Fig 4 - uploaded by Minghua Xia
Content may be subject to copyright.
An illustrative cellular network modeled by the Poisson-Voronoi tessellation (the polygons with red dash boundaries) or by the dual PoissonDelaunay triangulation (the triangles with blue solid boundaries), where the black circles ('•') refer to the BSs and the cross marks ('×') denote the UEs, with normalized coverage area of one squared kilometers.
Source publication
For Poisson-Delaunay triangulations in d-dimensional Euclidean space Rd, a structured and computationally efficient form of the probability density function (PDF) of the volume of a typical cell is analytically derived in this paper. In particular, the ensuing PDF and the corresponding cumulative density function (CDF) are exact and unified, applic...
Contexts in source publication
Context 1
... the CoMP strategies in conventional Poisson- Voronoi cells where a dynamic mechanism has to be relied upon to determine and update the cooperation set of a UE, in the following we propose a novel CoMP mechanism based on Poisson-Delaunay triangulation, whereby the cooperation set of a UE is fixed and uniquely determined by the geometric locations of its nearby BSs. In principle, the Poisson-Delaunay triangulation is the dual graph for a Poisson-Voronoi tessellation. For instance, as illustrated in Fig. 4, the Poisson-Delaunay triangulation dual to the Poisson-Voronoi tessellation shown in red dash boundaries consists of the triangles with blue solid boundaries. In practice, with the geo- metric locations of BSs, the Poisson-Delaunay triangulation dual to a Poisson-Voronoi tessellation is uniquely determined and can be efficiently constructed by using, e.g., the radial sweep algorithm or divide-and-conquer algorithm [27, ch. 4]. Subsequently, for each UE, the CoMP cooperation set is determined as ...
Context 2
... conventional cellular networks, each user equipment (UE) is associated with its nearest base station (BS) and gets service from this BS. Accordingly, the coverage area of a network is essentially divided into adjacent polygonal cells, as shown with red dash boundaries in Fig. 4 where the BSs and UEs are denoted by the '•' and '×' marks, respectively. In theory, this classic network structure can be effectively modelled by means of Poisson-Voronoi tessellation in the field of stochastic geometry [19]. To further improve the quality of service (QoS) of wireless networks, CoMP transmission is universally recog- nized as a promising technique for 5G wireless systems by academic researchers and standard bodies as well [20]- [22]. For instance, CoMP transmission was widely applied to 5G radio access design, like for dense networks in [23] or for could-RANs (radio access networks) in [24]- [26]. By using CoMP technique, multiple BSs are joined together to simul- taneously serve a particular UE. To this end, a critical step to implement CoMP technique in practice is to determine which BSs should be coordinated for a specific UE. More formally, a cooperation set of BSs must be constructed prior to data transmission, e.g., by choosing the nearest one or more than one BSs in the sense of Euclidean distance. The construc- tion of cooperation set is generally CSI dependent and time ...
Context 3
... conventional cellular networks, each user equipment (UE) is associated with its nearest base station (BS) and gets service from this BS. Accordingly, the coverage area of a network is essentially divided into adjacent polygonal cells, as shown with red dash boundaries in Fig. 4 where the BSs and UEs are denoted by the '•' and '×' marks, respectively. In theory, this classic network structure can be effectively modelled by means of Poisson-Voronoi tessellation in the field of stochastic geometry [19]. To further improve the quality of service (QoS) of wireless networks, CoMP transmission is universally recog- ...
Context 4
... a UE, in the following we propose a novel CoMP mechanism based on Poisson-Delaunay triangulation, whereby the cooperation set of a UE is fixed and uniquely determined by the geometric locations of its nearby BSs. In principle, the Poisson-Delaunay triangulation is the dual graph for a Poisson-Voronoi tessellation. For instance, as illustrated in Fig. 4, the Poisson-Delaunay triangulation dual to the Poisson-Voronoi tessellation shown in red dash boundaries consists of the triangles with blue solid boundaries. In practice, with the geo- metric locations of BSs, the Poisson-Delaunay triangulation dual to a Poisson-Voronoi tessellation is uniquely determined and can be efficiently ...
