Mehrnaz Afshang

Modeling and Performance Analysis of Clustered Device-to-Device Networks

Device-to-device (D2D) communication enables direct communication between proximate devices thereby improving the overall spectrum utilization and off-loading traffic from cellular networks. This paper develops a new spatial model for D2D networks in which the device locations are modeled as a Poisson cluster process. Using this model, we study the performance of a typical D2D receiver in terms of coverage probability under two realistic content availability setups: 1) content of interest for a typical device is available at a device chosen uniformly at random from the same cluster, which we term uniform content availability, and 2) content of interest is available at the kth closest device from the typical device inside the same cluster, which we term k-closest content availability. Using these coverage probability results, we also characterize the area spectral efficiency (ASE) of the whole network for the two setups. A key intermediate step in this analysis is the derivation of the distributions of distances from a typical device to both the intra-and inter-cluster devices. Our analysis reveals that an optimum number of D2D transmitters must be simultaneously activated per cluster in order to maximize ASE. This can be interpreted as the classical tradeoff between more aggressive frequency reuse and higher interference power. The optimum number of simultaneously transmitting devices and the resulting ASE increase as the content is made available closer to the receivers. Our analysis also quantifies the best and worst case performance of clustered D2D networks both in terms of coverage and ASE.

Fundamentals of Cluster-Centric Content Placement in Cache-Enabled Device-to-Device Networks

This paper develops a comprehensive analytical framework with foundations in stochastic geometry to characterize the performance of cluster-centric content placement in a cache-enabled device-to-device (D2D) network. Different from device-centric content placement, cluster-centric placement focuses on placing content in each cluster, such that the collective performance of all the devices in each cluster is optimized. Modeling the locations of the devices by a Poisson cluster process, we define and analyze the performance for three general cases: 1) k-Tx case: the receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at the kth closest device to the cluster center; 2) 1-Rx case: the receiver of interest is the Ith closest device to the cluster center and its content of interest is available at a device chosen uniformly at random from the same cluster; and 3) baseline case: the receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at a device chosen independently and uniformly at random from the same cluster. Easy-to-use expressions for the key performance metrics, such as coverage probability and area spectral efficiency of the whole network, are derived for all three cases. Our analysis concretely demonstrates significant improvement in the network performance when the device on which content is cached or device requesting content from cache is biased to lie closer to the cluster center compared with the baseline case. Based on this insight, we develop and analyze a new generative model for cluster-centric D2D networks that allows to study the effect of intra-cluster interfering devices that are more likely to lie closer to the cluster center.

Poisson Hole Process: Theory and Applications to Wireless Networks

Interference field in wireless networks is often modeled by a homogeneous Poisson point process (PPP). While it is realistic in modeling the inherent node irregularity and provides meaningful first-order results, it falls short in modeling the effect of interference management techniques, which typically introduces some form of spatial interaction among active transmitters. In some applications, such as cognitive radio and device-to-device networks, this interaction may result in the formation of holes in an otherwise homogeneous interference field. The resulting interference field can be accurately modeled as a Poisson hole process (PHP). Despite the importance of the PHP in many applications, the exact characterization of interference experienced by a typical node in the PHP is not known. In this paper, we derive several tight upper and lower bounds on the Laplace transform of this interference. Numerical comparisons reveal that the new bounds outperform all known bounds and approximations, and are remarkably tight in all operational regimes of interest. The key in deriving these tight and yet simple bounds is to capture the local neighborhood around the typical node accurately while simplifying the far field to attain tractability. Ideas for tightening these bounds further by incorporating the effect of overlaps in the holes are also discussed. These results immediately lead to an accurate characterization of the coverage probability of the typical node in the PHP under Rayleigh fading.

