طراحی و تحلیل یک الگوریتم وفقی LMS/Newton بهبودیافته در کاربرد حذف پژواک آکوستیکی
محورهای موضوعی : مهندسی برق و کامپیوتر
1 - دانشگاه صنعتی قم
کلید واژه: پژواک آکوستیکیفیلتر وفقیماتریس همبستگی پاسخ ضربه تنک ,
چکیده مقاله :
از چالش‌های مهم در حذف پژواک آکوستیکی با استفاده از فیلترهای وفقی، تنک‌بودن پاسخ ضربه مسیرهای آکوستیکی و وابستگی زیاد عملکرد الگوریتم‌های وفقی به پراکندگی مقادیر ویژه ماتریس همبستگی سیگنال ورودی می‌باشد که سبب افت کارایی حذف‌کننده‌های وفقی پژواک آکوستیکی می‌شود. در این مقاله به منظور بهبود عملکرد الگوریتم وفقی LMS/Newton در حذف پژواک آکوستیکی، محاسبه معکوس ماتریس همبستگی سیگنال ورودی اصلاح شده است. در این روش از لم معکوس ماتریس به صورتی بهره‌گیری می‌شود که در ابتدای همگرایی سهم ماتریس معکوس در به‌هنگام‌سازی وزن‌ها بیشتر بوده و در نتیجه وابستگی به پراکندگی مقادیر ویژه در شروع همگرایی کاهش یابد. همچنین برای تنظیم طول گام از یک روش تناسبی بهبودیافته استفاده می‌شود، به طوری که نقش وزن‌های با دامنه بزرگ‌تر در فرایند وفق در ابتدا بیشتر از سایر وزن‌ها بوده و به تدریج در طول همگرایی نقش تمامی وزن‌ها یکسان شود. این روش تناسبی علاوه بر بهبود سرعت همگرایی، سبب بهبود عملکرد حالت دایم الگوریتم وفقی در شناسایی پاسخ ضربه تنک مسیرهای آکوستیکی می‌گردد. نتایج شبیه‌سازی با استفاده از سیگنال رنگی دارای طیف شبه- گفتار نشان می‌دهد خطای عدم انطباق حالت دایم الگوریتم پیشنهادی در مقایسه با الگوریتم LMS/Newton در حدود dB 5/6 پایین‌تر است. همچنین همگرایی الگوریتم پیشنهادی در مقایسه با الگوریتم NLMS تناسبی، برای رسیدن به خطای عدم انطباقdB 17- حدود 6/3 ثانیه سریع‌تر است. تحلیل‌های نظری میزان عدم انطباق الگوریتم در حالت گذرا و حالت دایم نیز ارائه و با نتایج شبیه‌سازی مقایسه شده است.
Some of important issues in acoustic echo cancellation (AEC) using adaptive filters are the sparseness of the acoustic path impulse responses and strong dependency of the convergence performance of adaptive algorithm to the eigenvalue spread of the input signal correlation matrix. These issues result in a performance degradation of the adaptive AEC systems. In this paper, to improve the performance of the LMS/Newton adaptive algorithm in AEC, the matrix inverse computation is modified. To this end, the matrix inversion lemma is employed such that the contribution of the matrix inverse in the weight update is initially high and as a result, the dependency of the adaptive algorithm to the eigenvalue spread is low during the initial convergence. In addition, for the step-size adjustment, an improved proportionate method is applied such that during the convergence, the contribution of those weights having higher amplitudes in the adaptation process is gradually varied to become identical at the end of convergence. The proposed adaptive proportionate method, results in both convergence rate and steady-state performance improvement for identification of sparse acoustic impulse responses. Simulation results using a colored speech-like signal shows the steady-state misalignment of the proposed algorithm is typically 6.5 dB lower than that of the LMS/Newton algorithm. Moreover, the convergence of the proposed algorithm is typically 3.6 sec faster than that of the PNLMS algorithm, to achieve a misalignment of -17 dB. Theoretical misalignment analyses in the transient and steady state are presented and verified with simulation results.
[1] J. Benesty, M. M. Sondhi, and Y. Huang, Handbook of Speech Processing, Springer-Verlag, New York, Inc., Secaucus, NJ, 2008.
