Encumbered Constancy Least Mean Square Algorithm for AEC’s in Mobile Communication Systems

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International Journal of Emerging Technology and Advanced Engineering

Website: www.ijetae.com (ISSN 2250-2459, ISO 9001:2008 Certified Journal, Volume 6, Issue 5, May 2016)

99

Encumbered Constancy Least Mean Square Algorithm for

AEC’s in Mobile Communication Systems

P. Sekhar Babu

1

, Dr P. V Naganjaneyulu

2

, M. Sumalatha

3

1,3_{Associate .Professor, Dept of ECE, Sai Spurthi Institute of Technology-B.Gangaram}

2

Principal, M.V.R College of Engineering & Technology, Paritala, Vijayawada

Abstract- Acoustic Echo Cancellation (AEC) algorithm play a vital role in mobile communication systems, which control the step size by decreasing the estimated error while improving the convergence. Here, as it is investigated various adaptive filters named LMS, normalized LMS and Encumbered Constancy LMS (ECLMS) algorithms for a step size control method capable of slowly canceling acoustic echo resisting dual talk. The proposed method is an extension for the conventional AEC algorithm in which the step size has controlled by using a single adaptive filter. The proposed method uses two adaptive filter structures named as sub-adaptive filter (SADF) which controls the step size and the main adaptive filter (MADF) used for canceling the acoustic echo. Accordingly, the sub-adaptive filter can reduce the residual echo more rapidly than the main adaptive filter. The method applies the step size calculated using the normalized residual echo to the main adaptive filter and thereby rapidly and steadily reduces the acoustic echo. Simulations results have been shown that the proposed ECLMS performed superior to the LMS and NLMS even that of conventional adaptive filters in terms of convergence and estimated error.

Keywords- AEC, LMS, ECLMS, SADF & MADF

I. INTRODUCTION

In AEC systems, the adaptive filter coefficients are disturbed by mainly two factors. Those are power fluctuation of far end talker's signal which can be used to estimate the coefficients. Even though, by applying the block length control [1], [2] and [3], the disturbance can be easily stopped. The second one is the superposition of near end talker's signal on the acoustic echo, which is known as gibberish. By stopping the estimation during the gibberish, this superposition can be prevented. It means that the precise and quick detection of the superposition is requisite to the prevention. Many gibberish detection methods [2] [3] have been hence studied. The methods, however, have the drawback that the convergence speed of the coefficients is particularly slow while the estimation error is large. Because of its easiness, the Least Mean Square (LMS) algorithm [4] is the most widely used adaptive algorithm.

However, the LMS algorithm suffers from slow and data-dependent convergence behavior. The NLMS algorithm [5] an equally simple, but more robust variant of the LMS algorithm, shows a better balance between easiness and performance than the LMS algorithm, and has been given more attention in real time applications but NLMS also struggled from lack of stability which in results the decreasing of systems performance [5], [6], [7] and [8]. To overcome these drawbacks, here in this paper a new step size controlling scheme has been implemented to improve the convergence speed and to decrease the estimated error.

nj

dj

Fig1. Conventional System

In this new method, we measured two adaptive filters for the cancellation of gibberish. The two adaptive filters are SADF and MADF. The main aim of the paper is that the MADF will cancel the acoustic echo by adjusting the residual echo which will be provided by the SADF with the variable step size. The fixed step size and number of taps of the sub-adaptive filter are larger and fewer than those of the MADF accordingly, the residual echo reduces more rapidly than that provided by the MADF. The variable step size thereby increases quickly and consequently, the MADF can rapidly reduce the acoustic echo.

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International Journal of Emerging Technology and Advanced Engineering

100 This paper also substantiates that the proposed method can provide almost the same convergence speed as that gained by applying a fixed large step size to the MADF.

