A fast non-unitary joint diagonalization algorithm based on utilizations of parametric structures

A parametric structures based fast joint diagonalization (PSJD) algorithm for non-unitary diagonalization of a set of complex target matrices is presented to cope with the problem that the blind source separation by fast Frobenius diagonalization (FFDIAG) algorithm is not applicable in the complex-valued space and its separation performance is lower. The algorithm firstly transforms the complex target matrices into real-symmetric ones. Secondly, the problem of simultaneous diagonalization of matrices is transformed into a series of linear least-squares problems through second-order approximation to contract functions, and the elements of the updating matrix are directly estimated. The computational complexity for estimating the diagonalizer and for updating the target matrices is significantly reduced by making full use of the structure information of the transformed target matrices. In order to overcome the drawback of fixed step size adopted in the FFDIAG that may not strike a balance between the convergence rate and strictly diagonally dominant property of the update matrix, the proposed algorithm uses the adaptive learning rate determined from the estimation of the update matrix in each iteration to improve the convergence property. Results of numerical simulations show that the convergence rate of PSJD algorithm is not very sensitive in a wide range of step-size values. When the step size is 0.1, the number of iterations required to reach convergence is 42% less than that of the fixed step-size method. © 2016, Editorial Office of Journal of Xi'an Jiaotong University. All right reserved.