Similar publications
We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the $\phi^4$ model where we estimate the non-perturbative $\beta-$function...
The inherent broadcast nature has exposed the land mobile satellite (LMS) communication systems to severe secure threats in both the civil and military applications. This paper investigates the secrecy performance of a Shadowed-Rician fading multi-antenna LMS communication system with imperfect channel estimation, which consists of a satellite, a l...
We employ a recent resummation method to deal with divergent series, based on the Meijer G-function, which gives access to the non-perturbative regime of any QFT from the first few known coefficients in the perturbative expansion. Using this technique, we consider in detail the ϕ ⁴ model where we estimate the non-perturbative β-function and prove t...
In this paper, the secrecy performance of a dual-hop mixed radio-frequency/underwater optical wireless communication (RF/UOWC) system is investigated. The considered system consists of one single antenna source node (S) communicating with a destination node (D), considered as the legitimate receiver, through an amplify-and-forward (AF) relay node e...
In this paper, the secrecy performance of a dual-hop mixed Radio-frequency/Underwater optical wireless communication (RF/UOWC) system is investigated. The considered system consists of a 1-antenna source node (S) communicating with a destination node (D), considered as the legitimate receiver, through an amplify-and-forward (AF) relay node R equipp...
Citations
... The motivation of this paper comes from the works [30], [31], where the Poisson-Delaunay triangulation was exploited to model the 2D cellular networks for terrestrial UEs. A similar idea is employed in this paper to provide service for aerial UAVs, which benefits by maximizing the use of existing cellular network infrastructure and providing reliable communication connectivity for UAVs, in addition to terrestrial UEs. ...
... Figure 7 also shows that the handoff probability of the proposed CoMP scheme is a bit higher than that of the Voronoi scheme without CoMP. This phenomenon is not surprising as the average area of Delaunay triangular cells is half of their dual Voronoi cells [30]. On the other hand, it is observed that the simulation results based on the equivalent Voronoi approximation method match well with the simulation results, demonstrating this method's feasibility. ...
... APPENDIX A PROOF OF LEMMA 1 Given {ρ k , H k−1 , H k }, the conditional handoff probability can be computed as where (30) comes from the void probability of PPP, and c(q ′ 1 , R) denotes a circle with radius R centered at q ′ 1 . Also, the coverage area when the UAV moves from q 1 to q ′ 1 can be computed by: ...
This paper designs a novel ground-to-air communication scheme to serve unmanned aerial vehicles (UAVs) through legacy terrestrial base stations (BSs). In particular, a tractable coordinated multi-point (CoMP) transmission based on the geometry of Poisson-Delaunay triangulation is developed, which provides reliable and seamless connectivity for UAVs. An effective dynamic frequency allocation scheme is designed to eliminate inter-cell interference by using the theory of circle packing. For exact performance evaluation, the handoff probability of a typical UAV is characterized, and then the coverage probability with handoffs is attained. Simulation and numerical results corroborate that the proposed scheme outperforms the conventional CoMP scheme with three nearest cooperating BSs in terms of handoff and coverage probabilities. Moreover, as each UAV has a fixed and unique CoMP BS set, it avoids the real-time dynamic BS searching process, thus reducing the feedback overhead.
... The motivation of this paper is triggered by the recent works [26], [27], where the Poisson-Delaunay triangulation was used to model two-dimensional (2D) cellular networks and a novel CoMP transmission scheme was proposed. This principle is expanded here to model the considered 3D spatial deployment, which is expected to be an indispensable component of future 5G-and-beyond space-air-ground integrated networking setups [28]. ...
... Moreover, we consider a BPP network Φ, with N transmitting aBSs uniformly distributed in a finite ball b(0, R) centered at the origin o = (0, 0, 0) with radius R. By using the criteria of the nearest neighbor association, namely, each aUE is directly connected with its nearest aBS, 3D binomial-Voronoi cells are therefore formed. Unfortunately, the typical cell of this Voronoi tessellation is too complex to be mathematically tractable even in 2D space [26], [32]. It is noteworthy at this point that for an arbitrary dimensional binomial-Voronoi tessellation, its dual graph is the so-called binomial-Delaunay triangulation as shown in Fig. 2. In the 3D case considered herein, it is known as binomial-Delaunay tetrahedralization. ...