II. EXISTING METHOD

Fig1 shows the configuration of the echo canceller system [3]. In this configuration, the coefficient vector of the adaptive filter, Hn, is estimated using the following block

implementation adaptive algorithm,

(1)

where is the vector of reference signal, is the echo of

residual, is a step size constant, j is a index of sample time and n denotes the block number. This algorithm can guarantee that the estimation error decreases to

(2)

when the block is extended until the relation,

(3)

is satisfied, where is the environmental noise power,

and n is the number of taps of the adaptive filter [1]. The threshold can be easily estimated using

(4)

Obtained rearranging (2). By applying this block length control method to (1), the coefficient vector can be continuously estimated even when the reference signal power is low.

In this control method, (2) can be moreover rewritten as

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This equation also shows that the estimation error can be kept at C0 if the step size is controlled as

(6)

When the near end talker’s signal increases to .It is very difficult to estimate increased by the near end talker’s signal. As shown in the reference [3] the author proposed an approximate to it by,

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This can be naturally delays the estimation of eq. (1), because involves the echo of residue, which becomes large after the path of echo changed. Hence, this paper proposes a new method for estimating .

III. PROPOSED METHOD

Fig.2 shows the proposed system configuration, MADF will be represented by using the fig.1, and the SADF used to estimate the power of near end talker’s signal quickly. The number of taps of the SADF affording output is fewer than that of MADF, and its step size is fixed at a constant for maximizing the convergence speed. The SADF can accordingly reduce the residual echo more quickly than the MADF. On the other hand, the SADF cannot suffi-ciently cancel the acoustic echo . The proposed system

adds the echo replica synthesized using the latter half taps of the main adaptive filter, , to , and subtracts it from the

output of microphone, . Therefore, the residual echo

can be written as,

(8)

Then the residual echo decrease more rapidly than . The

proposed system estimates using calculated giving the smaller one of and

(7)

to eq. (6) and thereby increases the convergence speed.

Fig.2 Proposed AEC system

ρn

e

j

Pn

Uj

MADF Step Size

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International Journal of Emerging Technology and Advanced Engineering

101

a. Acoustic echo canceller using SADF

In order to get an approximation of the estimate error, it is necessary to use an adaptive filter which is independent of ambient noise. Therefore, we introduce the SADF independently from the MADF. The composition of the AEC with the SADF, the desired signal of the SADF is set to zero and the coefficients of the SADF are prepared to nonzero values. In a word, the coefficients of the SADF converge from nonzero to zero as the update advances. As a result, the optimal step-size parameter can be approximately calculated as follows,

The step-size parameter of the ADF is always enhanced according to (2) where the estimate error of the SADF is substituted for ADF.

b. Initial coefficients of SADF

In this method, the precision of step-size control can be improved as the initial value of the SADF and it is near to the impulse response of the actual acoustic echo path. Although the acoustic echo path is unknown unless it is measured, it is generally diminished exponentially. Thus, the initial coefficients of the SADF are also reduced exponentially. In particular, the rate of the reduction is computed from an approximation of the reverberation time, and then the initial coefficients are computed by attenuating random values based on this decay rate.

c. LMS Algorithm

Consider a length L, LMS based adaptive filter, depicted in fig.3, which takes an input sequence x(n) then the output of filter is as follows:

1. The output of the adaptive filter is calculated.

where, = is the tap

weight vector at the

_n

th index,

x(n)=[x(n)x(n-1)……..x(n-L+1)]t,

2. An error signal is calculated as the difference between the desired signal and the filter output.

e(n=d(n)-x(n)

3. The step size value for the input vector is calculated.

d.Implementation of the NLMS algorithm

The NLMS [6], [7] and [8] is an extension of the standard LMS algorithm; the NLMS algorithms practical implementation is very similar to that of the LMS algorithm. Each iterations of the NLMS algorithm require these steps in the following order:-

Where the can be written as,

Here µ is fixed convergence factor to control maladjustment. The filter tap weights are updated in preparation for the next iteration. Each iteration of the NLMS algorithm requires 3N+1 multiplications, this is only N more than the standard LMS algorithm. This is an acceptable increase considering the gains in stability and echo attenuation achieved.

