Uplink Performance of Large Optimum-Combining Antenna Arrays in Poisson-Cell Networks

The uplink of a wireless network with base stations distributed according to a Poisson Point Process (PPP) is analyzed. The base stations are assumed to have a large number of antennas and use linear minimum-mean-square-error (MMSE) spatial processing for multiple access. The number of active mobiles per cell is limited to permit channel estimation using pilot sequences that are orthogonal in each cell. The cumulative distribution function (CDF) of a randomly located link in a typical cell of such a system is derived when accurate channel estimation is available. A simple bound is provided for the spectral efficiency when channel estimates suffer from pilot contamination. The results provide insight into the performance of so-called massive Multiple-Input-Multiple-Output (MIMO) systems in spatially distributed cellular networks

Some Classical Problems in Random Geometry

International audienceThis chapter is intended as a first introduction to selected topics in random geometry. It aims at showing how classical questions from recreational mathematics can lead to the modern theory of a mathematical domain at the interface of probability and geometry. Indeed, in each of the four sections, the starting point is a historical practical problem from geometric probability. We show that the solution of the problem, if any, and the underlying discussion are the gateway to the very rich and active domain of integral and stochastic geometry, which we describe at a basic level. In particular, we explain how to connect Buffon’s needle problem to integral geometry, Bertrand’s paradox to random tessellations, Sylvester’s four-point problem to random polytopes and Jeffrey’s bicycle wheel problem to random coverings. The results and proofs selected here have been especially chosen for non-specialist readers. They do not require much prerequisite knowledge on stochastic geometry but nevertheless comprise many of the main results on these models