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A variable‐step size NLMS algorithm based on the cross‐correlation between the squared output error and the near‐end input signal

In this work, we introduce an adaptive variable‐step size normalized least mean squares algorithm to be used in finite impulse response structures. In our proposal, the step size is adjusted according to the cross‐correlation between the squared output error of the adaptive filter and the near‐end input signal. We show that the step increases or decreases as the error increases or decreases. This behavior is used to update the filter coefficients in the proposed adaptive filter. The proposed algorithm is named VSS‐CR, after variable step size based on cross‐correlation. This proposal was evaluated using computer simulations, and the obtained results show that it achieves higher levels of echo return loss enhancement and less misalignment than other algorithms. We identified a trade‐off between steady‐state performance and convergence time; the VSS‐CR achieves higher levels of echo reduction, but it takes some more time to reach its mean square error steady‐state value. This algorithm can be used in acoustic echo canceling in public switched telephone networks. © 2019 Institute of Electrical Engineers of Japan. Published by John Wiley & Sons, Inc.