Abstract - Rapid advances in the field of signal processing

are revolutionizing algorithms. This paper describes the concept of adaptive noise cancellation, an alternative method of estimating signals corrupted by additive noise or interference. The Adaptive algorithms are used to improve the convergence rate, signal to noise ratio, stability, mean square error, steady state behavior, tracking, misadjustment has become a focus on digital signal processing. Accurate cancellation of noise in signal processing is a key step of adaptive filter algorithms.

In this paper, Acoustic echo cancellation problem was discussed out of different noise cancellation techniques by concerning different parameters with their comparative results .The results shown are using some specific algorithms. The results show, improving convergence rate with less no of taps is the most difficult phase in signal processing applications for the perfect working of any system.

Keywords - Acoustic Echoes, Adaptive filters, least mean Square Algorithm, Recursive Least mean Square algorithms

I. INTRODUCTION

Adaptive filtering algorithms have been employed in many signal processing applications [18] such as equalization, active noise control, acoustic echo cancellation and biomedical engineering. Linear and nonlinear filtering techniques have received increasing attentions in recent adaptive signal processing literatures. Numerous researchers have contributed to the development in these fields [12]. Several adaptive filter algorithms are proposed for noise cancellation. The adaptive filter essentially minimizes the mean-squared error between noisy signal and a reference signal. In adaptive filters convergence rate is decreasing by increasing the number of taps especially if the reference signal spectrum has a large dynamic range [17]. Echo cancellation requires a method for adjusting the learning rate when noise or interference present in the signal. Most of the echo cancellation algorithms used to detect double talk conditions so have long been recognized as an essential component of two way voice communication systems for reducing the annoying effects of network and acoustic echoes [9]. The rest of the paper is organized as follows. Section II provides the overview of Filters, Section III reviews different type of noise, then in Section IV adaptive filter algorithms are described, Section V provides the overview of related work, followed by the conclusion in section VI.

II. FILTERS

The usual method of estimating a signal corrupted by

additive noise is to pass it through a filter that tends to suppress the noise while leaving the signal unchanged [1].

Filters are of two types: Linear and non linear. All the applications where non linear distortions have to be identified and compensated by adaptive signal processing. FIR and IIR both are linear filters but Volterra is a nonlinear filter. By using these filters people are working on time/frequency domain implementation but few are working on statistical methods for higher order spectral analysis. A. Volterra Filter

It can deal with general class of nonlinear systems but its output is still linear with respect to various higher order kernels or impulse responses [12]. So truncated Volterra models have been widely applied and became very popular. One key reason is that the number of the volterra coefficients increases geometrically as the delays and orders increasing [12]. B. Adaptive Filter

Filters used for above purpose can be fixed or adaptive. The design of fixed filters is based on prior knowledge of both the signal and the noise [1]. On the other side adaptive filters have the ability to adjust their own parameters automatically and their design requires little or no a priori knowledge of signal or noise characteristics [13]

The design of such filters is the domain of optimal filtering which originated with the wiener filter and was extended by work of kalman filter. Adaptive filter has "self regulation" and "tracking" capabilities [1]. Adaptive filter can be divided into linear and nonlinear filters. Non-linear adaptive filter has more signal processing capabilities. However, due to the non-linear adaptive filter more complicated calculations are there, but the actual use is still the linear adaptive filter where FIR is most practically and widely used filter [2].

PERFORMANCE AND CONVERGENCE ANALYSIS OF LMS ALGORITHM

Harjeet Kaur1, Rajneesh Talwar2

1Indira College of Engineering & Management, Pune University, Pune, India 2Swift Technical Campus, Rajpura, PTU Jalandhar, Punjab, India

(mail2hkaur@gmail.com, rtphdguidance@gmail.com)

978-1-4673-1344-5/12/$31.00 ©2012 IEEE

Fig. 1. Adaptive Filter

III. DIFFERENT NOISES

These different noises are based on many categories like linear and non linear noises. A. Acoustic echo

