## Abstract

We consider the joint optimization of beamformers and linear receivers in a MIMO interference network. Each transmitter transmits a single beam corresponding to a rankone precoder. When the number of users K is greater than the number of antennas at each terminal N, the maximum degrees of freedom is achieved via spatial interference alignment. Interference alignment is feasible for up to K = 2N-1 users, in which case there is a finite number of solutions to the alignment conditions. This number of solutions increases rapidly with N, and the solutions depend only on the cross-channel coefficients (i. e., they are independent of the direct channels). To maximize the achievable sum rate at high SNRs we therefore wish to select an aligned solution which is best matched to the direct channels. We evaluate the performance of this scheme for large K and N, assuming that the solution is the best out of a random subset of aligned solutions. We then compare numerically this performance with the performance of previously proposed numerical (e. g., forward-backward) techniques for optimizing beams, and a new technique which tracks the local optimum as the SNR is incrementally increased, similar to a homotopy method for improving convergence properties. We observe that the incremental technique typically achieves better performance than the previously proposed methods.

Original language | English (US) |
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Title of host publication | 2010 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010 |

Pages | 1182-1187 |

Number of pages | 6 |

DOIs | |

State | Published - Dec 1 2010 |

Event | 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010 - Monticello, IL, United States Duration: Sep 29 2010 → Oct 1 2010 |

### Other

Other | 48th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2010 |
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Country | United States |

City | Monticello, IL |

Period | 9/29/10 → 10/1/10 |

## ASJC Scopus subject areas

- Computer Networks and Communications
- Control and Systems Engineering