TY - JOUR

T1 - A sequentially drilled joint congruence (SeDJoCo) transformation with applications in blind source separation and multiuser MIMO systems

AU - Yeredor, Arie

AU - Song, Bin

AU - Roemer, Florian

AU - Haardt, Martin

PY - 2012/6

Y1 - 2012/6

N2 - 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.

AB - 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.

KW - Approximate joint diagonalization

KW - Blind source separation

KW - Coordinated beamforming

KW - HEAD

KW - Independent component analysis

KW - Multi-user MIMO

KW - STJOCO

UR - http://www.scopus.com/inward/record.url?scp=84861163973&partnerID=8YFLogxK

U2 - 10.1109/TSP.2012.2190728

DO - 10.1109/TSP.2012.2190728

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AN - SCOPUS:84861163973

SN - 1053-587X

VL - 60

SP - 2744

EP - 2757

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

IS - 6

M1 - 6168856

ER -