Over the past decade, many works on the modeling of wireless networks using stochastic geometry have been proposed. Results about probability of coverage, throughput or mean interference, have been provided for a wide variety of networks (cellular, ad-hoc, cognitive, sensors, etc). These results notably allow to tune network protocol parameters. Nevertheless, in their vast majority, these works assume that the wireless network deployment is flat: nodes are placed on the Euclidean plane. However, this assumption is disproved in dense urban environments where many nodes are deployed in high buildings. In this letter, we derive the exact form of the probability of coverage for the cases where the interferers form a 3D Poisson Point Process (PPP) and a 3D Modified Matern Process (MMP), and compare the results with the 2D case. The main goal of this letter is to show that the 2D model, although being the most common, can lead either to an optimistic or a pessimistic evaluation of the probability of coverage depending on the parameters of the model.
Many works modeling CSMA access through stochastic geometry have emerged in the literature these past ten years @cite_18 @cite_10 @cite_19 . These works are based on a modified version of the Matern Point Process for which the points cannot live too close to each others. This allows to model the contention radius of CSMA as follows. The nodes of the network form a PPP on the Euclidean plane and they contend to access to the medium. Each node picks uniformly a value between zero and one, the node is selected in the process if it does not detect any node with a smaller mark value (this models the backoff procedure). The resulting process is the Modified Matern Process (MMP) which will be detailed in section . As there is no known exact formulation of the interference in such process, @cite_18 @cite_10 and @cite_19 use approximation techniques. They show that their approximations lie close to simulations results. We extend these works by considering 3D distribution of the nodes and compare the resulting model to simulation. To the best of our knowledge, this has not been considered in the literature.
@cite_19 @cite_18 @cite_10
2028070124 2146115135 2154233760
For spectrum sharing and avoidance of mutual interference, carrier-sense multiple access (CSMA) protocols are very popular in distributed wireless networks. CSMA protocols aim to maximize the spatial frequency reuse while limiting the mutual interference and outage. The hard core point process (HCPP) is a very popular tool for modeling and analysis of random CSMA networks. However, the traditional HCPP suffers from the node intensity (and hence the interference) underestimation flaw. Therefore, we propose a modified hard core point process to mitigate this flaw. The proposed modified HCPP is generalized for any fading environment. To this end, we derive a closed-form expression for the intensity of simultaneously active transmitters in a random wireless CSMA network. Then, we derive a closed-form expression for approximating the outage probability experienced by a generic receiver in the network, and subsequently, use it to obtain the transmission capacity of the network. Finally, we show the existence of an optimal carrier-sensing threshold for the CSMA protocol that maximizes the transmission capacity of the network. Simulation results validate the analysis and also provide interesting insights into the design of practical CSMA networks. This paper presents a stochastic geometry model for the performance analysis and the planning of dense IEEE 802.11 networks. This model allows one to propose heuristic formulas for various properties of such networks like the probability for users to be covered, the probability for access points to be granted access to the channel or the average long term throughput provided to end-users. The main merit of this model is to take the effect of interferences and that of CSMA into account within this dense network context. This analytic model, which is based on Matern point processes, is partly validated against simulation. It is then used to assess various properties of such networks. We show for instance how the long term throughput obtained by end-users behaves when the access point density increases. We also briefly show how to use this model for the planning of managed networks and for the economic modeling of unplanned networks. In this paper, the performance of the ALOHA and CSMA MAC protocols are analyzed in spatially distributed wireless networks. The main system objective is correct reception of packets, and thus the analysis is performed in terms of outage probability. In our network model, packets belonging to specific transmitters arrive randomly in space and time according to a 3-D Poisson point process, and are then transmitted to their intended destinations using a fully-distributed MAC protocol. A packet transmission is considered successful if the received SINR is above a predefined threshold for the duration of the packet. Accurate bounds on the outage probabilities are derived as a function of the transmitter density, the number of backoffs and retransmissions, and in the case of CSMA, also the sensing threshold. The analytical expressions are validated with simulation results. For continuous-time transmissions, CSMA with receiver sensing (which involves adding a feedback channel to the conventional CSMA protocol) is shown to yield the best performance. Moreover, the sensing threshold of CSMA is optimized. It is shown that introducing sensing for lower densities (i.e., in sparse networks) is not beneficial, while for higher densities (i.e., in dense networks), using an optimized sensing threshold provides significant gain.