[2] M. Bekrani, A. W. H. Khong, and M. Lotfizad, "A linear neural network based approach to stereophonic acoustic echo cancellation," IEEE Trans. Audio Speech Language Processing, vol. 19, no. 6, pp. 1743-1753, Aug. 2011.
[3] M. Bekrani, A. W. H. Khong, and M. Lotfizad, "A clipping-based selective-tap adaptive filtering approach for stereophonic acoustic echo cancellation," IEEE Trans. Audio Speech Language Processing, vol. 19, no. 6, pp. 1826-1836, Aug. 2011.
[4] Y. R. Chien and J. L. You, "Convex combined adaptive filtering algorithm for acoustic echo cancellation in hostile environments," IEEE Access, vol. 6, pp. 16138-16148, Feb. 2018.
[5] B. Farhang-Boroujeny, Adaptive Filters: Theory and Applications, 2nd Ed., John Wiley & Sons, USA, 2013.
[6] S. Haykin, Adaptive Filter Theory, 5th Ed., Pearson, 2014.
[7] M. Bekrani and M. Lotfizad, "Clipped LMS/RLS adaptive algorithms: analytical evaluation and performance comparison with low-complexity counterparts," Circuits, Systems and Signal Processing, vol. 34, no. 5, pp. 1655-1682, May 2015.
[8] J. Maheshwari and N. V. George, "Robust modeling of acoustic paths using a sparse adaptive algorithm," Applied Acoustics, vol. 101, pp. 122-126, Jan. 2016.
[9] M. Bekrani and H. Zayyani, "A weighted soft-max PNLMS algorithm for sparse system identification," International J. of Information & Communication Technology Research, vol. 8, no. 3, pp. 7-14, Summer 2016.
[10] M. Godavarti and A. O. Hero, "Partial update LMS algorithms," IEEE Trans. Signal Process., vol. 53, no. 7, pp. 2382-2399, Jul. 2005.
[11] T. Aboulnasr and K. Mayyas, "MSE analysis of the M-max NLMS adaptive algorithm," in Proc. IEEE Int. Conf. on Acoustics, Speech, Signal Process., vol. 3, pp. 1669-1672, Seattle, WA, USA, 15-15 May 1998.
[12] A. W. H. Khong and P. A. Naylor, "Selective-tap adaptive filtering with performance analysis for identification of time-varying systems," IEEE Trans. Audio Speech Lang. Process., vol. 15, no. 5, pp. 1681-1695, Jul. 2007.
[13] M. Bekrani and A. W. H. Khong, "A new partial update NLMS for stereophonic acoustic echo cancellation," in Proc. 18th European Signal Processing Conf., pp. 11-15, Aalborg, Denmark, 23-27 Aug. 2010.
[14] A. W. H. Khong and P. A. Naylor, "Stereophonic acoustic echo cancellation employing selective-tap adaptive algorithms," IEEE Trans. Speech Audio Process., vol. 14, no. 3, pp. 785-796, May 2006.
[15] D. L. Duttweiler, "Proportionate normalized least-mean-squares adaptation in echo cancellers," IEEE Trans. Speech Audio Processing, vol. 8, no. 5, pp. 508-518, Sep. 2000.
[16] P. A. Naylor, J. Cui, and M. Brookes, "Adaptive algorithms for sparse echo cancellation," Signal Processing, vol. 86, no. 6, pp. 1182-1192, Jun. 2006.
[17] F. de Souza, R. Seara, and D. R. Morgan, "An enhanced IAF-PNLMS adaptive algorithm for sparse impulse response identification," IEEE Trans. Signal Processing, vol. 60, no. 6, pp. 3301-3307, Jun. 2012.
[18] J. Liu and S. L. Grant, "Proportionate adaptive filtering for block-sparse system identification," IEEE/ACM Trans. Audio Speech Language Processing, vol. 24, no. 4, pp. 623-630, Apr. 2016.
[19] H. X. Wen, S. Q. Yang, Y. Q. Hong, and H. Luo, "A partial update adaptive algorithm for sparse system identification," IEEE/ACM Trans. Audio, Speech Lang. Process., vol. 28, pp. 240-255, Nov. 2019.
