Performance analysis of under-modelling stereophonic acoustic echo cancellation by adaptive filtering LMS algorithm

This paper addresses the field of stereophonic acoustic echo cancellation (SAEC) with adaptive filtering algorithms. In SAEC applications, using the least mean square (LMS) algorithm, it is usually assumed that the lengths of the adaptive filters are equal to that of the unidentified system responses. Although, in many realistic situations, under-modelled lengths adaptive filters, whose lengths are less than that of the unidentified systems (under-modelled systems), are employed, and analysis results for the exact modelled stereophonic LMS algorithm are not automatically appropriate to the under-modeled lengths. In this paper, we present a statistical analysis of the under-modeled stereophonic LMS algorithm. Exact expressions and deterministic recursive equations to the mean coefficients behavior of the adaptive LMS filters are derived to completely characterize and assess the performances (transient and steady-state) of the under-modeling stereophonic LMS algorithm. The expected theoretical behaviour is compared with Monte Carlo simulations and practical experimental results, showing a very good agreement.

Graphical abstractFigure optionsDownload full-size imageDownload as PowerPoint slideHighlights► We propose a statistical analysis of the under-modelled stereophonic LMS algorithm (SAEC). ► Theoretical expressions of deficient SAEC by adaptive LMS algorithm in the mean sense were derived. ► The proposed analysis completely assesses the performances of the deficient SAEC by LMS algorithm. ► The performance of the proposed study is validated thorough several Monte-Carlo simulations. ► A perfect agreement between the proposed theory and the experimentation is shown.