۱- Introduction

۲- Background on IMSAF

۳- The SR-IMSAF algorithm

۴- The DSR-IMSAF algorithm

۵- General update equation

۶- Extension of the framework

۷- Mean-square performance analysis of the family of IMSAF algorithms

۸- Mean and mean-square stability of the family of IMSAF algorithms

۹- Computational complexity

۱۰- Simulation results

۱۱- Conclusion

References

Abstract

The improved multiband structured subband adaptive filter (IMSAF) utilizes the input regressors at each subband to speed up the convergence rate of MSAF. When the number of input regressors is increased, the convergence rate of the IMSAF algorithm improves at the cost of increased complexity. The current study introduces two new IMSAF algorithms with low computational complexity feature. In the first algorithm, a subset of input regressors at each subband is optimally picked out during the adaptation. In the second approach, the number of selected input regressors is dynamically changed at each subband for every iteration. The introduced algorithms are called selective regressor IMSAF (SR-IMSAF) and dynamic selective regressor IMSAF (DSR-IMSAF). The SR-IMSAF and DSR-IMSAF are shown to be capable of outperforming the full-update IMSAF while the computational complexity is kept low. In the following, the general update equation to establishment of the family of IMSAF algorithms is presented. Accordingly, the mean-square performance analysis of the algorithms is studied in a unified way and the general theoretical expressions for transient, steady-state, and the stability bounds for IMSAF, SR-IMSAF, and DSR-IMSAF are derived. The good performance of the introduced algorithms and the validity of the derived theoretical relations are justified by presenting various experimental results.

Introduction

Adaptive filters are applied in many applications such as system identification, channel equalization, signal prediction, and noise cancellation [1], [2], [3]. In these applications, the generated signals are processed to identify the impulse response of the unknown system. This objective is successfully achieved by using adaptive filters rather than conventional digital filters. The adaptive filters utilize a recursive algorithm to design itself. The algorithm updates the filter coefficients through successive iterations and finally converges to the optimal Wiener-Hopf solution. The performance of an adaptive filtering algorithm is evaluated by the rate of convergence, misadjustment, and computational complexity features. The conventional LMS adaptive filter algorithm has the advantage of being very simple; it is easy to implement; and it has a very low computational complexity. However, when the input signal is highly colored, the LMS convergence slows down [3], [4]. To improve the convergence behavior of the LMS, various adaptive algorithms such as affine projection algorithm (APA) and multiband-structured subband adaptive filter (MSAF) were proposed [5], [6]. To increase the convergence speed of MSAF, the variable step-size MSAF (VSS-MSAF) was introduced [7]. Due to VSS, the computational complexity in VSS-MSAF increases.