Diophantine approach to blind interference alignment of homogeneous k-user 2x1 MISO broadcast channels

Q. F. Zhou, Q. T. Zhang, Chung Ming Lau

Research output: Journal article publicationJournal articleAcademic researchpeer-review

19 Citations (Scopus)


The sufficient condition for a blindly interference-aligned 2-user 2x 1 broadcast channel (BC) in homogeneous block fading to achieve its maximal 4/3 degree-of-freedom (DoF) is well understood. However, the condition for the general case, i.e., a homogeneous K-user 2x 1 BC, to achieve the corresponding optimal \tfrac{2K}{2+K-1} DoF remains unsolved and is, thus, the focus of this paper. Here, a K-user 2x 1 BC is said to be BIA-feasible if it achieves the optimal DoF via blind interference alignment (BIA). In this paper, we cast this general BIA-feasibility problem in the framework of finding solutions for a system of linear Diophantine equations. Then by studying the solvability of the Diophantine system, we derive the necessary and sufficient conditions on the K users' fading block offsets to ensure the BIA feasibility of the K-user BC. Using the results above, we also examine a 2x 1 broadcast network with M homogeneous users, in which their offsets are independent of one another and are uniformly distributed over a coherence block. We show by simulations that when the network contains M=11 homogeneous users, there is more than 95% chance of finding 3 users to form a BIA-feasible 3-user 2x 1 BC. Furthermore, increasing M to infinity ensures a virtual multiple-input multiple-output (MIMO) channel to be formed from the DoF perspective.
Original languageEnglish
Article number6601777
Pages (from-to)2141-2153
Number of pages13
JournalIEEE Journal on Selected Areas in Communications
Issue number10
Publication statusPublished - 1 Oct 2013


  • Blind IA
  • DoF
  • homogeneous block fading
  • virtual MIMO

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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