By Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu Ciochină
Single-channel hands-free teleconferencing structures have gotten renowned. in an effort to increase the verbal exchange caliber of those structures, increasingly more stereophonic sound units with loudspeakers and microphones are deployed. a result of coupling among loudspeakers and microphones, there is robust echoes, which make real-time communique very tough. the way in which we all know to cancel those echoes is through a stereo acoustic echo canceller (SAEC), which are modelled as a two-input/two-output process with actual random variables. during this paintings, the authors recast this challenge right into a single-input/single-output method with complicated random variables due to the commonly linear version. From this new handy formula, they re-derive an important features of a SAEC, together with identity of the echo paths with adaptive filters, double-talk detection, and suppression.
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Additional info for A Perspective on Stereophonic Acoustic Echo Cancellation
24. J. Benesty, F. Amand, A. Gilloire, and Y. Grenier, “Adaptive ﬁltering algorithms for stereophonic acoustic echo cancellation,” in Proc. IEEE ICASSP, 1995, pp. 3099–3102. Chapter 5 A Class of Aﬃne Projection Algorithms Aﬃne projection algorithms (APAs) are very good candidates for echo cancellation. The two main reasons for that are: they may converge and track much faster than the NLMS algorithm and they can be eﬃcient from an arithmetic complexity viewpoint. In this chapter, we derive some useful APAs for SAEC with the WL model.
The conventional way to derive the stereo stochastic gradient algorithm is by approximating the deterministic algorithm. Indeed, in practice, the two quantities pxd and Rx are, in general, not known. 2) and replace them in the steepest-descent algorithm [eq. 40)], we get h(n) = h(n − 1) + μ pxd (n) − Rx (n)h(n − 1) = h(n − 1) + μx(n) d∗ (n) − xH (n)h(n − 1) . 3) This simple recursion is the LMS algorithm. Contrary to the deterministic algorithm, the LMS weight vector h(n) is now a random vector.
The question now is how to ﬁnd δ? , − E |← e (n)|2 = σv2 . 61) This is reasonable if we want to attenuate the eﬀects of the noise in the ← − estimator h (n). 61), we assume that L 1 and x(n) is stationary. As a result, xH (n)x(n) ≈ 2Lσx2 . 64) where βNLMS √ 2L 1 + 1 + SENR = SENR is the normalized regularization parameter of the NLMS. 6 Variable Step-Size NLMS (VSS-NLMS) Algorithm 39 We see that δ depends on three terms: the length 2L of the adaptive ﬁlter, the variance, σx2 , of the input signal, and the SENR.
A Perspective on Stereophonic Acoustic Echo Cancellation by Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu Ciochină