Abstract
The adaptive algorithm used for echo cancellation (EC) system needs to provide 1) low misadjustment and 2) high convergence rate. The affine projection algorithm (APA) is a better alternative than normalized least mean square (NLMS) algorithm in EC applications where the input signal is highly correlated. Since the APA with a constant step-size has to make compromise between the performance criteria 1) and 2), a variable step-size APA (VSS-APA) provides a more reliable solution. A nonparametric VSS-APA (NPVSS-APA) is proposed by recovering the background noise within the error signal instead of cancelling the a posteriori errors. The most problematic term of its variable step-size formula is the value of background noise power (BNP). The power difference between the desired signal and output signal, which equals the power of error signal statistically, has been considered the BNP estimate in a rough manner. Considering that the error signal consists of background noise and misalignment noise, a precise BNP estimate is achieved by multiplying the rough estimate with a corrective factor. After the analysis on the power ratio of misalignment noise to background noise of APA, the corrective factor is formulated depending on the projection order and the latest value of variable step-size. The new algorithm which does not require any a priori knowledge of EC environment has the advantage of easier controllability in practical application. The simulation results in the EC context indicate the accuracy of the proposed BNP estimate and the more effective behavior of the proposed algorithm compared with other versions of APA class.
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References
Digital network echo cancellers [S]. ITU-T Recommendation G.168, 2009.
BERSHAD N J, BIST A. Fast coupled adaptation for sparse impulse responses using a partial Haar transform [J]. IEEE Transactions on Signal and Processing, 2005, 53(3): 966–976.
BURTON G T, GOUBRAN A R. A generalized proportionate subband adaptive second-order Volterra filter for acoustic echo cancellation in changing environments [J]. IEEE Transactions on Audio, Speech and Language Processing, 2011, 19(8): 2364–2373.
DENG Hong-yang, DOROSLOVACKI M. Improving convergence of the PNLMS algorithm for sparse impulse response identification [J]. IEEE Signal Processing Letters, 2005, 12(3): 182–184.
DENG Hong-yang, DOROSLOVACKI M. Proportionate adaptive algorithms for network echo cancellation [J]. IEEE Transactions on Signal Processing, 2006, 54(5): 1794–1804.
YAO Jian-jun, FU Wei, HU Sheng-hai. Amplitude phase control for electro-hydraulic servo system based on normalized least-mean-square adaptive filtering algorithm [J]. Journal of Central South University of Technology, 2011, 18(3): 755–759.
YANG J, SOBELMAN G E. Efficient u-law improved proportionate affine projection algorithm for echo cancellation [J]. Electronics Letters, 2011, 47(2): 73–74.
ZENGLI Y, ZHENG Y R, GRANT S L. Proportionate affine projection sign algorithms for network echo cancellation [J]. IEEE Transactions on Audio, Speech and Language Processing, 2011, 19(8): 2273–2284.
PALEOLOGU H C, CIOCHINA S, BENESTY J. An efficient proportionate affine projection algorithm for echo cancellation [J]. IEEE Signal Processing Letters, 2010, 17(2): 165–168.
HUANG Hsu-Chang, LEE Junghsi. A new variable step-size NLMS algorithm and its performance analysis [J]. IEEE Transactions on Signal Processing, 2012, 60(4): 2055–2060.
SHIN J, YOO J, PARK P. Variable step-size affine projection sign algorithm [J]. Electronics Letters, 2012, 48(9): 483–485.
BENESTY J, REY H, VEGA L R. A nonparametric VSS NLMS algorithm [J] IEEE Signal Processing Letters, 2006, 13(10): 581–584.
IQBAL M A, GRANT L G. Novel variable step size NLMS algorithms for echo cancellation [C]// IEEE International Conference on Acoustics, Spech and Signal Processing. San Diego: Qualcomm Inc., 2008: 241–244.
PALEOLOGU H C, BENESTY J, GRANT S L, OSTERWISE C. Variable step-size NLMS algorithms designed for echo cancellation [C]// IEEE Conference Record of the Forty-Third Asliomar Conference on Signal, Systems and Computers. Bucharest: Politehnica University, 2010: 633–637.
PALEOLOGU H C, CIOCHINA S, BENESTY J. Variable step-size NLMS algorithm for under-modeling acoustic echo cancellation [J]. IEEE Signal Processing Letters, 2008, 15(1): 5–8.
PALEOLOGU H C, BENESTY J, CIOCHINA S. A variable step-size affine projection algorithm designed for acoustic echo cancellation [J]. IEEE Transactions on Audio, Speech and Language Processing, 2008, 16(8): 1466–1478.
GUNTHER J. Learning echo paths during continuous double-talk using semi-blind source separation [J]. IEEE Transactions on Audio, Speech and Language Processing, 2012, 20(2): 646–660.
SCHULDT C. A delay-based double-talk detector [J]. IEEE Transactions on Audio, Speech and Language Processing, 2012, 20(6): 1725–1733.
LEE K H, CHANG J H, KIM N S, KANG S, KIM Y. Frequency-domain double-talk detection based on the Gaussian mixture model [J]. IEEE Signal Processing Letters, 2010, 17(5): 453–456.
PAUL T K, OGUNFUNMI T. On the convergence behavior of affine projection algorithm for adaptive filters [J]. IEEE Transactions on Circuits and Systems, 2011, 58(8): 1813–1826.
KIM Seong-Eun, LEE Jae-Woo, SONG Woo-Jin. A theory on the convergence behavior of the affine projection algorithm [J]. IEEE Transactions on Signal Processing, 2011, 59(12): 6233–6239.
SANKARAN S G, BEEX A A. convergence behavior of affine projection algorithms [J]. IEEE Transactions on Signal Processing Letters, 2000, 48(4): 1086–1096.
DUTTWEILER D L. Proportionate normalized least-mean-squares adaptation in echo cancellers [J]. IEEE Transactions on Speech, Audio Processing, 2000, 8(5): 508–517.
GAY S L, TAVATHIA S. The fast affine projection algorithm [C]// IEEE International Conference on Acoustics, Spech and Signal Processing. Murray Hill: AT&T Bell Labs, 1995: 3023–3026.
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Wen, Hx., Lai, Xh., Chen, Ld. et al. Nonparametric VSS-APA based on precise background noise power estimate. J. Cent. South Univ. 22, 251–260 (2015). https://doi.org/10.1007/s11771-015-2516-8
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DOI: https://doi.org/10.1007/s11771-015-2516-8