... where f Γ1 (γ) denotes the PDF of Γ 1 and the integral ln(1 + γ) = γ 0 1 1+ω dω is exploited in the step (a). As to be shown at the end of Section V-A1, the numerical results computed by (26) coincide with those computed as per (12), which crossvalidates the preceding derivations. ...
In this paper, a novel 3D cellular model consisting of aerial base stations (aBSs) and aerial user equipments (aUEs) is proposed, by integrating the coordinated multi-point (CoMP) transmission technique with the theory of stochastic geometry. For this new 3D architecture, a tractable model for aBSs' deployment based on the binomial-Delaunay tetrahedralization is developed, which ensures seamless coverage for a given space. In addition, a versatile and practical frequency allocation scheme is designed to eliminate the inter-cell interference effectively. Based on this model, performance metrics including the achievable data rate and coverage probability are derived for two types of aUEs: i) the general aUE (i.e., an aUE having distinct distances from its serving aBSs) and ii) the worst-case aUE (i.e., an aUE having equal distances from its serving aBSs). Simulation and numerical results demonstrate that the proposed approach emphatically outperforms the conventional binomial-Voronoi tessellation without CoMP. Insightfully, it provides a similar performance to the binomial-Voronoi tessellation which utilizes the conventional CoMP scheme; yet, introducing a considerably reduced computational complexity and backhaul/ signaling overhead.
... The motivation of this paper is triggered by the recent works [26], [27], where the Poisson-Delaunay triangulation was used to model two-dimensional (2D) cellular networks and a novel CoMP transmission scheme was proposed. This principle is expanded here to model the considered 3D spatial deployment, which is expected to be an indispensable component of future 5G-and-beyond space-air-ground integrated networking setups [28]. ...
... Moreover, we consider a BPP network Φ, with N transmitting aBSs uniformly distributed in a finite ball b(0, R) centered at the origin o = (0, 0, 0) with radius R. By using the criteria of the nearest neighbor association, namely, each aUE is directly connected with its nearest aBS, 3D binomial-Voronoi cells are therefore formed. Unfortunately, the typical cell of this Voronoi tessellation is too complex to be mathematically tractable even in 2D space [26], [32]. It is noteworthy at this point that for an arbitrary dimensional binomial-Voronoi tessellation, its dual graph is the so-called binomial-Delaunay triangulation as shown in Fig. 2. In the 3D case considered herein, it is known as binomial-Delaunay tetrahedralization. ...
... where f Γ1 (γ) denotes the PDF of Γ 1 and the integral ln(1 + γ) = γ 0 1 1+ω dω is exploited in the step (a). As to be shown at the end of Section V-A1, the numerical results computed by (26) coincide with those computed as per (12), which crossvalidates the preceding derivations. ...
In this paper, a novel 3D cellular model consisting of aerial base stations (aBSs) and aerial user equipments (aUEs) is proposed, by integrating the coordinated multi-point (CoMP) transmission technique with the theory of stochastic geometry. For this new 3D architecture, a tractable model for aBSs' deployment based on binomial Delaunay-tetrahedralization is developed, which ensures seamless coverage for a given space. In addition, a versatile and practical frequency allocation scheme is designed to eliminate the inter-cell interference effectively. Based on this model, performance metrics including the ergodic data rate and coverage probability are derived for two types of aUEs: i) general aUE (i.e., an aUE having distinct distances from its serving aBSs) and ii) the worst-case aUE (i.e., an aUE having equal distances from its serving aBSs). Simulation and numerical results demonstrate that the proposed approach emphatically outperforms the conventional binomial-Voronoi tessellation without CoMP. Insightfully, it provides a similar performance as to the binomial-Voronoi tessellation which utilizes the conventional CoMP scheme; yet, introducing a considerably reduced computational complexity and backhaul/signaling overhead.
