Second-order blind signal separation with optimal step size

Abstract

This paper proposes a new computational procedure for solving the second-order gradient-based blind signal separation (BSS) problem with convolutive mixtures. The problem is formulated as a constrained optimization problem where the time domain constraints on the unmixing matrices are added to ease the permutation effects associated with convolutive mixtures. A linear transformation using QR factorization is developed to transform the constrained optimization problem into an unconstrained problem. A conjugate gradient procedure with the step size derived optimally at each iteration is then proposed to solve the optimization problem. The advantage of the procedure is that it has low computational complexity, as it does not require multiple evaluations of the objective function. In addition, fast convergence of the conjugate gradient algorithm makes it suitable for online implementation. The convergence of the conjugate gradient algorithm with optimal step size is compared to the fixed step size case and the optimal step size steepest descent algorithm. Evaluations are performed in real and simulated environments.