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.
Stochastic geometry provides a natural way of defining and computing macroscopic properties of classical channels of multiuser information theory. These macroscopic properties are obtained by some averaging over all node patterns found in a large random network of the Euclidean plane. One of the most important geometric objects are the coverage regions of a transmitter or a set of transmitters. This domain of research 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.
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.
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 first paper On Shared Rate Time Series for Mobile Users in Poisson Networks was focused on the noise limited case. The ongoing research is focused on the general case, with both interference and thermal noise taken into account.
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.