arXiv subjects

Mehrnaz Afshang

Publications and source records attributed to Mehrnaz Afshang.

23 records · Page 2Linked to original sources

arXiv2016

Fundamentals of Modeling Finite Wireless Networks using Binomial Point Process

Modeling the locations of nodes as a uniform binomial point process (BPP), we present a generic mathematical framework to characterize the performance of an arbitrarily-located reference receiver in a finite wireless network. Different from most of the prior works where the serving transmitter (TX) node is located at the fixed distance from the reference receiver, we consider two general TX-selection policies: i) uniform TX-selection: the serving node is chosen uniformly at random amongst transmitting nodes, and ii) k-closest TX-selection: the serving node is the k-th closest node out of transmitting nodes to the reference receiver. The key intermediate step in our analysis is the derivation of a new set of distance distributions that lead not only to the tractable analysis of coverage probability but also enable the analyses of wide range of classical and currently trending problems in wireless networks. Using this new set of distance distributions, we first investigate the diversity loss due to SIR correlation in a finite network. We then obtain the optimal number of links that can be simultaneously activated to maximize network spectral efficiency. Finally, we evaluate optimal caching probability to maximize the total hit probability in cache-enabled finite networks.

cs.IT↗

arXiv2016

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 $k^{th}$ 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.

cs.IT↗

arXiv2016

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: (i)$k$-Tx case: receiver of interest is chosen uniformly at random in a cluster and its content of interest is available at the $k^{th}$ closest device to the cluster center, (ii) $\ell$-Rx case: receiver of interest is the $\ell^{th}$ 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 (iii) 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 (ASE) 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 to 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.

cs.IT↗

arXiv2016

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 introduce 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 PHP in many applications, the exact characterization of interference experienced by a typical node in a 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 point 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 a PHP under Rayleigh fading.

cs.IT↗

arXiv2015

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 offloading 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: (i) 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 (ii) content of interest is available at the $k^{th}$ 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.

cs.IT↗