Application of orthonormal transforms to implementation of quasi-LMS/Newton algorithm

An efficient implementation of the LMS/Newton (LMSN) algorithm is proposed. The scheme uses a quasi-inverse of the correlation matrix of the input instead of its exact inverse. The proposed algorithm, which is an alternative formulation of a class of transform domain adaptive filters (TDAFs), has some advantages over the TDAF. A feature of the scheme that greatly simplifies its implementations is the possibility of coarse quantization of the stochastic gradient terms in the adjustment recursion. To back this up, an analysis of the LMSN algorithm, which includes the effect of coarse quantization of the stochastic gradient terms, is given for correlated Gaussian data. Computer simulation results that support the developed theories are also presented