This noise is a major problem for all telecommunication system where a non negligible coupling exists between loudspeaker and microphone and makes the communication difficult. Early systems relied on disciplined speakers like single duplex approaches (one way) and generate echoes. To cancel these echoes we identify the impulse response due to coupling [9]. So acoustic Echo Cancellers are used in teleconferencing systems to reduce undesired echoes [7]. Multichannel acoustic echo cancellers have become essential for higher realistic performance in speaker localization. B. Active noise control

The signal emitted by the loudspeaker is received by the microphone and transmitted to the remote end that can hear its own delayed voice and reverberated [3]. A more natural and full duplex approach is possible through the signal processing algorithms that subtract from the microphone signal to the original signal. It has ability to utilize the artificial noise interferences to cancel out the undesired noise interferences and to develop high speed DSP processor. It reduces low frequency noise and if used sound absorbing material then high frequency noise is also cancelled. C. Stereophonic acoustic echo

The poor mismatch between adaptive filter coefficients and the receiving room acoustic impulse responses. Stereophonic audio system provides spatial information leading to better perception of the transmitted speech as well as improving the ambience of the system This is a challenging area for applications including video/ teleconferencing as well as virtual gaming [11], [14]. It employs a pair of adaptive filters for the estimation of acoustic impulse response in the receiving room [14].Several de-correlation algorithms have been proposed

to mitigate the problem. However, almost all of these preprocessing methods will affect the stereo perception. D. Impulsive noise

This noise is one of the most dangerous signal distortions, not always considered when implementing algorithms, particularly in specific hardware platforms. Impulsive noise removal is an important research area e.g. in video broadcasting [14] and image filtering. E. Network Echo

Interference between customer premises and local exchange and caused by impendence mismatches in four to two-wire hybrid circuits [9]. It deals with long impulse response echo paths, which decreases the convergence rate [19].

IV. ADAPTIVE ALGORITHMS Most popular adaptive filter algorithms are Least

Mean square (LMS) algorithm and normalized Least Mean square (NLMS) algorithm [1]. The popularity of these algorithms is due to its simplicity and robust performance [2].The stability of this algorithm is governed by a step size parameter [1]. A. Least Mean Square (LMS) Algorithm

No of tap coefficient of a linear filter is an important parameter for calculating the performance of minimum mean square error (MMSE).By adjusting the tap length we can improve convergence rate. For fixed tap length segmented filter (SF) is used and for variable tap length gradient descent (GD) was used [2].

( ) ( ) ( ) ( )nenXnWnW ∗+=+ μ1 (1)

)()()()( nXnwndne H−= (2) B. Normalized Least Mean Square (NLMS) Algorithm

NLMS is widely used algorithm because of its simplicity and robust performance. The stability of the basic NLMS is controlled by a step size. This parameter also governs the rate of convergence, speed, tracking ability and the amount of steady-state excess mean-square error (MSE). Aiming to solve conflicting objectives of fast convergence and low excess MSE. It achieves a certain degree of success that converges slowly with colored input signals [1]-[2].

In the standard LMS algorithm if x (n) is large, it suffers from gradient noise amplification [2].But normalized LMS algorithm seeks to avoid gradient noise amplification [2]. The step size is time varying m (n), and optimized to minimize error.

( ) ( ) ( ) ( )[ ]nnnWnW ∇−=+ μ211

( ) ( ) ( )[ ]nRWpnnW −+= μ (3) C. Variable Step Size (VSS-NLMS) Algorithm

This VSS-LMS employs a larger step size when the estimation error is large, and vice versa. Aboulnasr pointed out that the advantageous performance of this VSS-LMS and several other variable step-size LMS algorithms is usually obtained in a high signal-to-noise environment The motivation is that a large MSE increases

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step size and a large system noise decreases step size, and vice versa[1]-[2]. D. NPVSS- NLMS: Non parametric VSS NLMS

This approach is used for controlling the step size, provides fast convergence, good tracking and low misadjustment [4]. This algorithm is working without assumptions compared to all other algorithms. Algorithm always works for stationary systems [1]-[2]. E. Normalized sub band adaptive filter NSAF

This approach is used for accelerating the convergence. It shows good performance with its computational complexity close to that of NLMS algorithm with colored input signals [17] .The idea of the NSAF is to use the sub band signals normalized by their respective sub band input variances to update the tap weights. For fixed step size, it requires a tradeoff between fast convergence rate and low misadjustment [17]. This problem is solved by set- membership where uses fixed step size concept [17]. F. Proportionate NLMS algorithm (PNLMS)

This algorithm is working for network echo cancellation. It is used to improve the convergence rate .If echo path changes it easily follow the changes [19].

