Stochastic Modeling of Wireless Networks

Topics

About wireless stochastic geometry

Stochastic geometry provides a natural way of defining and computing macroscopic properties of communication channels of multi-user information theory. These macroscopic properties are obtained by some averaging over all node patterns found in a large random network of the Euclidean plane or space. 

For more on the field, see the wikipedia page on the matter.

This domain of research is currently expanding exponentially fast as shown by this curve communicated by Martin Haenggi.

Correlated shadowing in wireless stochastic geometry

Junse Lee, Xinchen Zhang and François Baccelli proposed new models for analyzing spatially correlated shadowing fields. These models allow one to analyze the interference field created by a wireless infrastructure through the walls and floors of a building with variable size rooms. These models provide a mathematical characterization of the interference distribution, which further leads to closed-from expressions for the coverage probability in cellular networks. Three network scenarios are studied: 2-D outdoor, 2-D indoor, and 3-D inbuilding.

Coverage in wireless networks

One of the most important geometric objects are the coverage regions of a transmitter or a set of transmitters. This question is jointly studied by Jeffrey Andrews, François Baccelli, Gustavo de Veciana, Robert Heath and Sanjay Shakkottai. Most of the initial steps are based on Poisson point processes. Lately, this continued with Yingzhe Li (Simons PhD student, ECE, UT Austin) to the case of determinantal point processes. Another line of work on studying cell-association problems in multi-technology cellular networks was carried out in this paper by Abishek Sankararaman, Jeong-woo Cho and François Baccelli.

 

Extremes of spatial shot noise processes

Anup Biswas and François Baccelli studied the scaling limit of a class of shot-noise fields defined on an independently marked stationary Poisson point process and with a power law response function. Under appropriate conditions, they showed that the shot-noise field can be scaled suitably to have a non degenerate alpha-stable limit, as the intensity of the underlying point process goes to infinity. More precisely, finite dimensional distributions  converge and the finite dimensional distributions of the limiting random field have i.i.d. stable random components. This limit is hence called the alpha- stable white noise field. Analogous results are also obtained for the extremal shot-noise field which converges to a Fréchet white noise field.

Moving user time series in SNR stochastic geometry

With Pranav Madadi, F. Baccelli, and G. de Veciana analyzed the temporal variations in the Shannon rate experienced by a user moving along a straight line in a cellular network represented by a Poisson-Voronoi tessellation. We consider a network that is shared by static users distributed as a Poisson point process and analyzed the time series of the final shared rate and the number of users sharing the network. The paper On Shared Rate Time Series for Mobile Users in Poisson Networks was focused on the noise limited case.

Scaling laws for ergodic spectral efficiency in MIMO Poisson networks

Ergodic spectral efficiency quantifies the achievable Shannon transmission rate per unit area, and captures the effects of rate adaptation techniques. Junse Lee, Namyoon Lee and François Baccelli studied the benefits of multiple antenna communication in ad-hoc networks using this metric. In this work, the primary finding is that, with knowledge of channel state information between a receiver and its associated transmitter, the ergodic spectral efficiency can be made to scale linearly with both 1) the minimum of the number of transmit and receive antennas and 2) the density of nodes. This scaling law is achieved when the multiple transmit antennas send multiple data streams and the multiple receive antennas are leveraged to cancel interference. Spatial multiplexing transmission methods are shown to be essential for obtaining better and eventually optimal scaling laws in such random wireless networks.

Spatial Birth-Death Wireless Networks

In this paper, Abishek Sankararaman and François Baccelli introduce a new form of spatial dynamics motivated by ad-hoc wireless networks. They study a birth death process where particles arrive in space as a Poisson process in space and time, and depart the system on completion of file transfer. The instantaneous rate of file transfer of any link is given by the Shannon formula of treating interference as noise. As the instantaneous interference seen by a link is dependent on the configuration of links present, this dynamics is an example of one where dynamics shapes geometry and in turn the geometry shapes the dynamics. In this paper, the authors establish a sharp phase-transition for stability of such dynamics. Moreover, whenever such dynamics is stable, they prove that the steady state is a clustered point process. Through simulations, they also argue that such dynamics cannot be simplified to any form of non-spatial queuing type dynamics. Lately, this paper with Sergey Foss extended the dynamics on grids to show a similar stability phase-transition in the case of infinite network, i.e. in an infinite grid.

