## Abstract

Consider a multiuser communication system in a frequency selective environment whereby users share a common spectrum and can interfere with each other. Assuming Gaussian signaling and no interference cancelation, we study optimal spectrum sharing strategies for the maximization of sum-rate under separate power constraints for individual users. Since the sum-rate function is nonconcave in terms of the users' power allocations, there can be multiple local maxima for the sum-rate maximization problem in general. In this paper, we show that, if the normalized crosstalk coefficients are larger than a given threshold (roughly equal to 1/2), then the optimal spectrum sharing strategy is frequency division multiple access (FDMA). In case of arbitrary positive crosstalk coefficients, if each user's power budget exceeds a given threshold, then FDMA is again sum-rate optimal, at least in a local sense. In addition, we show that the problem of finding the optimal FDMA spectrum allocation is NP-hard, implying that the general problem of maximizing sum-rate is also NP-hard, even in the case of two users. We also propose several simple distributed spectrum allocation algorithms that can approximately maximize sum-rates. Numerical results indicate that these algorithms are efficient and can achieve substantially larger sum-rates than the existing Iterative Waterfilling solutions, either in an interference-rich environment or when the users' power budgets are sufficiently high.

Original language | English (US) |
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Pages (from-to) | 1153-1175 |

Number of pages | 23 |

Journal | IEEE Transactions on Information Theory |

Volume | 55 |

Issue number | 3 |

DOIs | |

State | Published - 2009 |

### Bibliographical note

Funding Information:Manuscript received June 25, 2006; revised June 12, 2008. Current version published February 25, 2009. This work was supported in part by the National Science Foundation, Grant DMS-0312416 and in part by the USDOD ARMY, Grant W911NF-05-1-0567. The work of S. Hayashi was performed while he was on a postdoctoral visit at the University of Minnesota.

## Keywords

- Frequency-division multiple-access (FDMA) optimality
- Multiuser communication system
- Spectrum management
- Sum-rate maximization