A sequentially drilled joint congruence (SeDJoCo) transformation with applications in blind source separation and multiuser MIMO systems

Arie Yeredor*, Bin Song, Florian Roemer, Martin Haardt

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

We consider a particular form of the classical approximate joint diagonalization (AJD) problem, which we call a sequentially drilled joint congruence (SeDJoCo) transformation. The problem consists of a set of symmetric real-valued (or Hermitian-symmetric complex-valued) target-matrices. The number of matrices in the set equals their dimension, and the joint diagonality criterion requires that in each transformed (diagonalized) target-matrix, all off-diagonal elements on one specific row and column (corresponding to the matrix-index in the set) be exactly zeros, yet does not care about the other (diagonal or off-diagonal) elements. The motivation for this form arises in (at least) two different contexts: maximum likelihood blind (or semiblind) source separation and coordinated beamforming for multiple-input multiple-output (MIMO) broadcast channels. We prove that SeDJoCo always has a solution when the target-matrices are positive-definite. We also propose two possible iterative solution algorithms, based on defining and optimizing two different criteria functions, using Newton's method for the first function and successive Jacobi-like transformations for the second. The algorithms' convergence behavior and the attainable performance in the two contexts above are demonstrated in simulation experiments.

Original languageEnglish
Article number6168856
Pages (from-to)2744-2757
Number of pages14
JournalIEEE Transactions on Signal Processing
Volume60
Issue number6
DOIs
StatePublished - Jun 2012

Keywords

  • Approximate joint diagonalization
  • Blind source separation
  • Coordinated beamforming
  • HEAD
  • Independent component analysis
  • Multi-user MIMO
  • STJOCO

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