International Journal of Electronics Engineering Research. ISSN 0975-6450 Volume 9, Number 6 (2017) pp. 823-830 Research India Publications http://www.ripublication.com Implementation of Optimized Proportionate Adaptive Algorithm for Acoustic Echo Cancellation in Speech Signals 1 G.Amjad Khan Research Scholar [PP.ECE.019], Rayalaseema University, A.P, India, Asst. Professor, Dept of ECE G Pulla Reddy Engineering College (Autonomous) 2 Dr. K E Sreenivasa Murthy Professor & Head, G Pullaiah College of Engineering, Kurnool, A.P., India. Abstract Acoustic echo cancellation plays a significant role in the field of Adaptive signal Processing. The most widely used adaptive algorithm for system identification problem is the Normalized Least mean Square Algorithm (NLMS) algorithm, there is a necessity to control the parameters of NLMS algorithm, the step size and the regularization parameters. Many papers have been published based on the step size and the regularization parameters. In this paper we are going to improve the complete performance of the NLMS algorithm by using Dual Optimized NLMS algorithm for controlling the step size and regularization parameter in the context of decreasing the misalignment parameters, Mean square error and SNR.The simulation results show that the proposed algorithm achieves ameliorate reduction in misalignment and mean square error when compared to the NLMS, Non Parametric variable step size and the kalman filter in the context of the state variable model. Keywords: NLMS, IPNLMS, JO-NLMS, Optimized NLMS, Step Size, Misalignment, Mean Square Error, SNR. I. INTRODUCTION Acoustic echo cancellation (AEC) is one of the important system identification problems [1], [2]. In this context, an adaptive filter is used to identify the acoustic echo path between the loudspeaker and the microphone, i.e., the room acoustic impulse response. The main challenges of AEC include the high-length and time-varying nature
824 G.Amjad Khan and Dr. K E Sreenivasa Murthy of the acoustic impulse response, as well as the no stationary character of the speech signal (or even of the background noise). The normalized least-mean-square (NLMS) algorithm [3] is frequently used for system identification. However, due to the specific nature of AEC, the overall performance of this popular algorithm must be improved in order to use it in this context. A natural approach is to control its main parameters, i.e., the normalized step-size and regularization terms, thus making them time dependent. The goal is to achieve a proper compromise between the conflicting performance criteria, i.e., fast convergence/tracking and low misadjustment. Consequently, many interesting variable step-size (VSS) and variable regularized (VR) versions of the NLMS algorithm were developed, e.g., [4] [12] and references therein. IN this paper, we propose an optimized NLMS algorithm for AEC, by following a joint-optimization on both the normalized step-size and regularization parameter. Moreover, we consider a state variable model in the development, assuming that the echo path is modelled by a time-varying system following a first-order Markov model, similar to Kalman filtering [2] [13]. The goal is to minimize the system misalignment, which represents the natural approach for this type of applications. Simulations performed in the context AEC indicate that the proposed algorithm achieves both fast convergence/tracking and low misadjustment, but also improves robustness to near end signal variations like double-talk. Consequently, it can be an attractive choice for real-world AEC scenarios. II.SYSTEM MODEL AND NLMS ALGORITHM In the system identification problem of acoustic echo cancellation [1-9].The far end signal,x(n) Goes through the echo path h(n), providing the echo signal y(n).the signal is added to the near end signal v(n)resulting thr microphone signal d(n).the adaptive filter, which is defined by the vector ĥ(n) produce the estimate of the echo y (n) and the error signal produces an estimate of the near end signal.the main goal of this application is to model an unknown system.
Implementation of Optimized Proportionate Adaptive Algorithm for Acoustic 825 The desired signal of the adaptive algorithm is given by d(n) = x T (n)h(n) + v(n) = y(n) + v(n) (1) Where x(n) = x(n) x(n 1) x(n L + 1) T is a real valued vector containing the most recent time samples of the input signal.x(n) and v(n).the well-known update equation of the NLMS algorithm is given by ĥ(n) = ĥ(n 1) + μx(n)e(n) x T (n)x(n)+δ (2) III. METHODOLOGY Proposed method: The impulse response of echo path is modeled by a time varying system of a first order Markov Model [9], a more applicable approach would be based on the kalman filter.we consider by assuming that h(n) is a zero mean random vector,which follows a markov model h(n) = h(n 1) + w(n) (3) Convergence Analysis: The update equation developing in the context of the aposteriori misalignment is given by m(n) = m(n 1) + w(n) μx(n)e(n) x T (n)x(n)+δ For large values of L (i. e., L 1),it holds that x T (n)x(n) Lσ x 2 consequently, μ x T (n)x(n)+δ μ Lσ x 2 +δ This term contains both the control parameters,i.e.,μ and δans the statistical information of the input signal.underthese circumstances taking the l 2 norm in (4)then mathematical expectation on both sides and removing the uncorrelated products, we obtain E[ m(n) 2 2 ] = E[ m(n 1) 2 2 ] + Lσ w 2 2μ Lσ x 2 +δ E[xT (n)w(n)e(n)] + μ2 (4) (5) 2μ Lσ x 2 +δ E[xT (n)m(n 1)e(n)] (Lσ x 2 +δ) 2 E[e 2 (n)x T (n)x(n)] (6) In order to further process (6),let us focus on its last three cross correlation terms,the a prior error signal can be written as e(n) = x T (n)m(n 1) + x T (n)w(n) + v(n) (7)
