Asymptotically Optimal Water lling in Vector MultipleAccess Channels

Dynamic resource allocation is an important means to increase the sum capacity of fading multiple access channels. In this paper we consider vector multiaccess channels (channels where each user has multiple degrees of freedom) and study the eeect of power allocation as a function of the channel state on the sum capacity (or spectral eeciency) deened as the maximum sum of rates of users per unit degree of freedom at which the users can jointly transmit reliably, in an information theoretic sense, assuming random directions of received signal. Direct Sequence Code Division Multiple Access (DS-CDMA) channels and multiple access channels with multiple antennas at the receiver are two systems that fall under the purview of our model. Our main result is the identiication of a simple dynamic power allocation 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 instantaneous amplitude of channel state of that user alone and the structure of the policy is \waterrlling". In the context of DS-CDMA and in the special case of no fading, the asymptotically optimal power policy of waterrlling simpliies to constant power allocation over all realizations of signature sequences; this result veriies the conjecture made in 28]. We study the behavior of the asymptotically optimal waterrlling policy in various regimes of number of users per unit degree of freedom and signal to noise ratio (SNR). We also generalize this result to multiple classes, i.e., the situation when users in diierent classes have diierent average power constraints.