Comparison of RLS, LMS, and sign algorithms for tracking randomly time-varying channels

An approach to variable step-size LMS algorithm

“…The misalignment, as we show, is due to both the effects of gradient noise (weighting coefficients variations around the average value) and the weighting vector lag (difference between the average and the optimal value), [3,6]. It can be written, for the i-th weighting coefficient:…”

“…is a zero-mean random variable with the (3) and (4) we can express bias and variance for the i-th weighting coefficient, in steady state, as: As shown in [3,6], from (3) it is possible to obtain the optimal algorithm step size for each coefficient:…”

“…For the adaptive LMS filters in nonstationary environment, with standard assumptions as in [3,6], the MSD is given by:…”

“…Variable step-size methods [4,5,6] aim to improve the convergence of the LMS algorithm, while preserving the steady-state performance. There are several criteria for varying the LMS algorithm step-size: sign changes of successive samples of the gradient [4], squared instantaneous error and square of a time-averaging estimate of the successive error autocorrelation [5].…”

“…There is a number of adaptive algorithms, [1,2,3,4,6,8], derived from the conventional LMS algorithm. Variable step-size methods [4,5,6] aim to improve the convergence of the LMS algorithm, while preserving the steady-state performance.…”