Interference alignment using finite and dependent channel extensions: The single beam case

Ruoyu Sun, Zhi Quan Luo

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12 Scopus citations


Vector space interference alignment (IA) is known to achieve high degrees of freedom (DoFs) with infinite-independent channel extensions, but its performance is largely unknown for a finite number of possibly dependent channel extensions. In this paper, we consider a K-user Mt×Mr MIMO interference channel (IC) with an arbitrary number of channel extensions T and arbitrary channel diversity order L (i.e., each channel matrix is a generic linear combination of L fixed basis matrices). We study the maximum DoF achievable via vector space IA in the single beam case (i.e., each user sends one data stream). We prove that the total number of users K that can communicate interference free using linear transceivers is upper bounded by NL+N2/4 , where N = min{MtT,MrT}. An immediate consequence of this upper bound is that for a Single-Input Single-Output (SISO) IC the DoF in the single beam case is no more than min {√5/4K,L+1/4T} When the channel extensions are independent, i.e., L achieves the maximum Mr MtT , we show that this maximum DoF lies in Mr+ Mt-1, Mr+Mt regardless of T. Unlike the well-studied constant MIMO IC case, the main difficulty is how to deal with a hybrid system of equation (zero-forcing condition) and inequalities (full rank condition). Our approach combines algebraic tools that deal with equations with an induction analysis that indirectly considers the inequalities.

Original languageEnglish (US)
Article number6951516
Pages (from-to)239-255
Number of pages17
JournalIEEE Transactions on Information Theory
Issue number1
StatePublished - Jan 1 2015

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  • Interference alignment
  • MIMO interference channel.
  • algebraic geometry
  • channel diversity


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