V. PREVIOUS WORK Significant work has been done for the cancellation of

different type of noise by different algorithms in different applications. Researchers defined the methods for different parameters like fast convergence rate, step size, stability and mean square error (MSE).

The echo cancellation method was proposed in [3] for good convergence speed and local noise (double talk) and changes in room impulse response. In this paper author proposed a neural network estimator based on a set of classic statistical estimators and a proper generalized offline training and output step size estimation gives good convergence speed and correct behavior for local noise [3].

The echo cancellation method was proposed in [4] for fast convergence rate, good tracking and low misadjustment. In this paper proposed variable step size Normalized Least Mean Square (VSS-NLMS) algorithm removes the problems of NLMS algorithm. This NLMS algorithm needs to find compromise between fast convergence and low misadjustment. To make the final misalignment of the NLMS closer to that of the NPVSS-NLMS. The step size has to be reduced so convergence rate is strongly reduced [4].

The echo cancellation method was proposed in [5] for recovery of near end signal and power estimation. In this paper variable Step Size Normalized Least mean square (VSS-NLMS) algorithm was proposed. This algorithm is

working for the near end signal power estimation. Large value leads to fast convergence rate and tracking ability while a small value leads to low misadjustment and good robustness features [5]. That is the motivation behind the development of VSS-NLMS algorithm. Main problem for echo cancellation is high length and time variant echo path with the presence of near end signal. VSS-NLMS algorithm is a combination between two classes of adaptive system identification first is “system Identification” and second “undesired signal” means to recover a “useful signal” [5].

The echo cancellation method was proposed in [7] for Correct identification of echo path and signal decor relation. In this paper proposed algorithm is based on estimation of fundamental frequency and correlates between two channels, prevents a correct identification of echo paths and signal décor relation also. Stereophonic acoustic echo cancellation is used for the better performance in terms of sound localization.

The echo cancellation method was proposed in [9] for psychoacoustic aspects of human hearing. Modified NLMS algorithm has been proposed in this paper. The focus is on wideband speech communication system with long round- trip delay of 200ms and up present in the transmission path. The results analyzed with the standard psychoacoustic model, revealing that steady-state echo return loss enhancement and mean square error cannot be used to determine whether residual echo is perceivable in the presence of background noise [9]. In this paper author shows that steady state echo canceller performance measures alone cannot be used to determine whether a residual echo signal is perceivable. Here algorithm places more emphasis on frequency bands. And by results reduce the perceivability of residual echo.

The echo cancellation method was proposed in [11] for Misalignment convergence of adaptive filter by adjusting the source position in the transmission room. In this paper proposed algorithm is XM tap–selection algorithm by employing a centre clipping algorithm .One solution of solving the problem of cancellation of stereophonic acoustic echo by pair of adaptive filters, but fundamental problem here is poor mismatch between adaptive filter coefficients and receiving room acoustic impulse responses. Several methods are proposed to address the misalignment problems [11]. The focus is on the location of source. The results analyzed better when source is placed near to microphone.

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TABLE I

COMPARISON OF DIFFERENT ALGORITHMS

VI. CONCLUSION

In this paper we discuss different types of noise cancellation methods by different adaptive filter algorithms. Every algorithm works on different methods for noise cancellation and improves system performance. But in all these algorithms authors worked on different parameters and try to improve their results.

VII. FUTURE SCOPE I want to design a new filter where these parameters

are improved and we get results at less no of taps because that is the major advantage of use of adaptive filter algorithm.

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Englewood Cliffs, NJ: Prentice- Hall, 1985. [2] S. Haykin, Adaptive Filter Theory, Fourth edition, Upper saddle

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NLMS Acoustic Echo Cancellation Using A Neural Network Approach” IEEE 2003.

[4] J. Benesty and H Rey, “A Nonparametric VSS NLMS Algorithm,” IEEE Signal Process. Letter, Vol. 13, Oct. 2006.

