SpaSWiN 2013

After a brief survey of well-known first-order properties of large wireless networks with Poisson distributed nodes, including the interference at a given location in time and space and the outage probability, we focus on the problems of analyzing the correlation structure of the interference and the transmission success events. We will show that the local delay, which is easier to calculate than the conditional outage probabilities, is a sensitive indicator of the temporal correlation. For receivers with multiple antennas, we quantify the diversity loss induced by interference correlation. In the last part of the talk, we discuss extensions to non-Poisson models. In this case, another type of second-order property becomes relevant, namely the second moment density or moment measure, which quantify the spatial dependence between points.

This work aims at combining adaptive protocol design, utility maximization and stochastic geometry. We focus on spatial adaptation of Aloha within the framework of ad hoc networks. We consider the cases where nodes maximize the global throughput or achieve either proportional fairness or max-min fairness. In the proportional fair case, nodes compute the optimal MAPs solving certain fixed point equations. In the maximum throughput case, the optimal MAPs are obtained through a Gibbs Sampling based algorithm. In the max-min case, these are obtained as the solution of a convex optimization problem. In the proportional fair case, when the nodes form a homogeneous Poisson point process in the Euclidean plane, the distribution of the optimal MAP can be obtained from that of a certain shot noise process, and the mean utility can also be derived from this distribution. Numerical results validate our findings and quantify the gains brought by spatial adaptation.

We study a multiple input multiple output (MIMO) cellular system where each base-station (BS) is equipped with a large antenna array and serves some single antenna mobile stations (MSs). With the same setup as in [Marzetta2010], the influence of orthogonal and non-orthogonal pilot sequences on the system performance is analytically characterized when each BS has infinitely many antennas. Using stochastic geometric modeling of the BS and MS locations, closed-form expressions are derived for the distribution of signal-to-interference-ratio (SIR) for both uplink and downlink. Moreover, they are shown to be equivalent for the orthogonal pilots case. Further, it is shown that the downlink SIR is greatly influenced by the correlations between the pilot sequences in the non-orthogonal pilots case. Finally, the mathematical tools can be used to study system performances with other general channel estimation methods and transmission-reception schemes.

Heterogeneous networks display a high degree of spatial randomness because of the deployment of smaller base stations (BSs) along with macro BSs wherever deemed necessary. An important aspect of analyzing heterogeneous networks involves understanding the interference that users in such networks encounter. The work delineated in this paper discerns the interference experienced in a heterogeneous network consisting of macro- and micro- BSs which are considered to be points of a Poisson cluster process. This paper has two main contributions: first is an expression for the generating functional of the interference and the second is a proof that shows that the interference in an area can be approximated to be completely described by a Gaussian distribution with zero mean and a variance that is dependent on the number of BSs in the area, along with functionals that represent the path loss, transmit power, fading, etc. which are ascribed to each BS.

In a two-tier heterogeneous network (HetNet) where small base stations (SBSs) coexist with macro base stations (MBSs), the SBSs may suffer significant performance degradation due to the inter- and intra-tier interferences. Introducing cognition into the SBSs through the spectrum sensing (e.g., carrier sensing) capability helps them detecting the interference sources and avoiding them via opportunistic access to orthogonal channels. In this paper, we use stochastic geometry to model and analyze the performance of two cases of cognitive SBSs in a multichannel environment, namely, the semi-cognitive case and the full-cognitive case. We show that a semi-cognitive SBS always outperforms a full-cognitive SBS and that there exists an optimal spectrum sensing threshold for the cognitive SBSs which can be obtained via the analytical framework presented in this paper.

Recently, spatial stochastic models for the analysis of cellular networks have been attracting much attention. However, many works on such spatial models assume, due to the tractability, that the base stations are deployed according to homogeneous Poisson point processes (PPPs). This means that the base stations are deployed independently with each other and their spatial correlation is ignored. In this talk, we consider the spatial models of cellular networks, where the base stations are deployed according to the Ginibre point process (GPP). The GPP is one of the determinantal point processes and accounts for the repulsion between the base stations. We first review the definition and some useful properties of GPP for the modeling of cellular networks. Then, for the proposed models, we give the integral representations for the coverage probability. Through some numerical experiments, we compare the GPP-based models with the traditional PPP-based models.

Presently, mobile devices have to be connected by cables to the electric grid for recharging and cutting these "last wires" is the theme of this talk. This problem can be solved by either wireless power transfer (WPT) or energy harvesting. This talk will introduce research on applying stochastic-geometry (SG) to design mobile networks powered using these new technologies. First, we will present a network architecture that overlays a cellular network with randomly deployed power beacons (PBs) for wireless recharging. Based on a SG network model, we will show the tradeoffs between the base-station and PB densities. Second, we will consider a mobile ad hoc network powered by energy harvesting. In this research, the network is modeled using a Poisson point process and random energy arrivals at transmitters are modelled as stochastic processes. Using this model, we derive the maximum network spatial throughput for a given energy arrival rate.

Both fractional frequency reuse and interference cancellation have been proposed as methodologies to improve the capacity of cellular systems. Using stochastic geometry techniques we analyze the impact of both these features in terms of rate outage and capacity. Finally, using analysis and simulations we study their applicability in a realistic cellular system.

There have been a bulk of analytic results about performance of cellular networks where base stations are regularly located on a hexagonal or square lattice. This regular model tends to overestimate the network performance and tractable analysis can be performed only for a fixed location user. In this paper, we use stochastic geometry approach, where base stations can be modeled as a Poisson Point Process. We also consider user density, and derive user outage probability that an arbitrary user is under outage due to low signal-to-interference-plus-noise ratio or high congestion by multiple users. Using the result, we calculate the density of success transmissions in the downlink cellular network. An interesting thing is the success transmission density increases with the base station density, but the increasing rate diminishes. This means the number of base stations installed should be more than $n$-times to increase the network capacity by a factor of $n$.

Delay-Tolerant Networks (DTNs) have emerged as an exciting research area with a number of useful applications. Most of these applications would benefit greatly by a reduction in the message delivery delay experienced in the network. The delay performance of DTNs is adversely affected by contention, especially severe in the presence of higher traffic rates and node densities. Many-to-Many (M2M) communication can handle this contention much better than traditional one- to one communication employing CSMA. In this paper, for the first time, we analytically model the expected delivery delay of a DTN employing epidemic routing and M2M communication. The accuracy of our model is demonstrated by matching the analytical results against those from simulations. We also show using simulations that M2M communication significantly improves the delay performance (with respect to one-to-one CSMA) for high-contention scenarios. We believe our work will enable the effective application of M2M communication to reduce delivery delays in DTNs.