### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 241-267 |

Number of pages | 27 |

Journal | IEEE Transactions on Information Theory |

Volume | 47 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Code-division multiple access (CDMA)
- Linear minimum mean-square error (MMSE) receivers
- Multiple antenna systems
- Power control
- Spectral efficiency
- Sum capacity
- Water-filling

### ASJC Scopus subject areas

- Information Systems
- Computer Science Applications
- Library and Information Sciences

### Cite this

*IEEE Transactions on Information Theory*,

*47*(1), 241-267. https://doi.org/10.1109/18.904525

**Asymptotically optimal water-filling in vector multiple-access channels.** / Viswanath, Pramod; Tse, David N.C.; Anantharam, Venkat.

Research output: Contribution to journal › Article

*IEEE Transactions on Information Theory*, vol. 47, no. 1, pp. 241-267. https://doi.org/10.1109/18.904525

}

TY - JOUR

T1 - Asymptotically optimal water-filling in vector multiple-access channels

AU - Viswanath, Pramod

AU - Tse, David N.C.

AU - Anantharam, Venkat

PY - 2001/1/1

Y1 - 2001/1/1

N2 - 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.

AB - 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.

KW - Code-division multiple access (CDMA)

KW - Linear minimum mean-square error (MMSE) receivers

KW - Multiple antenna systems

KW - Power control

KW - Spectral efficiency

KW - Sum capacity

KW - Water-filling

UR - http://www.scopus.com/inward/record.url?scp=0035091445&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035091445&partnerID=8YFLogxK

U2 - 10.1109/18.904525

DO - 10.1109/18.904525

M3 - Article

AN - SCOPUS:0035091445

VL - 47

SP - 241

EP - 267

JO - IEEE Transactions on Information Theory

JF - IEEE Transactions on Information Theory

SN - 0018-9448

IS - 1

ER -