[5] C. Paleologu, J Benesty and S. L Christopher “Variable Step Size NLMS Algorithm designed for Echo Cancellations,” IEEE 2009.

[6] J. M. Valin, “On Adjusting the Learning rate in Frequency Domain Echo cancellation With Double –Talk” IEEE Trans. Audio, Speech and Language,Vol-15,No. 3, March 2007.

[7] L. Romoli, S. Cecchi, P. Peretti and F. Piazza “A Mixed Décor relation Approach for Stereo acoustic Echo Cancellation Based on the estimation of the Fundamental Frequency” IEEE Trans .Audio, Speech and Language,Vol-20, No. 2, Feb. 2012.

[8] S. A. Jang, Y. J. Lee and D. T. Moon “Design and Implementation of Acoustic Echo canceller “IEEE 2002.

[9] D .Gordy, R.A. Goubran “On The Perceptual Performance Limitations of Echo Cancellers n Wideband Telephony ,”IEEE

Trans. Audio, Speech and Language, Vol-14,No. 1, Jan. 2006.

[10] S. Cecchi, L. Romoli, P. Peretti and F. Piazza “A Combined

Psychoacoustic Approach for Stereo Acoustic Echo Cancellation ,”IEEE Trans. Audio, Speech and Language,Vol-19,No. 6, Aug. 2011.

[11] M. Bekrani, A. W. H. Khong and M. Lotfizad, “A Clipping- Based Selective–Tap Adaptive Filtering Approach to Stereophonic Acoustic Echo Cancellation ,”IEEE Trans. Audio, Speech and Language,Vol-19,No. 6, Aug. 2011.

[12] H. Zhao and J. Jhang, “A Novel Adaptive Nonlinear Filter- based Pipelined Feed forward Second –order Volterra Architecture ,”IEEE Trans. Signal Proc.,Vol-57,No.1, Jan. 2009.

[13] B. Widrow, J. R. Glover “Adaptive Noise Cancelling: Principles and Applications,” IEEE Proceedings ,Vol-63,No.12, Dec. 1975.

[14] D. Q. Nguyen, W. S. Gan and A. W. H. Khong, “Time- Reversal Approach to the Stereophonic Acoustic Echo Cancellation Problem ,”IEEE Trans. Audio, Speech and Language,Vol-19,No.2, Feb. 2011.

[15] T. D. Wada, B. H. Juang, “Enhancement of Residual Echo For Robust Acoustic Echo Cancellation,” IEEE Trans. Audio, Speech and Language, Vol-20,No. 1, Jan. 2012.

[16] F. Yang, M. Wu and A. W. H. Khong, “Time- Reversal Approach to the Stereophonic Acoustic Echo Cancellation Problem,” IEEE Trans. Audio, Speech and Language, Vol-19,No. 2, Feb. 2011.

[17] J. Ni and F. Li “A Variable step size Matrix Normalized Sub band Adaptive Filter” IEEE Trans. Audio, Speech and Language,Vol-18, No. 6, Aug. 2010.

[18] Junghsi Lee, Jia-Wei Chen and Hsu-Chang Huang “Performance Comparison of Variable step size NLMS Algorithm” Proceedings Of The World Congress On Engineering and Computer Science USA, Vol-1, Oct. 2009

[19] Mehram Nekuii and Mojtaba Atarodi “A Fast Converging Algorithm For Network Echo Cancellation” IEEE Signal Processing Letters,Vol-11, No.4, April2004.

S. No Analyze STRB[11] SAES[16] VSS-NLMS[5]

NPVSS-NLMS[4]

LMS[7] NLMS[9] PNLMS[12] NSAF[17]

1. Convergence Rate

Faster Better Fast Fast Low Fast Fast(initial stage)

2. Misalignment

Improved Improved Low Low Low

4. MSE Efficient High High Low High

5. Application

Teleconferencing

Tele/video conferencing

Network Echo cancellation

6. Learning Rate/Tracking

Fast Good

7 Steady state error

Low Best LOW Higher

8 Step Size

Low Fixed Low Controlled Update

2012 IEEE International Conference on Computational Intelligence and Computing Research