The NLMS algorithm using a quasi-orthonormal initialization scheme for acoustic cancellation

In acoustic echo cancellation, we propose the normalized least-mean-square (NLMS) algorithm with a quasi-orthonormal initialization scheme to overcome slow convergence due to the correlated speech signals. The quasi-orthonormal initialization scheme is realized by a set of the causal sine vectors which are the low-pass filtered impulse signals at different time-scaled positions. Hence, the loudspeaker-room-microphone (LRM) system can be modeled by these causal sine vectors. The NLMS algorithm after our initialization processing can efficiently predict the outputs of the LRM system according to the inputs. In case of the outputs of the LRM system corrupted by additive white noises with a variance of 0.0001, the proposed initialization scheme can improve echo return loss enhancement (ERLE) of 50 dB. The computer simulation results demonstrate that finite impulse response (FIR) structure of the NLMS algorithm using the proposed initialization scheme employs fast convergence and low computational complexity