Variable Step-Size Adaptive Filters for Echo Cancellation

Abstract

The principal issue in acoustic echo cancellation (AEC) is to estimate the impulse response between the loudspeaker and the microphone of a hands-free communication device. Basically, we deal with a system identification problem, which can be solved by using an adaptive filter. The most common adaptive filters for AEC are the normalized least-mean-square (NLMS) algorithm and the affine projection algorithm (APA). These two algorithms have to compromise between fast convergence rate and tracking on the one hand and low misadjustment and robustness (against the near-end signal) on the other hand. In order to meet these conflicting requirements, the step-size parameter of the algorithms needs to be controlled. This is the motivation behind the development of variable step-size (VSS) algorithms. Unfortunately, most of these algorithms depend on some parameters that are not always easy to tune in practice. The goal of this chapter is to present a family of non-parametric VSS algorithms (including both VSS-NLMS and VSS-APA), which are very suitable for realistic AEC scenarios. They are developed based on another objective of AEC application, i.e., to recover the near-end signal from the error signal of the adaptive filter. As a consequence, these VSS algorithms are equipped with good robustness features against near-end signal variations, like double-talk. This idea can be extended even in the case of the recursive least-squares (RLS) algorithm, where the overall performance is controlled by a forgetting factor. Therefore, a variable forgetting factor RLS (VFF-RLS) algorithm is also presented. The simulation results indicate that these algorithms are reliable candidates for real-world applications.