A Perspective on Stereophonic Acoustic Echo Cancellation by Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu

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By Jacob Benesty, Constantin Paleologu, Tomas Gänsler, Silviu Ciochină

Single-channel hands-free teleconferencing platforms have gotten well known. so that it will increase the verbal exchange caliber of those platforms, increasingly more stereophonic sound units with loudspeakers and microphones are deployed. end result of the coupling among loudspeakers and microphones, there's powerful echoes, which make real-time communique very tricky. the way we all know to cancel those echoes is through a stereo acoustic echo canceller (SAEC), which might be modelled as a two-input/two-output method with genuine random variables. during this paintings, the authors recast this challenge right into a single-input/single-output approach with advanced random variables because of the generally linear version. From this new handy formula, they re-derive crucial elements of a SAEC, together with identity of the echo paths with adaptive filters, double-talk detection, and suppression.

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3) 2 Using Lagrange multipliers, we easily find the update equation of the algorithm, which is h(n) = h(n − 1) + X(n) XH (n)X(n) −1 e∗ (n). 4) cancels the a posteriori error vector. Also, by taking P = 1, we find the NLMS algorithm derived in the previous chapter. To make the APA more practical, we need to change it a bit by including the two classical parameters: the normalized step size, α (0 < α < 2), and the regularization, δ ≥ 0. 7) where IP is the P × P identity matrix. 2 Interpretation of the APA In this section, we assume that α = 1 and δ = 0.

Vol. 20, no. 1, pp. 33–61, 1998. 22. J. Benesty and S. L. Gay, “An improved PNLMS algorithm,” in Proc. IEEE ICASSP, 2002, pp. 1881–1884. 23. C. Paleologu, J. Benesty, and S. Ciochin˘ a, “A variable step-size proportionate NLMS algorithm for echo cancellation,” Revue Roumaine des Sciences Techniques – Serie Electrotechnique et Energetique, vol. 53, no. 3, pp. 309–317, 2008. 24. J. Benesty, F. Amand, A. Gilloire, and Y. Grenier, “Adaptive filtering algorithms for stereophonic acoustic echo cancellation,” in Proc.

While the formulation of this problem is straightforward, a good and reliable solution is not that easy to find. Many different schemes have been proposed in the last two decades [7], [8], [9], [10], [11], [12], [13], [14]. In this section, we show how to derive, in a very simple and elegant way, a non-parametric variable step-size NLMS algorithm [15]. 71) x(n) + v(n). Consider the update equation h(n) = h(n − 1) + μ(n)x(n)e∗ (n). 72) stable is to cancel the a posteriori error signal (see [16] and references therein).

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