Extension of the “Sequentially Drilled” Joint Congruence Transformation (SeDJoCo) Problem

The Sequentially Drilled Joint Congruence (SeDJoCo) transformation has been identified as an important tool in the context of both Blind Source Separation (BSS) and closed-form Coordinated Beamforming (CBF) for the multi-user MIMO downlink. It can be interpreted as a new tensor decomposition. In this contribution, we introduce an extension of the SeDJoCo problem and address its links to the field of Independent Vector Analysis (IVA) and to CBF in a multicast framework. A solution of the extended SeDJoCo problem is proposed by extending the LU decomposition-based concept that is frequently used for joint matrix diagonalization. Data sets in an IVA setup are used in numerical simulations which show that the proposed algorithm is very efficient in finding the exact solution for the extended SeDJoCo problem, at least in a two-data-set case.