Analyzing the effects of pseudo-optimum tap-length for an MSF-based acoustic echo canceller

Abstract Adaptive multiple subfilters (MSF)-based algorithms have gained attention in recent times for their applications in acoustic echo cancellation (AEC). The most advanced combined-error MSF algorithm maintains a trade-off between the different-error and common-error subfilter-based algorithms, and it is employed for echo cancellation applications which need faster convergence. Variable tap-length adaptive filtering algorithms find the optimum filter length and are used for optimizing the tap-length of the subfilters in MSF-based echo cancellers. In case of a long room impulse response, the MSF-based variable tap-length algorithm achieves a pseudo-optimum tap-length, which renders the overall design undermodelled. Therefore, it becomes necessary to analyze the effects of the undermodelled adaptive filter on the performance of the variable tap-length MSF (VT-MSF)-based echo cancellers. In this paper, we present a mathematical investigation of convergence, steady-state MSE, stability and tracking capability of the VT-MSF echo cancellers having deficient tap-length adaptive subfilters. Simulation results are presented in support of the analysis for the VT-MSF algorithm for AEC.