826 G.Amjad Khan and Dr. K E Sreenivasa Murthy Then the value is given by The update equation is given by 2 μ(n) Lσ 2 x + δ(n) = m(n 1) + Lσ w Lσ 2 v + (L + 2)σ 2 x [m(n 1) + Lσ 2 w ] ĥ(n) = ĥ(n 1) + m(n 1)+Lσ w 2 Lσ v 2 +(L+2)σ x 2 [m(n 1)+Lσ w 2 ] (8) SIMULATION RESULTS: Simulations were performed in an AEC configuration, as shown in Fig. 2. The measured acoustic impulse response was truncated to 512 coefficients (Fig.2), and the same length was used for the adaptive filter, i.e., L=512; the sampling rate is 8 khz. We should note that in many real-world AEC scenarios, the adaptive filter works most likely in an under-modeling situation, i.e., its length is smaller than the length of the acoustic impulse response. Hence, the residual echo caused by the part of the system that cannot be modeled acts like an additional noise (that corrupts the near-end signal) and disturbs the overall performance. However, for experimental purposes, we set the same length for both the unknown system (i.e., the acoustic echo path) and the adaptive filter In practice, it is usually more convenient to control the performance of the algorithm in terms of the normalized step-size, since its values are limited in a specific interval. On the other hand, it could be more difficult to control the adaptation in terms of the regularization term, since its values are increasing and could lead to overflows. Usually,
Implementation of Optimized Proportionate Adaptive Algorithm for Acoustic 827 an upper bound on the regularization parameter could be imposed, but this would introduce an extra tuning parameter in the algorithm. Due to these aspects, only the Proposed DO NLMS algorithm will be considered as a benchmark in the following Next, the proposed DO NLMS algorithm is also involved in the rest of experiments. As compared to its counterparts, this algorithm does not require an explicit regularization term. Its global step-size resulted based on the joint-optimization on both the normalized step-size and regularization parameter. the NLMS algorithm (for different values of α) is compared with the NPVSS-NLMS and Proposed DO NLMS algorithms, when the far-end signal is an AR(1) process or a speech sequence, respectively. According to these results, it can be noticed that the NLMS algorithm is clearly outperformed by the other algorithms, in terms of convergence rate, tracking, and misalignment. Also, the NPVSS-NLMS and JO-NLMS algorithms perform in a similar manner with a slight advantage for the JO-NLMS algorithm; besides, they are close to the performance of the JO-NLMS-id algorithm, which represents the ideal benchmark.
828 G.Amjad Khan and Dr. K E Sreenivasa Murthy IV. COMPARISON Table below gives the performance improvement in terms of SNR for NLMS, NPVSS, JO NLMS, Proposed SIGNAL TO NOISE RATIO TABLE I Algorithms Signal to Noise ratio (db) NLMS 14.8857 NPVSS 23.8809 IP NLMS 21.8768 PROPOSED 28.3345
Implementation of Optimized Proportionate Adaptive Algorithm for Acoustic 829 TABLE II. Based on Adaptive algorithm parameters Algorithm Parameters NLMS NPVSS IP NLMS Proposed ERLE(dB) 5 6 7 9 MSE 0.0062 0.0061 0.0058 0.0041 PSNR(dB) 22.0921 22.3187 22.4525 29.4582 V.CONCLUSION In this paper, we have presented several NLMS-based algorithms suitable for AEC applications. These algorithms are based on different control strategies for adjusting their main parameters, i.e., the normalized step-size and regularization term, in order to achieve a proper compromise between the performance criteria (i.e., fast convergence/tracking and low misadjustment). The main motivation behind this approach was the reference work of Hänsler and Schmidt from [1]. Following their ideas, we presented here two related solutions, i.e., the NPVSS-NLMS and DO-NLMS algorithms. The first one originally proposed represents a simple and efficient method to control the normalized step-size. Due to its non-parametric nature, it is a reliable choice in many practical applications. The second one is developed in the context of a state-variable model and follows an optimization criterion based on the minimization of the system misalignment. It is also a non-parametric algorithm, which does not require any additional control features (e.g., system change detector, stability thresholds, etc.). It also gives good robustness against double-talk, which is one of the most challenging situation in AEC. Consequently, it could be an appealing candidate for real-world applications. REFERENCES [1] J. Benesty, T. G ansler, D. R. Morgan, M. M. Sondhi, and S. L. Gay,Advances in Network and Acoustic Echo Cancellation. Berlin, Germany:Springer-Verlag, 2001. [2] G. Enzner, H. Buchner, A. Favrot, and F. Kuech, Acoustic echo control, in Academic Press Library in Signal Processing, vol. 4, ch. 30, pp. 807 877, Academic Press 2014. [3] S. Haykin, Adaptive Filter Theory. Fourth Edition, Upper Saddle River,NJ: Prentice-Hall, 2002. [4] G.Amjad Khan and Dr. K.E Sreenivasa Murthy Regularized NLMS Adaptive
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