Members

Ahmad AlAmmouri

Department of Electrical and Computer Engineering, UT Austin
alammouri@utexas.edu
Read More »

Chang-sik Choi

Department of Electrical and Computer Engineering, UT Austin
chang-sik.choi@utexas.edu
Read More »

Jae Oh Woo

Department of Mathematics and Department of Electrical and Computer Engineering, UT Austin
jaeoh.woo@utexas.edu
Read More »

Robert W. Heath Jr.

Department of Electrical and Computer Engineering, UT Austin
rheath@utexas.edu
512 686 8225
Read More »

Jeong Woo Cho, 2015

KTH, Stockholm, Sweden
jwcho@kth.se
Read More »

Jeffrey Andrews

Department of Electrical and Computer Engineering, UT Austin
jandrews@ece.utexas.edu
512 471 0536
Read More »

Junse Lee

Department of Electrical and Computer Engineering, UT Austin
junselee@utexas.edu
Read More »

Pranav Madadi

Department of Electrical and Computer Engineering, UT Austin
ee10b024@iith.ac.in
Read More »

Xinchen Zhang 2013-2014

Department of Electrical and Computer Engineering, UT Austin
xinchenzhang@gmail.com
Read More »

Abishek Sankararaman

Department of Electrical and Computer Engineering, UT Austin
abishek@utexas.edu
Read More »

Yingzhe Li

Department of Electrical and Computer Engineering, UT Austin
yzli@utexas.edu
Read More »

Gustavo de Veciana

Department of Electrical and Computer Engineering, UT Austin
gustavo@ece.utexas.edu
512 471 1573
Read More »

François Baccelli

Department of Mathematics and Deparment of Electrical and Computer Engineering, UT Austin
baccelli@math.utexas.edu
512 471 17 54
Read More »

Publications

2017-07-30_1001012 2017-06-01_1000994

Spatial Birth Death Wireless Networks

Abishek Sankararaman and François Baccelli IEEE Transactions on Information Theory 63(6): 3964-3982 (2017)
Download PDF
2017-04-01_1000817

SINR and Throughput of Dense Cellular Networks with Stretched Exponential Path Loss

Ahmad AlAmmouri, Jeffrey G. Andrews, and François Baccelli Submitted to IEEE Transactions on Wireless Communications
Download PDF
2016-09-25_1000612

A 3-D Spatial Model for In-building Wireless Networks with Correlated Shadowing

Junse Lee, Xinchen Zhang, Francois Baccelli Accepted to IEEE Transactions on Wireless Communications
Download PDF
2016-09-18_1000754

On Shared Rate Time Series for Mobile Users in Poisson Networks

Pranav Madadi, François Baccelli, Gustavo de Veciana https://arxiv.org/abs/1609.08845
Download PDF
2016-08-22_1000655

Scaling Laws for Ergodic Spectral Efficiency in MIMO Poisson Networks

Junse Lee, Namyoon Lee, Francois Baccelli Submitted to IEEE Transactions on Information Theory
Download PDF
2016_1000621

Performance-Oriented Association in Large Cellular Networks with Technology Diversity

Abishek Sankararaman, Jeong-woo Cho, François Baccelli 28th International Teletraffic Congress (ITC 28), 2016
Download PDF
2015-05-28_1000151

On Scaling Limits of Power Law Shot-noise Fields

François Baccelli and Anup Biswas To appear in Stochastic Models 2015
Download PDF
2014-12-05_1000282

Statistical Modeling and Probabilistic Analysis of Cellular Networks with Determinantal Point Processes

Yingzhe Li, François Baccelli, Harpreet S. Dhillon and Jeffrey G. Andrews Arxiv 2014
Download PDF
2014-10-28_1000283 2014-07-16_1000167

Spatial Reuse and Fairness in Ad Hoc Networks with Channel-Aware CSMA Protocols

Yuchul Kim, François Baccelli and Gustavo de Veciana IEEE Transactions on Information Theory 60(7):4139-57, July 2014
Download PDF
2000-01-01_1001035

Interference Queuing Networks on Grids

Abishek Sankararaman, François Baccelli and Sergey Foss ArXiv 2017
Download PDF