[20] K. Wagner and M. Doroslovacki, "Proportionate-type normalized least mean square algorithms with gain allocation motivated by mean-square-error minimization for white input," IEEE Trans. Signal Processing, vol. 59, no. 5, pp. 2410-2415, May 2011.
[21] M. Bekrani, R. Bibak, and M. Lotfizad, "Improved clipped affine projection algorithm," IET Signal Processing, vol. 13, no. 1, pp. 103-111, Feb. 2019.
[22] T. Zhang, H. Q. Jiao, and Z. C. Lei, "Individual-activation-factor memory proportionate affine projection algorithm with evolving regularization," IEEE Access, vol. 5, pp. 4939-4946, Mar. 2017.
[23] M. Bekrani, "Convergence performance improvement of affine projection adaptive algorithm for sparse linear system modeling with correlated input signals," J. of Modeling in Engineering, vol. 17, no. 58, pp. 171-186, Autumn 2019.
[24] F. Albu, J. Liu, and S. L. Grant, "A fast filtering block-sparse proportionate affine projection sign algorithm," in Proc. Int. Conf. on Communications, pp. 29-32, Bucharest, Romania, 9-10 Jun. 2016.
[25] M. Shukri-Ahmad, O. Kukrer, and A. Hocanin, "Recursive inverse adaptive filtering algorithm," Digital Signal Processing, vol. 21, no. 4, pp. 491-496, Jul. 2011.
[26] C. G. Tsinos and P. S. R. Diniz, "Data-selective LMS-Newton and LMS-Quasi-Newton algorithms," in Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, pp. 4848-4852, Brighton, United Kingdom, 12-17 May 2019.
[27] W. Y. Yuan, Y. Zhou, Z. Y. Huang, and H. Q. Liu, "A VAD-based switch fast LMS/Newton algorithm for acoustic echo cancellation," in Proc. IEEE Int Conf. on Digital Signal Processing, pp. 967-970, Singapore, Singapore, 21-24 Jul. 2015.
[28] M. Bekrani, M. Lotfizad, and A. W. H. Khong, "An efficient quasi LMS/Newton adaptive algorithm for stereophonic acoustic echo cancellation," in Proc. IEEE Asia Pacific Conf. on Circuits and Systems, pp. 684-687, Kuala Lumpur, Malaysia, 6-9 Dec. 2010.
[29] M. S. Salman, O. Kukrer, and A. Hocanin, "A fast implementation of quasi-newton LMS algorithm using FFT," in Proc. Int. Conf. Digit. Inf. Commun. Technol. Appl., pp. 510-513, Bangkok, Thailand, 16-18 May 2012.
[30] M. Hamidia and A. Amrouche, "A new robust double-talk detector based on the stockwell transform for acoustic echo cancellation," Digital Signal Processing, vol. 60, pp. 99-112, Jan. 2017.
[31] Y. Yu, H. He, B. Chen, J. Li, Y. Zhang, and L. Lu, "M-estimate based normalized subband adaptive filter algorithm: performance analysis and improvements," IEEE/ACM Trans. Audio Speech Lang. Process., vol. 28, pp. 225-239, Oct. 2019.
[32] J. Benesty and S. L. Gay, "An improved PNLMS algorithm," in Proc. IEEE Int. Conf. on Acoustic, Speech and Signal Processing, vol. 2, pp. 1881-1884, Orlando, FL, USA, 13-17 May 2002.
[33] P. S. R. Diniz, M. L. R. de Campos, and A. Antoniou, "Analysis of LMS-Newton adaptive filtering algorithms with variable convergence factor," IEEE Trans. Signal Processing, vol. 43, no. 3, pp. 617-627, Mar. 1995.
[34] M. Bekrani and A. W. H. Khong, "Convergence analysis of clipped input adaptive filters applied to system identification," in Proc. IEEE Asilomar Conf. Signals, Systems and Computers, pp. 801-805, Pacific Grove, CA, USA, 4-7 Nov. 2012.
[35] J. Allen and D. Berkley, "Image method for efficiently simulating small-room acoustics," J. of the Acoustical Society of America, vol. 65, no. 4, pp. 943-950, Apr. 1979.