We leverage stochastic geometry to characterize key performance metrics for neighboring Wi-Fi and LTE networks in unlicensed spectrum. Our analysis focuses on a single unlicensed frequency band, where the locations for the Wi-Fi access points and LTE eNodeBs are modeled as two independent homogeneous Poisson point processes. Three LTE coexistence mechanisms are investigated: 1) LTE with continuous transmission and no protocol modifications; 2) LTE with discontinuous transmission; and 3) LTE with listen-before-talk and random back-off. For each scenario, we derive the medium access probability, the signal-to-interference-plus-noise ratio coverage probability, the density of successful transmissions (DST), and the rate coverage probability for both Wi-Fi and LTE. Compared with the baseline scenario where one Wi-Fi network coexists with an additional Wi-Fi network, our results show that Wi-Fi performance is severely degraded when LTE transmits continuously. However, LTE is able to improve the DST and rate coverage probability of Wi-Fi while maintaining acceptable data rate performance when it adopts one or more of the following coexistence features: a shorter transmission duty cycle, lower channel access priority, or more sensitive clear channel assessment thresholds.
In recent years, stochastic geometry has become a popular and powerful mathematical tool to analyze cellular and Wi-Fi systems. Specifically, key performance metrics can be derived by modeling the locations of base stations (BSs) access points (APs) as a realization of certain spatial random point processes. @cite_0 , the coverage probability and average Shannon rate were derived for macro cellular networks with BSs distributed according to the complete spatial random Poisson point process (PPP). The analysis has been extended to several other cellular network scenarios, including heterogeneous cellular networks (HetNets) @cite_27 @cite_40 @cite_3 , MIMO @cite_12 @cite_22 , and carrier aggregation @cite_37 @cite_11 . More realistic macro BS location models than PPP are investigated in @cite_19 @cite_8 @cite_35 . Stochastic geometry can also model CSMA CA-based Wi-Fi networks. A modified Mat ' e rn hard-core point process, which gives a snapshot view of the simultaneous transmitting CSMA CA nodes, has been proposed and validated in @cite_30 for dense 802.11 networks. This Mat ' e rn CSMA model is also used for analyzing other CSMA CA based networks, such as ad-hoc networks with channel-aware CSMA CA protocols @cite_41 , and cognitive radio networks @cite_4 .
@cite_30 @cite_35 @cite_37 @cite_4 @cite_22 @cite_8 @cite_41 @cite_3 @cite_0 @cite_19 @cite_40 @cite_27 @cite_12 @cite_11
2121822142 2065735671 2146115135 2167353407
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. Stochastic geometry models for wireless communication networks have recently attracted much attention. This is because the performance of such networks critically depends on the spatial configuration of wireless nodes and the irregularity of the node configuration in a real network can be captured by a spatial point process. However, most analysis of such stochastic geometry models for wireless networks assumes, owing to its tractability, that the wireless nodes are deployed according to homogeneous Poisson point processes. This means that the wireless nodes are located independently of each other and their spatial correlation is ignored. In this work we propose a stochastic geometry model of cellular networks such that the wireless base stations are deployed according to the Ginibre point process. The Ginibre point process is one of the determinantal point processes and accounts for the repulsion between the base stations. For the proposed model, we derive a computable representation for the coverage probability—the probability that the signal-to-interference-plus-noise ratio (SINR) for a mobile user achieves a target threshold. To capture its qualitative property, we further investigate the asymptotics of the coverage probability as the SINR threshold becomes large in a special case. We also present the results of some numerical experiments. 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. The spatial structure of base stations (BSs) in cellular networks plays a key role in evaluating the downlink performance. In this paper, different spatial stochastic models (the Poisson point process (PPP), the Poisson hard-core process (PHCP), the Strauss process (SP), and the perturbed triangular lattice) are used to model the structure by fitting them to the locations of BSs in real cellular networks obtained from a public database. We provide two general approaches for fitting. One is fitting by the method of maximum pseudolikelihood. As for the fitted models, it is not sufficient to distinguish them conclusively by some classical statistics. We propose the coverage probability as the criterion for the goodness-of-fit. In terms of coverage, the SP provides a better fit than the PPP and the PHCP. The other approach is fitting by the method of minimum contrast that minimizes the average squared error of the coverage probability. This way, fitted models are obtained whose coverage performance matches that of the given data set very accurately. Furthermore, we introduce a novel metric, the deployment gain, and we demonstrate how it can be used to estimate the coverage performance and average rate achieved by a data set.