On implementation of adaptive bilinear filters for nonlinear active noise control

• Two efficient BFXLMS algorithms are proposed for nonlinear active noise control.
• Computational complexity for each proposed algorithm is analyzed.
• Computer simulations validate the satisfied control performances.

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=15L=15 (memory length of the bilinear filter), P=2P=2 (the corresponding number of the diagonal channels for the SDBFXLMS algorithm is L+2P=19L+2P=19 and the corresponding number of the diagonal channels for the CRDBFXLMS algorithm is 2P=4)2P=4), and M=64M=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.