Asymptotically optimal water-filling in vector multiple-accesschannels
Viswanath, P.; Tse, D.N.C.; Anantharam, V.
Information Theory, IEEE Transactions on
Volume 47, Issue 1, Jan 2001 Page(s):241 - 267
Digital Object Identifier 10.1109/18.904525
Summary:Dynamic resource allocation is an important means to increase the
sum capacity of fading multiple-access channels (MACs). In this paper,
we consider vector multi-access 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
information-theoretic sense, assuming random directions of received
signal. Direct-sequence code-division multiple-access (DS-CDMA) channels
and MACs with multiple antennas at the receiver are two systems that
fall under the model. Our main result is the identification 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 “water-filling.” In
the contest of DS-CDMA and in the special case of no fading, the
asymptotically optimal power policy of water-filling simplifies to
constant power allocation over all realizations of signature sequences;
this result verifies the conjecture made in Verdu and Shamai (1999). We
study the behavior of the asymptotically optimal water-filling 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 different classes have
different average power constraints
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