... This regularity makes the applications of Poisson-Delaunay triangulation more mathematically tractable [18]. In our recent work [19], Poisson-Delaunay triangulation was used to model cellular networks and a novel CoMP transmission scheme was proposed. Unlike the conventional usercentric CoMP operations, such as [4]- [9], [12] where on-line searching and feedback overhead are necessary to determine the cooperation set of a UE, one of the key features of the said CoMP scheme [19] is that the set of cooperative BSs pertaining to any UE is fixed and can be off-line determined once the geographic locations of BSs are known, which is feasible in real-world cellular networks. ...
... In our recent work [19], Poisson-Delaunay triangulation was used to model cellular networks and a novel CoMP transmission scheme was proposed. Unlike the conventional usercentric CoMP operations, such as [4]- [9], [12] where on-line searching and feedback overhead are necessary to determine the cooperation set of a UE, one of the key features of the said CoMP scheme [19] is that the set of cooperative BSs pertaining to any UE is fixed and can be off-line determined once the geographic locations of BSs are known, which is feasible in real-world cellular networks. As a companion work to [19], this paper investigates the network performance of Poisson-Delaunay triangulation based CoMP transmission, in terms of the coverage probability and the spectral efficiency. ...
... Unlike the conventional usercentric CoMP operations, such as [4]- [9], [12] where on-line searching and feedback overhead are necessary to determine the cooperation set of a UE, one of the key features of the said CoMP scheme [19] is that the set of cooperative BSs pertaining to any UE is fixed and can be off-line determined once the geographic locations of BSs are known, which is feasible in real-world cellular networks. As a companion work to [19], this paper investigates the network performance of Poisson-Delaunay triangulation based CoMP transmission, in terms of the coverage probability and the spectral efficiency. ...
Coordinated multi-point (CoMP) transmission is a cooperating technique among base stations (BSs) in a cellular network, with outstanding capability at inter-cell interference (ICI) mitigation. ICI is a dominant source of error, and has detrimental effects on system performance if not managed properly. Based on the theory of Poisson-Delaunay triangulation, this paper proposes a novel analytical model for CoMP operation in cellular networks. Unlike the conventional CoMP operation that is dynamic and needs on-line updating occasionally, the proposed approach enables the cooperating BS set of a user equipment (UE) to be fixed and off-line determined according to the location information of BSs. By using the theory of stochastic geometry, the coverage probability and spectral efficiency of a typical UE are analyzed, and simulation results corroborate the effectiveness of the proposed CoMP scheme and the developed performance analysis.
This paper designs a novel ground-to-air communication scheme to serve unmanned aerial vehicles (UAVs) through legacy terrestrial base stations (BSs). In particular, a tractable coordinated multi-point (CoMP) transmission based on the geometry of Poisson-Delaunay triangulation is developed, which provides reliable and seamless connectivity for UAVs. An effective dynamic frequency allocation scheme is designed to eliminate inter-cell interference by using the theory of circle packing. For exact performance evaluation, the handoff probability of a typical UAV is characterized, and then the coverage probability with handoffs is attained. Simulation and numerical results corroborate that the proposed scheme outperforms the conventional CoMP scheme with three nearest cooperating BSs in terms of handoff and coverage probabilities. Moreover, as each UAV has a fixed and unique CoMP BS set, it avoids the real-time dynamic BS searching process, thus reducing the feedback overhead.
Coordinated multi-point (CoMP) transmission is a cooperating technique among base stations (BSs) in a cellular network, with outstanding capability at inter-cell interference (ICI) mitigation. ICI is a dominant source of error, and has detrimental effects on system performance if not managed properly. Based on the theory of Poisson-Delaunay triangulation, this paper proposes a novel analytical model for CoMP operation in cellular networks. Unlike the conventional CoMP operation that is dynamic and needs on-line updating occasionally, the proposed approach enables the cooperating BS set of a user equipment (UE) to be fixed and off-line determined according to the location information of BSs. By using the theory of stochastic geometry, the coverage probability and spectral efficiency of a typical UE are analyzed, and simulation results corroborate the effectiveness of the proposed CoMP scheme and the developed performance analysis.
