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A new algorithm, the binonnalized data-reusing least mean-squares (LMS) algorithm is presented. The new algorithm has been found to converge faster than other LMS-like algorithms, such as the Normalized LMS algorithm and several data-reusing LMS algorithms, in cases where the input signal is strongly correlated. The computational complexity of this new algorithm is only slightly higher than a recently proposed normalized new data-reusing LMS algorithm. Superior performance in convergence speed is, however, followed by a higher misadjustment if the step-size is close to the value which allows the fastest convergence. An optimal step-size sequence for this algorithm is proposed after considering a number of simplifying assumptions. Moreover, this work brings insight in how to deal with these conflicting requirements of fast convergence and minimum steady-state mean-square error (MSE).
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