Abstract: A novel cost function and a corresponding iterative algorithm for the non-orthogonal joint diagonalization of a set of eigen-matrices are proposed. The proposed cost function, improved from the classical least squares cost function that is the fourth function associated with the mixture matrix, is quadratic if two of the three parameter sets are fixed. Therefore, a new iterative algorithm based on the gradient descend method contains three sub-steps. In each sub-step, the closed solution is found by minimizing the cost function associated with one parameter group while fixing the others. Furthermore, global convergence is analyzed even in the presence of the estimation error of the eigen-matrix group. Finally, the results of the simulations illustrate that the proposed algorithm has better convergence performance, lower computational complexity, and can accurately retrieve the source signals from a set of received signals.

Key words: blind source separation (BSS), non-orthogonal joint diagonalization, least-squares approach, tri-iterative algorithm (TIA)