THE USE OF PARTIAL UPDATE SCHEMES TO REDUCE INTER-CHANNEL COHERENCE IN ADAPTIVE STEREOPHONIC ACOUSTIC ECHO CANCELLATION
Andy W. H. Khong, Patrick A. Naylor · 2003
The use of partial update adaptive filters for stereophonic acoustic echo cancellation is investigated. The MMax-NLMS algorithm is studied in this context and its inherent robustness to subsampling of the tap-input vector is demonstrated. It is proposed to employ the subsampling of the tap input vector, that is intrinsic to partial update schemes, to decorrelate the two tap-input vectors of the stereo adaptive structure thereby enhancing convergence. We investigate the trade-off between improvement in convergence due to decorrelation of the two tap-input vectors and degradation in convergence due to subsampling in the MMax-NLMS partial update scheme. The exclusive MMax-NLMS (XM-NLMS) is proposed which approximates the joint optimization of these factors and simulation results are presented. I. INTRODUCTION Direct application of adaptive filters to the problem of stereophonic acoustic echo cancellation (SAEC) is known to be ineffective due to the high coherence between the two input signals. This has led to several approaches to the problem that involve techniques to decorrelate the two input signals using, for example, non-linear processing [1] or additive signals [2]. Furthermore, the computational complexity of stereophonic echo cancellers can be high because the number of taps can be large and also because the use of least-squares-based algorithms is often preferred in order to obtain sufficient levels of cancellation. Therefore, there exists a dual motivation to develop algorithms which have improved convergence performance due to reduction of interchannel coherence whilst maintaining computational complexity to be as low as possible for practical reasons. In partial update adaptive filtering, the tap-input vector is subsampled so that only a subset of filter taps is updated at each iteration [3] [4]. The aim of this work is to investigate whether such subsampling can bring a reduction in the inter-channel coherence of the tap-input vectors that results in improved convergence. The problem has been structured as a joint optimization of two scores - one describing the inter-channel coherence between the tap-input vectors and the other describing the ‘closeness’ of the tap selection to that of the MMax-NLMS scheme. In this context, the ideal tap selection is therefore one which selects the elements of the tap input vectors such that the inter-channel coherence is minimized whilst maximizing their L1 norm. A brief discussion of MMax-NLMS is presented in Section II. We shall look at the effect of decorrelation in Section III. Section IV presents XM-NLMS algorithm while Section V concludes the present work and discusses the ongoing research work.