Asymptotically optimal waterfilling in multiple antenna multiple access channels

This paper considers "vector multiple access channels" (VMAC) where each user has multiple "degrees of freedom" and studies the effect of power allocation as a function of the channel state on the "sum capacity" defined as the maximum sum of rates of users per unit degree of freedom at which the users can jointly reliably transmit, in an information theoretic sense. A concrete example of a VMAC is a MAC with multiple antennas at the receiver where the antennas provide spatial degrees of freedom. Our main result is the identification of a simple dynamic power allocation scheme that is optimal in a large system, i.e., in the regime of a large number of users and a correspondingly large number of antennas. A key feature of this policy is that, for any user, it depends only on the instantaneous amplitude of the slow fading component of the vector channel of that user alone and the structure of the policy is "waterfilling".