On proportionate-type NLMS algorithms for fast decay of output error at all times

Recently, we have proposed three schemes for gain allocation in proportionate-type NLMS algorithms for fast decay at all time. The gain allocation schemes are based on: (1) maximization of one-step decay of the mean square output error, (2) maximization of one-step conditional probability density for true weight values, and (3) adaptation of ¿-law for compression of weight estimates using the output square error. Scheme (1) implies sorting and time consuming calculations that can restrict its ability to work in real-time. We will propose usage of computationally simplified schemes and show that the loss in performance is negligible. Scheme (3) needs calculation of a logarithmic function that we will replace by calculation of a piecewise linear function and show that there is no significant loss in performance. Schemes (1) and (2) use fast-converging biased estimates to calculate gain allocation. The performance deterioration because of the biased estimates is especially noticeable in the steady-state regime. We are going to consider combining the fast-converging biased estimates with slow-converging unbiased estimates. The combination will be related to the magnitude of the output square error. Comparison between the original and modified algorithms in sparse echo-cancellation scenarios will be presented for white input, color input, and voice inputs.