Convergence time reduction provided by a block length control method applied to the “summational” NLMS algorithm.

It is known in the normalized least mean square (NLMS) algorithm that the convergence time can be reduced by applying a control in which the step gain is gradually reduced, as the estimation precision is improved. A problem in realizing this idea is that the instantaneous value of the estimation precision which is needed in the control of the step gain cannot be observed directly from the residual signal which contains external disturbances. This paper considers a block length control, which can be used in the “summational” NLMS method. The method is able to improve the convergence of the estimation precision, as in step gain control, and a method of reducing the convergence time is proposed, utilizing the fact that saturation of the convergence behavior can be observed iteratively by extending the block. In addition, it is highly likely in an actual adaptive system that the reference signal, the power of the external disturbance, and the impulse response of the unknown system to be estimated as the coefficients of the finite impulse response (FIR) filter will change. It is not realistic to ignore the possibility of these changes in discussing the control of convergence. In the last part of this paper, it is shown that the proposed control method can handle these changes. © 1999 Scripta Technica, Electron Comm Jpn Pt 3, 82(12): 54–64, 1999 [ABSTRACT FROM AUTHOR]