### Abstract

A unified approach to power control is proposed for maximizing utility in terms of energy efficiency in code-division multiple access (CDMA) networks. The approach is applicable to a large family of multiuser receivers including the matched filter, the decorrelator, the linear minimum mean-square error (MMSE) receiver, and the (nonlinear) optimal detectors. It exploits the linear relationship between the transmit power and the output signal-to-interference-plus-noise ratio (SIR) for each user in the large-system limit. Suppose that each user seeks to selfishly maximize its own energy efficiency, a unique Nash equilibrium is shown to exist and be SIR-balanced, thus extending a previous result on linear receivers. A unified power control algorithm for reaching the Nash equilibrium is proposed, which adjusts transmit powers iteratively by computing the large-system multiuser efficiency, which is independent of instantaneous spreading sequences. The convergence of the algorithm is proved for linear receivers, and is demonstrated via simulation for the multiuser maximum likelihood detector. Moreover, the performance of the algorithm in finite-size systems is studied and compared with that of a conventional power control scheme, in which user powers depend on the instantaneous spreading sequences.

Original language | English (US) |
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Pages (from-to) | 1208-1216 |

Number of pages | 9 |

Journal | IEEE Transactions on Wireless Communications |

Volume | 7 |

Issue number | 4 |

DOIs | |

State | Published - Apr 8 2008 |

### All Science Journal Classification (ASJC) codes

- Computer Science Applications
- Electrical and Electronic Engineering
- Applied Mathematics

### Keywords

- Code-division multiple access (CDMA)
- Nash equilibrium
- efficiency
- energy
- game theory
- large systems
- multiuser detection
- multiuser efficiency
- power control

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## Cite this

*IEEE Transactions on Wireless Communications*,

*7*(4), 1208-1216. https://doi.org/10.1109/TWC.2008.05667