Enriched

One of the principal underlying assumptions of current approaches to the analysis of heterogeneous cellular networks (HetNets) with random spatial models is the uniform distribution of users independent of the base station (BS) locations. This assumption is not quite accurate, especially for user-centric capacity-driven small cell deployments where low-power BSs are deployed in the areas of high user density, thus inducing a natural correlation in the BS and user locations. In order to capture this correlation, we enrich the existing

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-Tier HetNet Model to Enable the Analysis of User-Centric Small Cell Deployments

-tier Poisson point process (PPP) HetNet model by considering user locations as Poisson Cluster Process with the BSs at the cluster centers. In particular, we provide the formal analysis of the downlink coverage probability in terms of a general density function describing the locations of users around the BSs. The derived results are specialized for two cases of interest: 1) Thomas cluster process, where the locations of the users around BSs are Gaussian distributed and 2) Matérn cluster process, where the users are uniformly distributed inside a disc of a given radius. Tight closed-form bounds for the coverage probability in these two cases are also derived. Our results demonstrate that the coverage probability decreases as the size of user clusters around BSs increases, ultimately collapsing to the result obtained under the assumption of PPP distribution of users independent of the BS locations when the cluster size goes to infinity. Using these results, we also handle mixed user distributions consisting of two types of users: 1) uniformly distributed and 2) clustered around certain tiers.

Spatial modeling of device-to-device networks: Poisson cluster process meets Poisson Hole Process

This paper combines Poisson Cluster Process (PCP) with a Poisson Hole Process (PHP) to develop a new spatial model for an inband device-to-device (D2D) communications network, where D2D and cellular transmissions share the same spectrum. The locations of the devices engaging in D2D communications are modeled by a modified Thomas cluster process in which the cluster centers are modeled by a PHP instead of more popular homogeneous Poisson Point Process (PPP). While the clusters capture the inherent proximity in the devices engaging in D2D communications, the holes model exclusion zones where D2D communication is prohibited in order to protect cellular transmissions. For this setup, we characterize network performance in terms of coverage probability and area spectral efficiency.

Optimal geographic caching in finite wireless networks

Cache-enabled device-to-device (D2D) networks turn memory of the devices at the network edge, such as smart phones and tablets, into bandwidth by enabling asynchronous content sharing directly between proximate devices. Limited storage capacity of the mobile devices necessitates the determination of optimal set of contents to be cached on each device. In order to study the problem of optimal cache placement, we model the locations of devices in a finite region (e.g., coffee shop, sports bar, library) as a uniform binomial point process (BPP). For this setup, we first develop a generic framework to analyze the coverage probability of the target receiver (target-Rx) when the requested content is available at the kth closest device to it. Using this coverage probability result, we evaluate optimal caching probability of the popular content to maximize the total hit probability. Our analysis concretely demonstrates that optimal caching probability strongly depends on the number of simultaneously active devices in the network.

Nearest-Neighbor and Contact Distance Distributions for Thomas Cluster Process

We characterize the statistics of nearest-neighbor and contact distance distributions for Thomas cluster process (TCP), which is a special case of Poisson cluster process. In particular, we derive the cumulative distribution function of the distance to the nearest point of TCP from a reference point for three different cases: 1) reference point is not a part of the point process; 2) it is chosen uniformly at random from the TCP; and 3) it is a randomly chosen point from a cluster chosen uniformly at random from the TCP. While the first corresponds to the contact distance distribution, the other two provide two different viewpoints for the nearest-neighbor distance distribution. Closed-form bounds are also provided for the first two cases.

Coverage and Area Spectral Efficiency of Clustered Device-to-Device Networks

This paper develops a new spatial model for device-to-device (D2D) networks in which the device locations are modeled as a Thomas cluster process. The devices inside a given cluster form D2D links amongst themselves and the direct communication across clusters is not required. This model captures the fact that the devices engaged in D2D communications need to be in close proximity of each other. For this model, we derive easy-to-use expressions for both coverage probability and area spectral efficiency (ASE) assuming that the content of interest is available at a device chosen uniformly at random from the same cluster. One of the important consequences of this analysis is that there exists an optimal number of simultaneously active D2D-Txs that maximizes the ASE. This can be interpreted as the classical tradeoff between more aggressive frequency reuse and higher interference power. Our analysis also provides insights into the effect of scattering variance of each cluster and the density of cluster centers on coverage probability and ASE.