On the Contact and Nearest-Neighbor Distance Distributions for the ${n}$ -Dimensional Matérn Cluster Process

Pandey, Kaushlendra; Dhillon, Harpreet S.; Gupta, Abhishek

doi:10.1109/lwc.2019.2957221

Cited by 13 publications

(8 citation statements)

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“…Remark 4 In (8), the term G Φ (h * r ) is the complementary contact distance distribution and that is obtained by taking the expectation of (9) with respect to P, instead of P 0 Ψ (see, e.g., [33]). The result of Proposition 2 is consistent with the existing ones in, e.g., [3,4,11,37] and gives a unified approach to derive the nearestneighbor distance distributions for stationary PPCPs.…”

Section: Nearest-neighbor Distance Distributionssupporting

confidence: 86%

Neveu's exchange formula for analysis of wireless networks with hotspot clusters

Miyoshi¹

2022

Preprint

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Theory of point processes, in particular Palm calculus within the stationary framework, plays a fundamental role in the analysis of spatial stochastic models of wireless communication networks. Neveu's exchange formula, which connects the respective Palm distributions for two jointly stationary point processes, is known as one of the most important results in the Palm calculus. However, its use in the analysis of wireless networks seems to be limited so far and one reason for this may be that the formula in a well-known form is based upon the Voronoi tessellation. In this paper, we present an alternative form of Neveu's exchange formula, which does not rely on the Voronoi tessellation but includes the one as a special case. We then demonstrate that our new form of the exchange formula is useful for the analysis of wireless networks with hotspot clusters modeled using cluster point processes.

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Section: Nearest-neighbor Distance Distributionssupporting

confidence: 86%

Neveu's exchange formula for analysis of wireless networks with hotspot clusters

Miyoshi¹

2022

Preprint

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“…Similarly, a rectangle of width r + r d − x and height 2 min(r, r d ) will completely cover the intersecting area hence acts as an upper bound. For detailed discussion over the bounds readers are advised to refer [10], [13].…”

Section: Appendix Amentioning

confidence: 99%

“…The two important variants of PCP are the Matérn cluster process (MCP) and Thomas cluster process (TCP). The characterization of contact and nearest neighbor distance distribution for these processes is presented in [10], [11]. To model the coverage region of WSNs exhibiting such clustering, we propose to use Boolean Poisson cluster models (BPCM) where the underlying process to model sensors' locations is a PCP and each sensor has an independent sensing region around it.…”

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confidence: 99%

On the Coverage Performance of Boolean-Poisson Cluster Models for Wireless Sensor Networks

Pandey¹,

Gupta²

2020

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In this paper, we consider wireless sensor networks (WSNs) with sensor nodes exhibiting clustering in their deployment. We model the coverage region of such WSNs by Boolean Poisson cluster models (BPCM) where sensors nodes' location is according to a Poisson cluster process (PCP) and each sensor has an independent sensing range around it. We consider two variants of PCP, in particular Matérn and Thomas cluster process to form Boolean Matérn and Thomas cluster models. We first derive the capacity functional of these models. Using the derived expressions, we compute the sensing probability of an event and compare it with sensing probability of a WSN modeled by a Boolean Poisson model where sensors are deployed according to a Poisson point process. We also derive the power required for each cluster to collect data from all of its sensors for the three considered WSNs. We show that a BPCM WSN has less power requirement in comparison to the Boolean Poisson WSN, but it suffers from lower coverage, leading to a trade-off between per-cluster power requirement and the sensing performance.A cluster process with desired clustering may provide better coverage while maintaining low power requirements. I. INTRODUCTIONIn WSNs, sensors are deployed over a region such as forest or wetlands, to form a wireless network and exchange mutual data to sense an event. WSN may have a central hub to facilitate the joint detection. There are two essential aspects of WSNs. The first aspect is the coverage aspect i.e. to maximize the region covered by sensors, termed the coverage or sensing region.

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“…For higher dimensions (n > 2), tight bounds for expressions can be computed using bounds over A(r, r d , x). Readers are advised to refer [14] for the same.…”

Section: Mat éRn Cluster Processmentioning

confidence: 99%

“…The CDF F R k (r) of the kth CD for any PP is equal to the probability that there are at least k points inside the ball of radius r. Similarly, for the NND, CDF is equal to the probability that there are at least k points inside the ball of radius r under Palm [12]. For MCP, the CDFs of CD and NND for k = 1 is reported in [13], [14]. To the best of our knowledge, the expression for the kth CD and NND of MCP for general k has not been reported in the past literature.…”

Section: Introductionmentioning

confidence: 99%

kth Distance Distributions of n-Dimensional Matérn Cluster Process

Pandey¹,

Gupta²

2020

Preprint

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In this letter, we derive the CDF (cumulative distribution function) of kth contact distance (CD) and nearest neighbor distance (NND) of the n-dimensional (n-D) Matérn cluster process (MCP). We present a new approach based on the probability generating function (PGF) of the random variable (RV) denoting the number of points in a ball of arbitrary radius to derive its probability mass function (PMF).The proposed method is general and can be used for any point process with known probability generating functional (PGFL). We also validate our analysis via numerical simulations and provide insights using the presented analysis. We also discuss two applications, namely-macro-diversity in cellular networks and caching in D2D networks, to study the impact of clustering on the performance.

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On the Contact and Nearest-Neighbor Distance Distributions for the ${n}$ -Dimensional Matérn Cluster Process

Cited by 13 publications

References 13 publications

Neveu's exchange formula for analysis of wireless networks with hotspot clusters

Neveu's exchange formula for analysis of wireless networks with hotspot clusters

On the Coverage Performance of Boolean-Poisson Cluster Models for Wireless Sensor Networks

kth Distance Distributions of n-Dimensional Matérn Cluster Process

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