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 -