LMSNLMS

LMSNLMS refers to a class of adaptive filtering algorithms that combine ideas from the standard least-mean-squares (LMS) approach with normalized LMS (NLMS) concepts. The aim is to maintain the simplicity of LMS while achieving the robustness to input power variations that NLMS provides. In practice, LMSNLMS methods adjust the filter coefficients in response to the error between a desired signal and the filter output, using a step size or update rule that accounts for input signal power.

A representative implementation employs an NLMS-style normalization within the LMS framework, so the weight update uses a normalized step size. This can be expressed in a form similar to w(n+1) = w(n) + [mu / (epsilon + ||x(n)||^2)] e(n) x(n), where e(n) is the error and x(n) is the input vector. Another common variant is a hybrid scheme that blends or switches between LMS and NLMS updates based on input statistics or error magnitude, seeking a balance between convergence speed and stability.

LMSNLMS methods are used in a range of adaptive filtering applications, including acoustic echo cancellation, channel identification and equalization, adaptive noise control, and system identification. They typically offer faster convergence than pure LMS under colored inputs and provide better invariance to input power changes, while maintaining low computational complexity.

Key considerations include the choice of the base step size and the regularization parameter used in normalization, which affect convergence speed, misadjustment, and stability. Like other adaptive filters, LMSNLMS can be sensitive to nonstationary environments and noise, and may require careful initialization and parameter tuning.

See also: LMS, NLMS, adaptive filtering, echo cancellation.