Step-size optimization of the BNDR-LMS algorithm

The binormalized data-reusing least mean squares (BNDR-LMS) algorithm has been recently proposed and has been shown to have faster convergence than other LMS-like algorithms in cases where the input signal is strongly correlated. This 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).