstrate that the ${\mathsf {HCP}}$ strategy is effective for small cache sizes and a small communication radius, which are likely conditions for ${\mathsf {D2D}}$ .

Model based on matern process for ICI mitigation in multi cell cooperation

Ever increasing need of data rate and coverage can be achieved by mitigating the impairments of wireless communication system. Inter cell interference (ICI) is one of the most challenging impairment of wireless communication. To mitigate ICI, multi cell cooperation (MCC) based technique has been proposed in literature. In this paper, ICI mitigation is achieved by using Matern Hard-Core Point Process (MHCP) instead of Poisson point process (PPP). In MHCP a minimum distance between base stations is maintained. Therefore, MHCP corresponds to real deployment scenario. Also, use of MHCP reduces the analytical complexity significantly compared to that of PPP. A closed form expression for complementary cumulative distribution function (CCDF) of signal-to-interference ratio is derived using MHCP for MCC based system in terms of number of base stations, number of antennas and path loss. Using derived expression of CCDF, analytical expressions for probability density function and ergodic capacity is also presented in the closed form. Finally, performance analysis is shown in terms of ergodic capacity. Results are validated by comparing the proposed results with [4].

Energy Efficiency Optimization in 3-D Small Cell Networks-Based Sleep Strategy

In this letter, we focus on energy efficiency in small cell networks where a large number of small cells are spatial deployed in dense urban area. We optimize the energy efficiency by sleep mechanism under average connection ratio (ACR) and average user rate constrains. First, we derive the average rate in 3-D small cell networks by Matern Hardcore point process. Then, based on monotonicity analysis, the optimal small cell sleep probability is calculated to satisfy both ACR and average rate constrains. In addition, we also formulate an optimal maximum connection number of small cell that minimizes the energy consumption subject to the joint constraint of ACR and average rate. Numerical results show that with the sleep strategy, the small cell networks energy consumption can be reduce about 21% of the total. Our optimal sleep probability and maximum connection number can be effectively applied to design small cell sleep strategy for 3-D small cell networks.

Throughput assurance of wireless body area networks coexistence based on stochastic geometry.

Wireless body area networks (WBANs) are expected to influence the traditional medical model by assisting caretakers with health telemonitoring. Within WBANs, the transmit power of the nodes should be as small as possible owing to their limited energy capacity but should be sufficiently large to guarantee the quality of the signal at the receiving nodes. When multiple WBANs coexist in a small area, the communication reliability and overall throughput can be seriously affected due to resource competition and interference. We show that the total network throughput largely depends on the WBANs distribution density (λp), transmit power of their nodes (Pt), and their carrier-sensing threshold (γ). Using stochastic geometry, a joint carrier-sensing threshold and power control strategy is proposed to meet the demand of coexisting WBANs based on the IEEE 802.15.4 standard. Given different network distributions and carrier-sensing thresholds, the proposed strategy derives a minimum transmit power according to varying surrounding environment. We obtain expressions for transmission success probability and throughput adopting this strategy. Using numerical examples, we show that joint carrier-sensing thresholds and transmit power strategy can effectively improve the overall system throughput and reduce interference. Additionally, this paper studies the effects of a guard zone on the throughput using a Matern hard-core point process (HCPP) type II model. Theoretical analysis and simulation results show that the HCPP model can increase the success probability and throughput of networks.

