### Abstract

We consider an interference network with multi-carrier transmission over M parallel sub-channels. There are K transmitter-receiver pairs, each transmitter transmits a single data stream with a rank-one precoding matrix, and the receivers are assumed to be linear. We show that a necessary condition for zero interference (alignment across sub-channels) is K ≤ 2M-2. In contrast, for a Multi-Input Multi-Output (MIMO) interference network with M×M spatial channels (full channel matrices) the corresponding condition is known to be K ≤ 2M -1. We also characterize the sum rate at high Signal-to-Noise Ratios (SNR) by bounding the SNR offset (x-intercept) of the asymptote of the sum rate vs SNR curve. For a randomly chosen aligned solution as M increases, this offset shifts to the right as logM. In contrast, the SNR offset for a MIMO interference network does not increase with M. An approximation for the performance of sampling the best out of L aligned solutions is also presented. Numerical results show the analytical asymptotes accurately predict the sum rate curves at moderate to high SNRs.

Original language | English (US) |
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Title of host publication | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 |

Pages | 26-30 |

Number of pages | 5 |

DOIs | |

State | Published - Oct 26 2011 |

Event | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation Duration: Jul 31 2011 → Aug 5 2011 |

### Other

Other | 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 |
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Country | Russian Federation |

City | St. Petersburg |

Period | 7/31/11 → 8/5/11 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Information Systems
- Modeling and Simulation
- Applied Mathematics

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## Cite this

*2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011*(pp. 26-30). [6034039] https://doi.org/10.1109/ISIT.2011.6034039