In adaptive filtering, the least-mean-square-type algorithms are widely used but suffer from slow convergence for colored signals. The affine projection (AP) algorithm was proposed to speed up the convergence, which produces a good tradeoff between the convergence speed and the complexity. Nevertheless, as the projection order increases, the convergence rate of the AP algorithm is improved at a relatively high complexity. Many efforts have been made to reduce the complexity.

However, most of the efficient versions of the AP-type algorithms are based on the fast approximate filtering (FAF) scheme originally proposed in the fast AP (FAP) algorithm. The approximation leads to degraded convergence performance. To overcome this limitation, a fast exact filtering (FEF) approach to the AP algorithm (FEAP) was presented by Y. Zakharov. Still, in the FEAP algorithm, calculation of the error vector requires the update of the weight vector explicitly that provides the largest contribution towards the algorithm complexity.

Lately, researchers from the Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences propose an enhanced FEF approach to the AP (EFEAP) algorithm to further reduce the complexity of the FEAP algorithm, given that the calculation of the weight vector is not the primary objective for the application at hand.

The proposed FEF scheme is then extended to a family of AP-type algorithms such as the dichotomous coordinate descent (DCD)-AP, affine projection sign, and modified filtered-x affine projection algorithms. The complexity of AP-type algorithms based on the proposed FEF approach is comparable to that based on the FAF scheme. Moreover, computer simulations results show that the complexity reduction of the new algorithms is achieved without any performance degradation. A detailed comparison (memory size, computational complexity) of different implementation methods in hardware platforms such as FPGA and DSP is the future work.

Fig. 1. Complexity comparison of several fast AP algorithms, L=1024 (Image by YANG).

References:

YANG Feiran, WU Ming, YANG Jun, KUANG Zheng. A Fast Exact Filtering Approach to a Family of Affine Projection-type Algorithms. Signal Processing (Vol.101, August 2014, Pages 1–10).  DOI: 10.1016/j.sigpro.2014.01.030

Contact:

YANG Jun

Key Laboratory of Noise and Vibration Research, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China

Email: jyang@mail.ioa.ac.cn