LS detection guided NLMS estimation of sparse systems

In various estimation problems, the system being estimated may be represented by a sparse parameter vector, such that only a ´small´ number of the vector elements are ´significant´ or ´active´. In this paper we propose a normalised least mean square (NLMS) estimator which incorporates a least squares based active parameter criterion; such that NLMS adaptation is applied only to those system parameters detected as being active. This results in a significant improvement in convergence rates, as compared to the standard NLMS estimator. Importantly, for sparse systems, the computational cost of the newly proposed detection guided NLMS estimator is only slightly greater than that of the standard NLMS estimator.