Blind separation of temporally correlated noncircular sources using complex matrix joint diagonalization

Abstract

In this paper, we introduce a new blind source separation (BSS) method for temporal correlated noncircular sources that uses widely linear filter (WLF) model to efficiently describe the temporal structure. The algorithm consists of a WLF coefficients estimator followed by complex matrix joint diagonalization. In the derivation of the new BSS algorithm, an emerging matrix joint diagonalization issue needs to be addressed. Subsequently, a complex matrix joint diagonalization algorithm based on successive Shear and Givens rotations (SGR) is proposed to deal with the new joint diagonalization problem. Simulations of SGR show that it converges fast and converges to excellent value, and it shows a satisfactory anti-perturbation performance of matrix for the new BSS algorithm. We compare the performance of the new BSS algorithm with several competing algorithms, and the simulation results demonstrate the superior performance of the proposed BSS algorithm for both noncircular complex Gaussian and non-Gaussian sources.