Delayed adaptive filtering based on NLMS algorithm with an error adjustment procedure

In delayed adaptive filtering, the customary tool is the delayed least-mean-square (DLMS) algorithm. However, in the DLMS algorithm, selection of suitable step-size is always done by trial and error. This paper proposes an alternative to the DLMS algorithm which avoids this drawback. The proposed algorithm is formulated using a normalized least-mean-square (NLMS) algorithm. The customized step-size is simply unity and an error adjustment procedure is used. In addition, we modify the proposed algorithm using a quantizing method to reduce the number of multiplications and divisions per input sample (MADPS). The simulated behavior is shown to agree well with theoretical prediction.