An NLMS-type adaptive filter using multiple fixed preconditioning matrices

The normalized least mean squares (NLMS) algorithm is widely used in adaptive filtering applications, due to its robustness and low computational complexity. However, its convergence properties are suboptimal for non-white input signals. One variation that has been proposed [1] in order to alleviate this problem, is the introduction of a fixed preconditioning matrix into the filter update equation, making the convergence properties optimal for a different signal class, which can then be chosen by the designer. We propose here an algorithm that uses multiple such preconditioning matrices, and chooses the optimal preconditioner for use at any given moment during execution. If one of these preconditioners is the identity, the convergence performance will always be at least as good as that of the traditional NLMS. The choice of sparse, circulant preconditioners ensures that implementation can be realized by few additional computations compared to the NLMS.