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A “Sequentially Drilled” Joint Congruence (SeDJoCo) Transformation With Applications in Blind Source Separation and Multiuser MIMO Systems

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4 Author(s)
Yeredor, A. ; Sch. of Electr. Eng., Tel-Aviv Univ., Tel-Aviv, Israel ; Bin Song ; Roemer, F. ; Haardt, M.

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.

Published in:

Signal Processing, IEEE Transactions on  (Volume:60 ,  Issue: 6 )

Date of Publication:

June 2012

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