Toronto Networking Seminar

Traditionally capacity issues in wireless systems have been posed as finding the maximum rate that is supportable under a given power budget. A simple solution to this problem is to transmit to the user with the best channel at maximum power and then determine the rate. However, in practice users have throughput delay tradeoffs in that they have minimum rate requirements that will allow them to obtain guarantees on delays when they have channel access. Meeting minimum rate guarantees opens up power to be shared amongst users who can achieve their minimum rates and thus more than one user can be allowed.

In this talk I will present results on the maximum number of simultaneous users that can be supported under independent fading conditions. In particular, a power allocation scheme is proposed to maximize the number of active terminals in fading multi-user channels in which a minimum rate must be maintained for all active users. It is assumed that receivers and transmitters have perfect channel state information. Both uplink and downlink scenarios are considered and under the assumption of independent Rayleigh fading channels for different terminals, the optimal number of active terminals is asymptotically obtained as the total number of users, n, is large enough. For broadcast channels with successive interference cancellation at receivers and multiple access channels with joint decoding at the receiver, the maximum number of active terminals is shown to be arbitrarily close to with probability approaching one, where Ptotal and Rmin denote total transmit power and the minimum rate respectively, and represents the background noise variance.

We then look at the more general setting of multihop ad hoc networks and study how many simultaneous links can be supported and determine the sum rate capacity when there are a large number of nodes. This allows us to estimate the scaling law for achievable rate in multi-hop wireless networks. For small networks where fading rather than path loss is dominant the number of rate constrained active links is O(log n) while for wide area networks with fading and path loss the number of active links is O(n). A corollary is that the per-user multi-hop capacity of such networks scales as 1 over square root of n.

The proofs involve several interesting properties related to order statistics.

Joint work with Hengameh Keshavarz and Liang-Liang Xie of the University of Waterloo.

The speaker was educated at the Indian Institute of Technology, Bombay (B.Tech, 1977), Imperial College, London (MSc, DIC, 1978) and UCLA (PhD, 1983).

He is currently a University Research Chair Professor in the Dept. of ECE at the University of Waterloo, Ont., Canada where he has been since September 2004. Prior to this he was Professor of ECE at Purdue University, West Lafayette, USA where he continues to be an Adjunct Professor.

He is an editor of the IEEE/ACM Trans on Networking and has served as guest editor for a number of special issues of networking and applied probability related journals. He is a Fellow of the IEEE and the Royal Statistical Society. He received the INFOCOM 2006 Best Paper Award and was runner-up for the Best Paper Award at INFOCOM 1998.

His research interests are in modeling, control, and performance analysis of both wireline and wireless networks, and in applied probability and stochastic analysis with applications to queueing, filtering, and optimization.