Sparse system identification has attracted much attention in the field of adaptive algorithms, and the adaptive filters for sparse system identification are studied. Firstly, a new family of proportionate normalized least mean square (PNLMS) adaptive algorithms that improve the performance of identifying block-sparse systems is proposed. The main proposed algorithm, called block-sparse PNLMS (BS-PNLMS), is based on the optimization of a mixed ℓ2,1 norm of the adaptive filter\u27s coefficients. A block-sparse improved PNLMS (BS-IPNLMS) is also derived for both sparse and dispersive impulse responses. Meanwhile, the proposed block-sparse proportionate idea has been extended to both the proportionate affine projection algorithm (PAPA) and the proportionate affine projection sign algorithm (PAPSA).
Secondly, a generalized scheme for a family of proportionate algorithms is also presented based on convex optimization. Then a novel low-complexity reweighted PAPA is derived from this generalized scheme which could achieve both better performance and lower complexity than previous ones. The sparseness of the channel is taken into account to improve the performance for dispersive system identification. Meanwhile, the memory of the filter\u27s coefficients is combined with row action projections (RAP) to significantly reduce the computational complexity.
Finally, two variable step-size zero-point attracting projection (VSS-ZAP) algorithms for sparse system identification are proposed. The proposed VSS-ZAPs are based on the approximations of the difference between the sparseness measure of current filter coefficients and the real channel, which could gain lower steady-state misalignment and also track the change in the sparse system --Abstract, page iv
