A new reduced-bias multichannel gradient-based steepest descent algorithm for ill-conditioned correlation matrices

The convergence speed of the steepest descent (SD) adaptive algorithm is determined by the eigenvalue spread of the correlation matrix. When the correlation matrix is singular, the algorithm will take a long time to converge. The problem can be regularized by adding a small constant to the diagonal, but this comes at the price of introducing bias. This paper introduces a new adaptive algorithm that uses a family of steepest descent iterations which converge quickly while making the bias arbitrarily small. A numerical example discusses in some detail the operation of the new algorithm.