Adaptive filtering is widely utilized for many applications, such as acoustic echo cancellation, channel equalization, and active noise control. Subband adaptive filtering techniques have advantages in convergence performance for input signals that have a large spectral dynamic range. Nonetheless, the aliasing and band-edge effects degrade the convergence rate of traditional subband adaptive filters.

The improved multiband-structured subband adaptive filter (IMSAF) algorithm could enhance the convergence performance of multiband-structured subband adaptive filter algorithms and affine projection. However, the original improved multiband-structured subband adaptive filter algorithm with a fixed step-size factor has to compromise between convergence rate and steady-state misalignment.

To resolve the conflict between fast convergence rate and low steady-state misalignment of the fixed step-size improved multiband-structured subband adaptive filter algorithm, new improved multiband-structured subband adaptive filter algorithms with variable step-size matrix (VSM) are recently developed by researchers YAN Zhenhai, YANG Feiran, and YANG Jun from the Institute of Acoustics of the Chinese Academy of Science.

The formula of variable step-size matrix could be deduced by an assumption that the power of the subband a posteriori error is equal to the power of the subband noise. Two real-time estimation methods are introduced to calculate the power of subband noise.

One is based on the cross-correlation between the input signal and the a priori error signal. Consequently, different step sizes can be assigned to different subbands. The other is based on the assumption that the fullband filter vector has converged. Thus, the echo signals can be approximated by the output signals of adaptive filter. And then, the power of subband noise is calculated, assuming that the subband noise and the echo signals are uncorrelated.

The complexity of the proposed algorithm is compared with the improved multiband-structured subband adaptive filter algorithm. The sole difference between the proposed VSM algorithm and the standard improved multiband-structured subband adaptive filter algorithm is the calculation of the step size matrix.

The low-implementation schemes of the improved multiband-structured subband adaptive filter algorithm can be utilized in the proposed algorithm in a straightforward manner. The performance of the proposed approach is evaluated by computer simulations in the context of system identification and acoustic echo cancellation. Different input signals and different signal to noise ratio are used in the evaluation method, and the superiority of the proposed algorithm is fully proved.

The proposed algorithm is an excellent solution to the existing conflict. Whether the input signal is auto regressive signal or speech signal, research results demonstrate that the new algorithms can achieve better performance in convergence rate, steady-state misalignment, and tracking performance than the original improved multiband-structured subband adaptive filter algorithm with a fixed step-size factor. The method with variable step-size matrix can be also extended to other similar adaptive filtering algorithms.