On the correlation between the volumes of the typical Poisson-Voronoi cell and the typical Stienen sphere

Olsbo, Viktor

doi:10.1239/aap/1198177230

Cited by 4 publications

(2 citation statements)

References 10 publications

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“…For Model 1, the union of all the disks x∈Φ b(x, ρ x /2) is the so-called Stienen model [27]. The area fraction covered by the Stienen model is 1/4.…”

Section: System Model a Noma System Modelmentioning

confidence: 99%

Downlink Non-Orthogonal Multiple Access (NOMA) in Poisson Networks

Ali

Haenggi

ElSawy

et al. 2019

IEEE Trans. Commun.

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A network model is considered where Poisson distributed base stations transmit to N power-domain nonorthogonal multiple access (NOMA) users (UEs) each that employ successive interference cancellation (SIC) for decoding. We propose three models for the clustering of NOMA UEs and consider two different ordering techniques for the NOMA UEs: mean signal power-based and instantaneous signal-tointercell-interference-and-noise-ratio-based. For each technique, we present a signal-to-interference-and-noise ratio analysis for the coverage of the typical UE. We plot the rate region for the two-user case and show that neither ordering technique is consistently superior to the other. We propose two efficient algorithms for finding a feasible resource allocation that maximize the cell sum rate Rtot, for general N , constrained to: 1) a minimum throughput T for each UE, 2) identical throughput for all UEs. We show the existence of: 1) an optimum N that maximizes the constrained Rtot given a set of network parameters, 2) a critical SIC level necessary for NOMA to outperform orthogonal multiple access. The results highlight the importance in choosing the network parameters N , the constraints, and the ordering technique to balance the Rtot and fairness requirements. We also show that interference-aware UE clustering can significantly improve performance.

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“…For Model 1, the union of all the disks x∈Φ b(x, ρ x /2) is the so-called Stienen model [27]. The area fraction covered by the Stienen model is 1/4.…”

Section: System Model a Noma System Modelmentioning

confidence: 99%

Downlink Non-Orthogonal Multiple Access (NOMA) in Poisson Networks

Ali

Haenggi

ElSawy

et al. 2019

IEEE Trans. Commun.

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“…In [22,Lemma 3.1], the correlation between the volume of the typical Stienen sphere and the volume of the typical cell is derived. Using the approach of [22], we provide the covariance of the volumes of B r (o) ∩ V o and V o in the following lemma.…”

Section: Lemma 4 the First And Second Moments Of The Volume Of The In...mentioning

confidence: 99%

Distance from the Nucleus to a Uniformly Random Point in the 0-cell and the Typical Cell of the Poisson-Voronoi Tessellation

Mankar,

Parida,

Dhillon

et al. 2019

Preprint

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Consider the distances R o and Ro from the nucleus to a uniformly random point in the typical and Crofton cells, respectively, of the d-dimensional Poisson-Voronoi (PV) tessellation. The main objective of this paper is to characterize the exact distributions of R o and Ro . First, using the well-known relationship between the Crofton cell and the typical cell, we show that the random variable Ro is equivalent in distribution to the contact distance of the Poisson point process. Next, we derive a multi-integral expression for the exact distribution of R o . Further, we derive a closed-form approximate expression for the distribution of R o , which is the contact distribution with a mean corrected by a factor equal to the ratio of the mean volumes of the Crofton and typical cells. An additional outcome of our analysis is a direct proof of the well-known spherical property of the PV cells having a large inball.

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2013

Stochastic Geometry and Its Applications

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On the correlation between the volumes of the typical Poisson-Voronoi cell and the typical Stienen sphere

Cited by 4 publications

References 10 publications

Downlink Non-Orthogonal Multiple Access (NOMA) in Poisson Networks

Downlink Non-Orthogonal Multiple Access (NOMA) in Poisson Networks

Distance from the Nucleus to a Uniformly Random Point in the 0-cell and the Typical Cell of the Poisson-Voronoi Tessellation

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