A family of flexible NLMS-type adaptive filter algorithms

The LMS adaptive filter algorithm can be viewed as the application of a simple iterative linear equation solver to an estimated time variant Wiener-Hopf equation. With this interpretation we can utilize the "bag-of-tricks" available in numerical linear algebra in devising new adaptive filter algorithms. Making use of the preconditioning paradigm, we present in this paper a new family of NLMS-type adaptive filter whose performance can be tailored to possible a priori knowledge of the autocorrelation properties of the input signal. The design of circulant preconditioning matrices for such adaptive filter algorithms is the main contribution of the paper.