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.
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