Fig3. Structure of adaptive filter

e. Proposed ECLMS Algorithm

The ECLMS is an extension of the standard LMS and even that of NLMS algorithms. The practical implementation of ECLMS is very similar to that of the LMS and NLMS algorithms. A common major drawback of LMS and NLMS algorithms is the large value of excess mean-square error which results in signal distortion in the noise-canceled signal. In the ECLMS algorithm, the time-varying step-size that is inversely proportional to the squared norm of the difference between two consecutive input vectors rather than the input data vector as in the NLMS. This algorithm provides significant improvements in decreasing mean-squared error (EMSE) and consequently minimizing signal distortion.

The step size value for the input vector is calculated.

W(n)

+

Error

y(n)

d(n)

x(n)

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International Journal of Emerging Technology and Advanced Engineering

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Where is the difference

between two consecutive input vectors. Also is the difference in the priori error sequence. The weight adaptation rule can be made more robust by introducing a small p and by multiplying the weight increment by a constant step size to control the speed of the adaptation. This gives the weight update relation for proposed algorithm in its final form as follows,

The parameter p is set to avoid denominator being too small, step size parameter too big and to prevent numerical instabilities in case of a vanishingly small squared norm.

IV. SIMULATION RESULTS

Simulation results have been done in MATLAB 2014a version with 4.00 GB RAM and i3 processor. Here, the paper presents a new ECLMS algorithm for echo cancellation. In order to implement the experimental analysis, it has been considered a speech signal as an input and applied all the conventional algorithms and proposed algorithm on to the Echo signal. Then it was observed a comparison between existing and proposed echo cancellation schemes with LMS, NLMS and ECLMS. Original speech, echo speech and desired speeches have been shown in fig.4 (a), (b) and (c) respectively.

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(b)

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Fig4. (a) Original speech signal, (b) Echoed speech signal and (c) Desired speech signal

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International Journal of Emerging Technology and Advanced Engineering

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Fig5. Residual error of (a) LMS (b) NLMS and (c) ECLMS

Fig6. Performance analysis of conventional and proposed systems

V. CONCLUSION

In this paper, it is presented that the novel AEC algorithm ECLMS with step size control method has been proposed and verified its performance by computer simulations in MATLAB. The new method can provide the better performance as that obtained using the step size maximizing the convergence speed and steadily cancel the acoustic echo resisting the gibberish. Finally, when compared the results of Convergence parameter for existing algorithms conventional, LMS and NLMS with the proposed ECLMS algorithm, the proposed method have got better results than the existing ones.

REFERENCES

[1] J. Benesty, T. Gaensler, D. R. Morgan, M. M. Sondhi, and S. L. Gay, Advances in Network and Acoustic Echo Cancellation. Berlin, Germany: Springer-Verlag, 2001.

[2] K. Fujii and J. Ohga, ―Convergence time reduction provided by a block length control method applied to the summational NLMS algorithm‖, IEICE Transaction fundamentals, vol. J80-A, pp: 27-35, Jan. 1997.

[3] C. Breining, P. Dreiseitel, E. Haensler, A. Mader, B. Nitsch, H. Puder, T. Schertler, G. Schmidt, and J. Tilp, ―Acoustic echo control—An application of very-high-order adaptive ﬁlters,‖ IEEE Signal Process.Mag., vol. 16, no. 4, pp. 42–69, Jul. 1999.

[4] S. Haykin, Adaptive Filter Theory, 4th ed. Upper Saddle River, NJ:Prentice-Hall, 2002.

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International Journal of Emerging Technology and Advanced Engineering

104 [6] Sandip A. Zade, Prof. Sameena Zafar, ―To Study LMS & NLMS

Algorithm for Adaptive Echo Cancellation‖, International Journal of Advance Research In Science And Engineering, Vol. 4, No. 1, April 2015.

[7] S. K. Mendhe, Dr. S. D. Chede and Prof. S. M. Sakhare, ―Design and Implementation of Acoustic Echo Cancellation Based LMS and NLMS‖, International Journal of Application or Innovation in Engineering & Management (IJAIEM), Vol. 3, No. 8, June 2014.