Low-Complexity Decorrelation NLMS Algorithms: Performance Analysis and AEC Application

In the traditional decorrelation normalized least-mean-square (D-NLMS) algorithm, high computational complexity is mainly caused by finding the decorrelated-vector. To address this issue, this paper proposes a low-complexity implementation approach, which cleverly utilizes the periodic update of the decorrelation parameter and delay characteristics of the decorrelated-vector. We firstly develop two low-complexity decorrelation algorithms, (i) fast D-NLMS (FD-NLMS) and (ii) approximate FD-NLMS (AFD-NLMS) which is an approximate version of the first algorithm with even smaller computational requirement. Theoretical performance of the FD-NLMS scheme is also derived. To further obtain low steady-state error in the acoustic echo cancellation (AEC) application, separated-decorrelation AEC structure and robust step-size schemes are designed, resulting in two improved algorithms, namely, fast separated-decorrelation NLMS (FSD-NLMS) and approximate FSD-NLMS (AFSD-NLMS). Finally, extensive simulation study on system identification and AEC is undertaken to verify the efficiency of the proposed methods.