The least mean square algorithm is widely used in many areas due to its simplicity and robustness. Within the LMS algorithm, the tap-length of the filter, defined as the number of tap coefficients of the adaptive filter, is an important factor that influences the performance and complexity of the LMS adaptive filter. If the tap-length is too long, it causes heavy computational burden and slows convergence rate, whereas if the tap-length is underestimated, the mean squared error (MSE) tends to increase. Therefore, segmented filter LMS (SF-LMS) algorithm, gradient descent LMS (GD-LMS) algorithm, and fractional tap-length LMS (FT-LMS) algorithm have been used to regulate the tap-length of filters. Among these variable LMS algorithms, the fractional tap-length least mean square (FT-LMS) algorithm has attracted attentions recently due to its less computational complexity and better convergence performance than other variable tap-length algorithms.
According to the steady-state performance analysis of the FT-LMS algorithm, correct choice of the step size for tap-length adaptation is very important. It provides a trade-off between the convergence rate and the steady-state bias of tap-length.
Jon Kwan Hak, a section head at the Faculty of Communications, has proposed an improved variable tap-length algorithm with variable step size for tap-length adaptation γ.
He confirmed the performance of the proposed algorithm by simulations for high and low noises, respectively. The results showed that for both noise conditions, the proposed algorithm obtains both fast convergence rate of the tap-length and small steady-state tap-length fluctuation.
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