This letter develops theoretical analysis of the normalized LMS algorithm (NLMSA) for use in complex-domain adaptive filters in the presence of impulse noise at filter input. We propose a new "stochastic" model for such impulse noise, and assume that filter reference input process is a white process, e.g., digital QAM data, White & Gaussian process, etc. In the analysis, we derive a simple difference equation for mean square tap weight misalignment (MSTWM). Experiment is carried out to demonstrate effectiveness of the NLMSA in robust filtering in the presence of the impulse noise at the filter input. Good agreement between simulated and theoretically calculated filter convergence, in a transient phase as well as in a steady-state, proves the validity of the analysis.

A pipelined architecture is proposed for the normalized least mean square (NLMS) adaptive digital filter (ADF). Pipelined implementation of the NLMS has not yet been proposed. The proposed architecture is the first attempt to implement the NLMS ADF in the pipelined fashion. The architecture is based on an equivalent expression of the NLMS derived in this study. It is shown that the proposed architecture achieves a constant and a short critical path without producing output latency. In addition, it retains the advantage of the NLMS, i. e. , that the step size that assures the convergence is determined automatically. Computer simulation results that confirm that the proposed architecture achieves convergence characteristics identical to those of the NLMS.

Single-reference and multi-reference noise canceller (SRNC and MRNC) performances are investigated based on correlation between signal and noise. Exact relations between these noise canceller performances and signal-noise correlation have not been well discussed yet. In this paper, the above relations are investigated based on theoretical, analysis and computer simulation. The normalized LMS (NLMS) algorithm is employed. Uncorrelate, partially correlated, and correlated signal and noise combinations are taken into account. Computer simulation is carried out, using real speech, white noise, real noise sound, sine wave signals, and their combinations. In the SRNC problem, spectral analysis is applied to derive the canceller output power spectrum. From the simulation results, it is proven that the SRNC performance is inversely proportional to the signal-noise correlation as expected by the theoretical analysis. From the simulation results, the MRNC performance is more sensitive to the signal-noise correlation than that of SRNC. When the signal-noise correlation is high, by using a larger number of adaptive filter taps, the noise is reduced more, and, the signal distortion is increased. This means the signal components included in the noise are canceled exactly.

This paper presents an equation capable of briefly evaluating the length of white noise sequence to be sent as a training signal. The equation is formulated by utilizing the formula describing the convergence property, which has been derived from the IIR filter expression of the NLMS algorithm. The result revealed that the length is directly proportional to I/[K(2-K)] where K is a step gain and I is the number of the adaptive filter taps.

This letter presents a new algorithm for echo cancellers, which prevents the reduction of echo return loss due to a double-talk. The essence of the algorithm is to introduce signal delays to avoid the reduction. A convergence condition in the algorithm was examined by using the IIR filter expression of the NLMS algorithm, and it was concluded that the IIR filter should be a low pass filter with unity gain. The condition is accomplished by selecting a small step gain.