On the optimum step size for the adaptive sign and LMS algorithms

A derivation is presented of the optimum step size to yield the most rapid convergence under a desired mean-square error (MSE) for adaptive finite impulse response digital filters equipped with the sign algorithm or the least-mean-square (LMS) algorithm. For white input data, the optimum step size is a simple closed-form function of the number of filter taps, the input signal variance, the initial MSE, and the desired MSE. This characteristic makes it easily designed in many practical applications. Computer simulations are employed to show the correctness and effectiveness of the derived results. >

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