### Abstract

We explore the degrees of freedom of M, × N user wireless X networks, i.e., networks of M transmitters and N receivers where every transmitter has an independent message for every receiver. We derive a general outer bound on the degrees of freedom region of these networks. When all nodes have a single antenna and all channel coefficients vary in time or frequency, we show that the total number of degrees of freedom of the X network is equal to MN/M + N - 1 per orthogonal time and frequency dimension. Achievability is proved by constructing interference alignment schemes for X networks that can come arbitrarily close to the outer bound on degrees of freedom. For the case where either M = 2 or N = 2 we find that the degrees of freedom characterization also provides a capacity approximation that is accurate to within O(1). For these cases the degrees of freedom outer bound is exactly achievable.

Original language | English (US) |
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Pages (from-to) | 3893-3908 |

Number of pages | 16 |

Journal | IEEE Transactions on Information Theory |

Volume | 55 |

Issue number | 9 |

DOIs | |

State | Published - Sep 4 2009 |

### All Science Journal Classification (ASJC) codes

- Information Systems
- Computer Science Applications
- Library and Information Sciences

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## Cite this

*IEEE Transactions on Information Theory*,

*55*(9), 3893-3908. https://doi.org/10.1109/TIT.2009.2025541