Abstract: To deal with the trade-off between the mis-adjustment and the convergence speed in constant step-size adaptive filtering algorithms for under-modeling acoustic echo cancellation, a variable step-size proportionate normalized sub-band adaptive filtering algorithm, namely VSS-PNSAF, is proposed. Taking into account under-modeling noise and disturbance noise with a great impact on the performances of acoustic echo cancellation applications, the proposed algorithm obtains a step size control approach for VSS-PNSAF by forcing the posterior error to cancel negative effect of these noise and using the relation between the posteriori and the priori error signals. Echo cancellation simulation results confirm that the proposed algorithm can constitute a significant improvement in the convergence speed with very small mis-adjustment when compared with the constant step-size PNSAF algorithm.

Key words: under-modeling, acoustic echo cancellation, sparse impulse response, variable step size

摘要： 针对欠定模型条件下定步长比例归一化子带自适应滤波（PNSAF）算法收敛速度和稳态误差之间的矛盾，提出了一种变步长VSS-PNSAF算法。该算法将系统干扰噪声和欠定模型噪声对系统性能的影响考虑进滤波器系数更新过程中，利用后验误差对其进行补偿，根据先验误差与后验误差之间的联系，导出了一种适用于比例归一化子带自适应滤波算法的步长调节方法。该算法综合了子带自适应滤波、比例自适应算法及变步长方法的优点。仿真结果表明：与定步长比例归一化子带自适应滤波算法相比，所提算法具有更低的稳态误差和更快的收敛速度。

关键词: 欠定模型, 回声消除, 稀疏冲激响应, 变步长