In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson cluster process on the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its distribution. We consider the probability of successful transmission in an interference-limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds. We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes, and the Campbell-Mecke theorem.
In @cite_8 , Ilow and Hatzinakos model the interference as a shot noise process and show that the interference is a symmetric @math -stable process @cite_7 when the nodes are Poisson distributed on the plane. They also show that channel randomness affects the dispersion of the distribution, while the path-loss exponent affects the exponent of the process. The throughput and outage in the presence of interference are analyzed in @cite_14 @cite_22 @cite_9 . In @cite_14 , the shot-noise process is analyzed using stochastic geometry when the nodes are distributed as Poisson and the fading is Rayleigh. In @cite_23 upper and lower bounds are obtained under general fading and Poisson arrangement of nodes.
@cite_14 @cite_22 @cite_7 @cite_8 @cite_9 @cite_23
2086605530 2143252188 2740650368 2022637917
We define and analyze a random coverage process of the @math -dimensional Euclidian space which allows one to describe a continuous spectrum that ranges from the Boolean model to the Poisson-Voronoi tessellation to the Johnson-Mehl model. Like for the Boolean model, the minimal stochastic setting consists of a Poisson point process on this Euclidian space and a sequence of real valued random variables considered as marks of this point process. In this coverage process, the cell attached to a point is defined as the region of the space where the effect of the mark of this point exceeds an affine function of the cumulated effect of all marks. This cumulated effect is defined as the shot noise process associated with the marked point process. In addition to analyzing and visualizing this continuum, we study various basic properties of the coverage process such as the probability that a point or a pair of points be covered by a typical cell. We also determine the distribution of the number of cells which cover a given point, and show how to provide deterministic bounds on this number. Finally, we also analyze convergence properties of the coverage process using the framework of closed sets, and its differentiability properties using perturbation analysis. Our results require a pathwise continuity property for the shot noise process for which we provide sufficient conditions. The model in question stems from wireless communications where several antennas share the same (or different but interfering) channel(s). In this case, the area where the signal of a given antenna can be received is the area where the signal to interference ratio is large enough. We describe this class of problems in detail in the paper. The obtained results allow one to compute quantities of practical interest within this setting: for instance the outage probability is obtained as the complement of the volume fraction; the law of the number of cells covering a point allows one to characterize handover strategies etc. In the analysis of large random wireless networks, the underlying node distribution is almost ubiquitously assumed to be the homogeneous Poisson point process. In this paper, the node locations are assumed to form a Poisson cluster process on the plane. We derive the distributional properties of the interference and provide upper and lower bounds for its distribution. We consider the probability of successful transmission in an interference-limited channel when fading is modeled as Rayleigh. We provide a numerically integrable expression for the outage probability and closed-form upper and lower bounds. We show that when the transmitter-receiver distance is large, the success probability is greater than that of a Poisson arrangement. These results characterize the performance of the system under geographical or MAC-induced clustering. We obtain the maximum intensity of transmitting nodes for a given outage constraint, i.e., the transmission capacity (of this spatial arrangement) and show that it is equal to that of a Poisson arrangement of nodes. For the analysis, techniques from stochastic geometry are used, in particular the probability generating functional of Poisson cluster processes, the Palm characterization of Poisson cluster processes, and the Campbell-Mecke theorem. We consider a single cell wireless uplink in which randomly arriving devices transmit their payload to a receiver. Given SNR per user, payload size per device, a fixed latency constraint T, total available bandwidth W, i.e., total symbol resources is given by N = TW. The total bandwidth W is evenly partitioned into B bins. Each time slot of duration T is split into a maximum number of retransmission attempts M. Hence, the N resources are partitioned into N MB resources each bin per retransmission. We characterize the maximum average rate or number of Poisson arrivals that can successfully complete the random access procedure such that the probability of outage is sufficiently small. We analyze the proposed setting for i) noise-limited regime and ii) interference-limited regime. We show that in the noise-limited regime the devices share the resources, and in the interference-limited regime, the resources split such that devices do not experience any interference. We then incorporate Rayleigh fading to model the channel power gain distribution. Although the variability of the channel causes a drop in the number of arrivals that can successfully complete the random access phase, similar scaling results extend to the Rayleigh fading case. In mobile networks, distance variations caused by node mobility generate fluctuations in the channel gains. Such fluctuations can be treated as another type of fading besides multipath effects. In this paper, the interference statistics in mobile random networks are characterized by incorporating the distance variations of mobile nodes to the channel gain fluctuations. The mean interference is calculated at the origin and at the border of a finite mobile network. The network performance is evaluated in terms of the outage probability. Compared to a static network, the interference in a single snapshot does not change under uniform mobility models. However, random waypoint mobility increases (decreases) the interference at the origin (at the border). Furthermore, due to the correlation of the node locations, the interference and outage are temporally and spatially correlated. We quantify the temporal correlation of the interference and outage in mobile Poisson networks in terms of the correlation coefficient and conditional outage probability, respectively. The results show that it is essential that routing, MAC, and retransmission schemes need to be smart (i.e., correlation-aware) to avoid bursts of transmission failures.