Analysis of low rank transform domain adaptive filtering algorithm

This paper analyzes an SVD-based low rank transform domain adaptive filtering algorithm and proves that it performs better than the normalized LMS. The method extracts an under-determined solution from an overdetermined least squares problem, using a part of the unitary transformation formed by the right singular vectors of the data matrix. The aim is to get as close to the solution of an overdetermined system as possible, using an under-determined system. Previous work based on the same framework, but with the DFT as the transformation, has shown considerable improvement in performance over conventional time domain methods like NLMS and affine projection. The analysis of the SVD-based variant helps us to understand the convergence behavior of the DFT-based low complexity method. We prove that the SVD-based method gives a lower residual than NLMS. Simulations confirm the theoretical results.