A new noise-constrained normalized least mean squares adaptive filtering algorithm

This paper proposes a new noise-constrained normalized least mean squares (NC-NLMS) adaptive filtering algorithm and studies its mean and mean square convergence behaviors. The new NC-NLMS algorithm is obtained by extending the noise-constrained LMS (NC-LMS) algorithm of Wei, which was proposed to explore the prior information on the noise variance in identifying unknown finite impulse response channels. It gives rise to a variable step-size LMS algorithm that is capable of achieving better tradeoff between the requirements to maximize convergence rate and to minimize misadjustment. Using a novel transformation approach, a new NC-NLMS algorithm is derived based on the NC-LMS framework. Additionally, robust statistics technique is employed to improve the robustness of the NC-NLMS algorithm in impulsive noise environment. Simulation shows that the proposed NC-NLMS offers improved performance than the NC-LMS algorithm due to the data normalization and its robust version can achieve satisfactory performance against impulse noise. Extension to the least M-estimate (LMM) and normalized least M-estimate (NLMM) algorithms were also proposed.