Complex Non-Orthogonal Joint Diagonalization Based on LU and LQ Decompositions

In this paper, we propose a class of complex non-orthogonal joint diagonalization (NOJD) algorithms with successive rotations. The proposed methods consider LU or LQ decompositions of the mixing matrices, and propose to solve the NOJD problem via two successive stages: L-stage and U (or Q)-stage. Moreover, as the manifolds of target matrices in these stages could be appropriately parameterized by a sequence of simple elementary triangular or unitary matrices, which depend on only one or two parameters, the high-dimensional minimization problems could be replaced by a sequence of lower-dimensional ones. As such, the proposed algorithms are of simple closed-form in each iteration, and do not require the target matrices to be Hermitian nor positive definite. Simulations are provided to compare the proposed methods to other complex NOJD methods.