We analyze the capacity scaling laws of clustered ad hoc networks in which nodes are distributed according to a doubly stochastic shot-noise Cox process. We identify five different operational regimes, and for each regime we devise a communication strategy that allows to achieve a throughput to within a poly-logarithmic factor (in the number of nodes) of the maximum theoretical capacity.
In this paper, we follow the stream of work @cite_4 @cite_0 @cite_8 , analyzing the information-theoretic capacity of clustered random networks containing significant inhomogeneities in the node spatial distribution. In particular, we consider nodes distributed according to a doubly stochastic Shot-Noise Cox Process (SNCP) over a square region whose edge size can scale with the number of nodes.
@cite_0 @cite_4 @cite_8
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We consider static ad hoc wireless networks comprising significant inhomogeneities in the node spatial distribution over the area and analyze the scaling laws of their transport capacity as the number of nodes increases. In particular, we consider nodes placed according to a shot-noise Cox process (SNCP), which allows to model the clustering behavior usually recognized in large-scale systems. For this class of networks, we propose novel scheduling and routing schemes that approach previously computed upper bounds to the per-flow throughput as the number of nodes tends to infinity. We analyze the capacity scaling laws of wireless ad hoc networks comprising significant inhomogeneities in the node spatial distribution over the network area. In particular, we consider nodes placed according to a shot-noise Cox process, which allows to model the clustering behavior usually recognized in large-scale systems. For this class of networks, we introduce novel techniques to compute upper bounds to the available per-flow throughput as the number of nodes tends to infinity, which are tight in the case of interference limited systems. 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. Stochastic geometry proves to be a powerful tool for modeling dense wireless networks adopting random MAC protocols such as ALOHA and CSMA. The main strength of this methodology lies in its ability to account for the randomness in the nodes' location jointly with an accurate description at the physical layer, based on the SINR, that allows to consider also random fading on each link. Existing models of CSMA networks adopting the stochastic geometry approach suffer from two important weaknesses: 1) they permit to evaluate only spatial averages of the main performance measures, thus hiding possibly huge discrepancies in the performance achieved by individual nodes; 2) they are analytically tractable only when nodes are distributed over the area according to simple spatial processes (e.g., the Poisson point process). In this paper we show how the stochastic geometry approach can be extended to overcome the above limitations, allowing to obtain node throughput distributions as well as to analyze a significant class of topologies in which nodes are not independently placed.