Complex non-orthogonal joint diagonalization with successive givens and hyperbolic rotations

Complex blind source separation (BSS) received growing interests in many practical applications in the past decades, and non-orthogonal joint diagonalization (JD) of a set of complex matrices plays an instrumental role in solving these problems. In this paper, we propose a new complex non-orthogonal JD algorithm. This algorithm successively finds the optimal Givens and hyperbolic rotation matrices that constitute the elementary rotation matrix in each iteration in an alternating manner. It does not require the target matrices to be Hermitian, and thus could be well adapted to BSS problems that involve fourth-order cumulant slices or time-lagged covariance matrices. Simulations are provided to compare the proposed algorithm with other JD algorithms.