Interference Analysis for Automotive Radar Using Matern Hard-Core Point Process

The content retrieval delay is an important performance metric for enhancing user experience in wireless networks. In this paper, by modeling the locations of the base stations (BSs) as the Matern hard-core point process of type II (MHP), we analyze the content retrieval delay for a typical cache-enabled device in wireless networks under the most popular content policy. Since it is intractable to get the size distribution of a Voronoi cell in the MHP model, we propose an approximate formula based on the empirical result in the Poisson point process and derive the cellular load which denotes the number of the user devices connected to a randomly chosen BS. Since the probability generating functional for MHP does not exist, we also propose approximate methods for the coverage probability of the MHP model. At last, we derive the cumulative distribution function of the content retrieval delay. Simulation results validate the accuracy of our analytical conclusions for user content retrieval delay.

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On One of Matérn's Hard-core Point Process Models

Mathematische Nachrichten ◽

10.1002/mana.19851220121 ◽

1985 ◽

Vol 122 (1) ◽

pp. 205-214 ◽

Cited By ~ 28

Author(s):

Dietrich Stoyan ◽

Helga Stoyan

Keyword(s):

Point Process ◽

Hard Core ◽

Process Models ◽

Core Point ◽

Point Process Models ◽

Hard Core Point Process

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Research on an uplink carrier sense multiple access algorithm of large indoor visible light communication networks based on an optical hard core point process

Applied Optics ◽

10.1364/ao.55.010392 ◽

2016 ◽

Vol 55 (36) ◽

pp. 10392 ◽

Cited By ~ 1

Author(s):

Zhufen Nan ◽

Xuefen Chi

Keyword(s):

Visible Light ◽

Point Process ◽

Communication Networks ◽

Multiple Access ◽

Hard Core ◽

Visible Light Communication ◽

Carrier Sense Multiple Access ◽

Carrier Sense ◽

Hard Core Point Process ◽

Visible Light Communication Networks

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A generalization of Matérn hard-core processes with applications to max-stable processes

Journal of Applied Probability ◽

10.1017/jpr.2020.66 ◽

2020 ◽

Vol 57 (4) ◽

pp. 1298-1312

Author(s):

Martin Dirrler ◽

Christopher Dörr ◽

Martin Schlather

Keyword(s):

Point Process ◽

Point Processes ◽

Hard Core ◽

Domain Of Attraction ◽

Stable Processes ◽

Poisson Point Processes ◽

Original Process ◽

Mixed Moving Maxima

AbstractMatérn hard-core processes are classical examples for point processes obtained by dependent thinning of (marked) Poisson point processes. We present a generalization of the Matérn models which encompasses recent extensions of the original Matérn hard-core processes. It generalizes the underlying point process, the thinning rule, and the marks attached to the original process. Based on our model, we introduce processes with a clear interpretation in the context of max-stable processes. In particular, we prove that one of these processes lies in the max-domain of attraction of a mixed moving maxima process.

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Capacity and Error Exponents of Stationary Point Processes under Random Additive Displacements

Advances in Applied Probability ◽

10.1239/aap/1427814578 ◽

2015 ◽

Vol 47 (1) ◽

pp. 1-26 ◽

Cited By ~ 1

Author(s):

Venkat Anantharam ◽

François Baccelli

Keyword(s):

Large Deviations ◽

Point Process ◽

Stationary Point ◽

Point Processes ◽

Hard Core ◽

Entropy Spectrum ◽

Probability Of Error ◽

Error Exponent ◽

Error Exponents ◽

Noise Process

Consider a real-valued discrete-time stationary and ergodic stochastic process, called the noise process. For each dimension n, we can choose a stationary point process in ℝn and a translation invariant tessellation of ℝn. Each point is randomly displaced, with a displacement vector being a section of length n of the noise process, independent from point to point. The aim is to find a point process and a tessellation that minimizes the probability of decoding error, defined as the probability that the displaced version of the typical point does not belong to the cell of this point. We consider the Shannon regime, in which the dimension n tends to ∞, while the logarithm of the intensity of the point processes, normalized by dimension, tends to a constant. We first show that this problem exhibits a sharp threshold: if the sum of the asymptotic normalized logarithmic intensity and of the differential entropy rate of the noise process is positive, then the probability of error tends to 1 with n for all point processes and all tessellations. If it is negative then there exist point processes and tessellations for which this probability tends to 0. The error exponent function, which denotes how quickly the probability of error goes to 0 in n, is then derived using large deviations theory. If the entropy spectrum of the noise satisfies a large deviations principle, then, below the threshold, the error probability goes exponentially fast to 0 with an exponent that is given in closed form in terms of the rate function of the noise entropy spectrum. This is obtained for two classes of point processes: the Poisson process and a Matérn hard-core point process. New lower bounds on error exponents are derived from this for Shannon's additive noise channel in the high signal-to-noise ratio limit that hold for all stationary and ergodic noises with the above properties and that match the best known bounds in the white Gaussian noise case.

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Shearer's point process, the hard-sphere model, and a continuum Lovász local lemma

Advances in Applied Probability ◽

10.1017/apr.2016.76 ◽

2017 ◽

Vol 49 (1) ◽

pp. 1-23

Author(s):

Christoph Hofer-Temmel

Keyword(s):

Point Process ◽

Lower Bounds ◽

Hard Sphere ◽

Hard Core ◽

Combinatorial Structure ◽

Hard Sphere Model ◽

Sphere Model ◽

Lovász Local Lemma ◽

Local Lemma ◽

Lovasz Local Lemma

AbstractA point process isR-dependent if it behaves independently beyond the minimum distanceR. In this paper we investigate uniform positive lower bounds on the avoidance functions ofR-dependent simple point processes with a common intensity. Intensities with such bounds are characterised by the existence of Shearer's point process, the uniqueR-dependent andR-hard-core point process with a given intensity. We also present several extensions of the Lovász local lemma, a sufficient condition on the intensity andRto guarantee the existence of Shearer's point process and exponential lower bounds. Shearer's point process shares a combinatorial structure with the hard-sphere model with radiusR, the uniqueR-hard-core Markov point process. Bounds from the Lovász local lemma convert into lower bounds on the radius of convergence of a high-temperature cluster expansion of the hard-sphere model. This recovers a classic result of Ruelle (1969) on the uniqueness of the Gibbs measure of the hard-sphere model via an inductive approach of Dobrushin (1996).

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