Energy efficiency and area spectral efficiency tradeoff for coexisting wireless body sensor networks

The coexistence of wireless body sensor networks (WBSNs) is a very challenging problem, due to strong interference, which seriously affects energy consumption and spectral reuse. The energy efficiency and spectral efficiency are two key performance evaluation metrics for wireless communication networks. In this paper, the fundamental tradeoff between energy efficiency and area spectral efficiency of WBSNs is first investigated under the Poisson point process (PPP) model and Matern hard-core point process (HCPP) model using stochastic geometry. The circuit power consumption is taken into consideration in energy efficiency calculation. The tradeoff judgement coefficient is developed and is shown to serve as a promising complementary measure. In addition, this paper proposes a new nearest neighbour distance power control strategy to improve energy efficiency. We show that there exists an optimal transmit power highly dependant on the density of WBSNs and the nearest neighbour distance. Some important properties are also addressed in the analysis of coexisting WBSNs based on the IEEE 802.15.4 standard, such as the impact of intensity nodes distribution, optimal guard zone, and outage probability. Simulation results show that the proposed power control design can reduce the outage probability and enhance energy efficiency. Energy efficiency and area spectral efficiency of the HCPP model are better than those of the PPP model. In addition, the optimal density of WBSNs coexistence is obtained.

Nearest Neighbor Distance Distribution in Hard-Core Point Processes

In this letter, we present an analytic framework for formulating the statistical distribution of the nearest neighbor distance in hard-core point processes. We apply this framework to Matern hard-core point process (MHC) to derive the cumulative distribution function of the contact distance in three cases. The first case is between a point in an MHC process and its nearest neighbor from the same process. The second case is between a point in an independent Poisson point process and the nearest neighbor from an MHC process. The third case is between a point in the complement of an MHC process and its sibling MHC process. We test the analytic results against Monte Carlo simulations to verify their consistency.

Modeling and Analysis of Cloud Radio Access Networks Using Matérn Hard-Core Point Processes

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.

Impact of interference on the coverage and connectivity of Ad hoc networks in a fading environment

In this paper, we consider the effect of interference on the coverage and connectivity of an ad hoc network that operates in the presence of fading and shadowing. We assume that the number of interfering signals at each receiving node of a wireless network is a random variable that belongs to a Matern Hard-core point process (MPP). The aggregate interference at the receiver is approximated using the shifted Gamma distribution. We derive closed-form expressions for node isolation probability using a moment matching method. This performance measure is useful for evaluating the overall network connectivity in a wireless channel with co-channel interference and noise. The analysis does not assume knowledge of the fading distribution for the desired or interfering signals. The analytical results are verified with computer simulations.

Secrecy Outage Analysis in Cellular Networks

The study of the inherent secrecy capacity of wireless networks of random topologies is currently of great interest to the communication and information theory communities. Indeed, a good amount of work exists on the secrecy analysis of random networks, the majority of which relies on Poisson point processes to model the spatial distribution of devices. It has been recently demonstrated, however, that Matern hard-core point processes—rather than Poisson point processes—are better suited to characterize the random location of users and base stations of cellular systems. In this letter, we therefore offer an analysis of the secrecy outage of random networks under the Matern hard-core point process model, with the objective of shedding some light on the security limitations/capabilities inherent encountered in cellular systems.

On optimizing CSMA for wide area ad hoc networks

The recent deployment of data-rich smart phones has led to a fresh impetus for understanding the performance of wide area ad hoc networks. The most popular medium access mechanism for such ad hoc networks is CSMA/CA with RTS/CTS. In CSMA-like mechanisms, spatial reuse is achieved by implementing energy-based guard zones. We consider the problem of simultaneously scheduling the maximum number of links that can achieve a given signal to interference ratio (SIR). In this paper, using tools from stochastic geometry, we study and maximize the medium access probability of a typical link. Our contributions are two-fold: (i) We show that a simple modification to the RTS/CTS mechanism, viz., changing the receiver yield decision from an energy-level guard zone to an SIR guard zone, leads to performance gains; and (ii) We show that this combined with a simple modification to the transmit power level--setting it inversely proportional to the square root of the link gain--leads to significant improvements in network throughput. Further, this simple power-level choice is no worse than a factor of two away from optimal over the class of all "local" power level selection strategies for fading channels, and further is optimal in the non-fading case. The analysis relies on an extension of the Matern hard core point process which allows us to quantify both these SIR guard zones and this power control mechanism.