On the use of multiple subspace multigrid linear equation solvers for improved convergence of NLMS-type adaptive filters

Largely overlooked insights into the convergence behavior of the (N)LMS algorithm focusing on its worst and best case performance is presented. These insights motivate the use of the multigrid paradigm, well known from the numerical solution of partial differential equations, as an important tool in achieving improved convergence speed in (N)LMS-type adaptive filters. We present such a multigrid adaptive filter algorithm, employing two subspaces, giving superior convergence performance relative to the (N)LMS algorithm at a very modest price in terms of computational complexity.