Asymptotically optimal water-filling in vector multiple-access channels

Abstract

Abstract-Dynamic resource allocation is an important means to increase the sum capacity of fading multiple-access 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 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 purview of our 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 context 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 [28]. 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.Index Terms-Code-division multiple access (CDMA), linear minimum mean-square error (MMSE) receivers, multiple antenna systems, power control, spectral efficiency, sum capacity, water-filling.

Information theoretic capacity of Gaussian cellular multiple-access MIMO fading channel

“…For an isolated cell asymptotic results on the sum capacity of MIMO Multiple Access Channels with the number of receive antennas and the number of transmitters increasing to infinity were obtained by Telatar [6] and by Viswanath et al [7]. The sum capacity with perfect Channel State information available at the receiver (CSIR) was found to grow linearly with min(n r , Kn t ).…”

Energy efficient multiuser scheduling: Exploiting the loss tolerance of the application

“…When we have asymptotically large population of the users in the system, the system state model represents the state space of a single user and each user takes her scheduling decisions independent of the other users. Such decoupling principle has been applied in [9], [10] to solve different communication problems.…”

“…Equation (10) specifies that a packet is scheduled only if y > κ p . Using (10), the cdf of the scheduled users is given by…”

Simplified power allocation for the DSL multi-access channel through column-wise diagonal dominance

“…This was the case for all scenarios we evaluated. Examining the PSD found with conventional waterfilling we see that the introduction of interference into the waterfilling equation in (6) results in a power allocation at lower frequencies. This is logical since crosstalk coupling increases with frequency.…”

“…Provided an optimal receiver structure is used the achievable rate sum can be shown to be [6] This problem was addressed in [6] where the optimal power allocation was shown to be a vector form of waterfilling which must occur simultaneously for all users within the system. The optimal power allocation is …”