“Random Matrices and Scaling of Multi-Access Capacity in Dense Networks”

Abstract

To understand in a dense network how MIMO, user diversity, network topology and limited cooperation influence the uplink cell throughput, we consider multi-access in cell-based dense wireless networks (e.g., cellular and WiFi with access points) when the communications are interference-limited. Each cell has n $N_t$-antenna users and K neighboring $N_r$-antenna cells, and the channels are i.i.d. Rayleigh. Multi-users are allowed to transmit in one cell simultaneously, and each cell decodes by treating signals coming from other cells as noise. We assume that only the receivers have channel state information, and every cell has a common number of active users. It is shown that $(N_r / (1+K N_t N_r)) log n$ bit/s/Hz is achievable for every cell by selecting $exp{(1 / (1+K N_t N_r)) log n}$ users per cell according to a simple threshold rule, and decoding using successive interference cancelation. On the other hand, this is also shown to be an upper bound on the per cell throughput, no matter how users are chosen. Simulations will also be provided. The analysis relies on an interesting result on random matrices not known before. Specifically, consider the sum of the Gram matrices of $n_s$ matrices chosen from a set of n i.i.d. ones. We show that the determent of the sum is lower bounded by a certain scaling function when $n_s$ exceeds a threshold depending on the dimensions and n, no matter how they are chosen.

Bio

Feng Xue is a research scientist with Intel Research, Santa Clara, California. His current research interests include 1) enabling advanced physical/cross-layer cooperation and cognitive resource management in dense wireless networks, and 2) solving the related optimization and information theory problems.  Feng Xue received the BS, MS, PhD degrees from Shandong University, Chinese Academy of Sciences and University of Illinois, Urbana-Champaign (UIUC), respectively. From 2000 to 2006, he was a research assistant with the Coordinated Science Lab and the Department of Electrical and Computer Engineering, UIUC, working on the capacity and coverage issues of ad hoc wireless networks. He received the Robert T. Chien Memorial Award from the department, and co-authored the monograph “Scaling laws for ad hoc wireless networks: An information theoretic approach” with Professor P.R. Kumar.