 
Summary: IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 47, NO. 1, JANUARY 2001 241
Asymptotically Optimal WaterFilling in Vector
MultipleAccess Channels
Pramod Viswanath, Member, IEEE, David N. C. Tse, Member, IEEE, and Venkat Anantharam, Fellow, IEEE
AbstractDynamic resource allocation is an important means
to increase the sum capacity of fading multipleaccess channels
(MACs). In this paper, we consider vector multiaccess channels
(channels where each user has multiple degrees of freedom) and
study the effect of power allocation as a function of the channel
state on the sum capacity (or spectral efficiency) defined as the
maximum sum of rates of users per unit degree of freedom at
which the users can jointly transmit reliably, in an informa
tiontheoretic sense, assuming random directions of received
signal. Directsequence codedivision multipleaccess (DSCDMA)
channels and MACs with multiple antennas at the receiver are two
systems that fall under the purview of our model. Our main result
is the identification of a simple dynamic powerallocation scheme
that is optimal in a large system, i.e., with a large number of users
and a correspondingly large number of degrees of freedom. A
key feature of this policy is that, for any user, it depends on the
