We present a new structure for parallel affine projection (AP) filters with different step-sizes. By observing their error signals, the proposed alternating AP (A-AP) filter selects one of the two AP filters and updates the weights of the selected filter for each iteration. As a result, the total computations required for the proposed structure is almost the same as that for a single AP filter. Experimental results show that the proposed alternating selection scheme extracts the best properties of each component filter, namely fast convergence and small steady-state error.

This paper provides a novel normalized sign least-mean square (NSLMS) algorithm which updates only a part of the filter coefficients and simultaneously performs sparse updates with the goal of reducing computational complexity. A combination of the partial-update scheme and the set-membership framework is incorporated into the context of L∞-norm adaptive filtering, thus yielding computational efficiency. For the stabilized convergence, we formulate a robust update recursion by imposing an upper bound of a step size. Furthermore, we analyzed a mean-square stability of the proposed algorithm for white input signals. Experimental results show that the proposed low-complexity NSLMS algorithm has similar convergence performance with greatly reduced computational complexity compared to the partial-update NSLMS, and is comparable to the set-membership partial-update NLMS.

We present a low-complexity complementary pair affine projection (CP-AP) adaptive filter which employs the intermittent update of the filter coefficients. To achieve both a fast convergence rate and a small residual error, we use a scheme combining fast and slow AP filters, while significantly reducing the computational complexity. By employing an evolutionary method which automatically determines the update intervals, the update frequencies of the two constituent filters are significantly decreased. Experimental results show that the proposed CP-AP adaptive filter has an advantage over conventional adaptive filters with a parallel structure in that it has a similar convergence performance with a substantial reduction in the total number of updates.