On implementation of adaptive bilinear filters for nonlinear active noise control

In this technical note, the simplified diagonal-structure bilinear filtered-X least mean square (SDBFXLMS) and channel-reduced diagonal-structure bilinear filtered-X least mean square (CRDBFXLMS) algorithms are proposed. Computational complexity for each proposed algorithm is analyzed to show the significant computational reduction in comparison with the diagonal-structure bilinear FXLMS (DBFXLMS) algorithm. For L=15$L=15$ (memory length of the bilinear filter), P=2$P=2$ (the corresponding number of the diagonal channels for the SDBFXLMS algorithm is L+2P=19$L+2P=19$ and the corresponding number of the diagonal channels for the CRDBFXLMS algorithm is 2P=4)$2P=4)$, and M=64$M=64$ (memory length of the secondary path estimate), the SDBFXLMS algorithm achieves 45% and 40% reduction of multiplications and additions, respectively, while the CRDBFXLMS algorithm acquires 78% reduction of multiplications and 76% reduction of additions. Computer simulations validate the satisfied control performances of the proposed algorithms.