## Abstract

A spatially correlated broadcast setting with M antennas at the base station and M users (each with a single antenna) is considered. We assume that the users have perfect channel information about their links and the base station has only statistical information about each user's link. The base station employs a linear beamforming strategy with one spatial eigen-mode allocated to each user. The goal of this work is to understand the structure of the beamforming vectors that maximize the ergodic sum-rate achieved by treating interference as noise. In the M = 2 case, we first fix the beamforming vectors and compute the ergodic sum-rate in closed-form as a function of the channel statistics. We then show that the optimal beamforming vectors are the dominant generalized eigenvectors of the covariance matrices of the two links. It is difficult to obtain intuition on the structure of the optimal beamforming vectors for M > 2 due to the complicated nature of the sum-rate expression. Nevertheless, in the case of asymptotic M, we show that the optimal beamforming vectors have to satisfy a set of fixed-point equations.

Original language | English |
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Title of host publication | 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Proceedings |

Place of Publication | Piscataway, NJ |

Publisher | Institute of Electrical and Electronics Engineers (IEEE) |

Pages | 2268-2272 |

Number of pages | 5 |

ISBN (Print) | 9781424469604 |

DOIs | |

Publication status | Published - 2010 |

Externally published | Yes |

Event | 2010 IEEE International Symposium on Information Theory, ISIT 2010 - Austin, TX, United States Duration: 13 Jun 2010 → 18 Jun 2010 |

### Other

Other | 2010 IEEE International Symposium on Information Theory, ISIT 2010 |
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Country | United States |

City | Austin, TX |

Period | 13/06/10 → 18/06/10 |