IJECT Vol. 6, IssuE 3, July - sEpT 2015 ISSN : 2230-7109 (Online) | ISSN : 2230-9543 (Print)

w w w . i j e c t . o r g 132 InternatIonal Journal of electronIcs & communIcatIon technology

Fast LMS Based Acoustic Echo Cancellation and Noise Reduction Algorithm

1Bhupender, 2Sanjeev Dhull1,2Dept. of ECE, Guru Jambheshwar University of Science and Technology Hisar, Haryana, India

AbstractThe rapid growth of technology in past few years has changed the whole dimension of communications. Over the past years, hands-free systems have found increasing applications in areas such as video-conferencing systems and also it is used for safety and convenience in mobile communications. Today people are more interested in hands-free communication. The advantage of this system is to allow more than one person to participate in a conversation at the same time. Another advantage is that it would allow the person to have hands free conversations and moves freely in the room. The adaptive filter makes a replica of the echo and subtracts it from the combination of the actual echo and the near-end signal. The objective of the research is to produce an improved echo and fast cancellation algorithm, which is capable of providing convincing results. This paper surveys Application of Adaptive filters in echo Cancellation.

KeywordsAdaptive Filters, LMS, RLS, Echo Cancellation

I. Acoustic EchoAcoustic echo is generated within analog and digital handsets, with the degree of echo is related to the type and quality of equipment being used. This form of echo is produced due to poor voice coupling between the earpiece and microphone in handsets and hands-free devices. Also voice degradation is caused, as voice compressing encoding/decoding devices process the voice paths within the handsets and in the wireless networks. This results in returned echo signals with very high variable properties. With compounded inherent digital transmission delays, call quality is greatly diminished for the wire line caller [5]. Apart from Acoustic echo, background noise is generated through the network when analog and digital phones are operated hands-free. As additional sounds are directly and indirectly picked up by the microphone, and a multipath audio is created and transmitted back to talker. The surrounding noise, whether in automobiles or in crowded-public environment, when passes through the digital cellular vocoder, it causes distorted speech for the wireline caller [8]. Digital processing delay and speech-compression techniques further contribute in echo generation and in degraded voice quality of wireless networks. Delays are encountered when signals are processed through various routes within the networks, including copper wire, optical fiber, microwave connections, international gateways, and satellite transmission. This is true especially with mixed technology digital networks, where calls are processed across numerous network infrastructures [2].

II. The Process of Echo Cancellation An echo canceller is a device which detects and removes the echo of the signal from far end after it has echoed on the local end’s equipment. In case of circuit switched long distance networks, echo canceller resides in the metropolitan Central Office that connect to the long distance network. This echo canceller removes electrical echoes made noticeable by delay in the long distance

network. Echo canceller consists of three main Components:

Adaptive filter• Doubletalk detector• Non-linear processor•

A brief overview of all these components is presented in this chapter.

Fig. 1: Block Diagram of a Generic Echo Canceller

III. Adaptive Filters for Echo Cancellation An adaptive filter is made up of an echo estimator and a sub tractor. The echo estimator monitors the received path and dynamically builds a mathematical model of line that creates the returning echo. The model of the line is convolved with the voice stream on the received path. This yields an estimate of echo, which is applied to sub tractor. The sub tractor eliminates the linear part of echo from the line in send path [7].

A. Nonlinear Processor The non-linear processor evaluates the residual echo. The nonlinear processor removes all signals below some threshold and replaces them with simulated background noise which seems like the original background noise without the echo.

IV. Least Mean Square (LMS) AlgorithmThe Least Mean Square, (LMS), is basically a search algorithm which is widely used in various applications of adaptive filtering. The main features of the LMS algorithm are proof of convergence in stationary environments, low computational complexity and stable behavior when implemented with finite precision arithmetic. Figure 2 illustrates the working of the algorithm. A path that changes the signal x is called h. Transfer function of the filter is unknown in the beginning. The LMS algorithm is used to estimate the transfer function of the filter. The signal distortion is calculated by convolution and it is denoted by r. In this case h is the transfer function and r is the echo of the hybrid. The near-end speech signal v is added to the echo. The adaptive algorithm creates a filter w. The transfer function of the filter is an estimate of transfer function for the hybrid. This transfer function in turn is used to calculate an estimate of the echo. The echo estimate is denotedby ˆ ˆd r v r r v e− = + − = +

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Fig. 2: LMS Algorithm

The signals are added so that the output signal from the algorithm is v + r – = v + e,where e denotes the error signal. The error signal e and the input signal x are used to estimate the filter coefficient vector w. One of the main problem associated with choosing the filter weight is that the path h is not stationary. Therefore, the filter weights are updated frequently so that the adjustment to the variations can be performed. The filter is a FIR filter with the form given as

w = b0 + b1z -1 + ··· +bL-1 z – (L – 1).

A perfect FIR filter is linear, time-invariant and BIBO stable. However, in a real-time environment, linearity is never a possibility and the first criterion is not fulfilled so the filter can never be a perfect one. The Updating of filter weights is realized in accordance with

w(k + 1) = w(k) -µgw(k)

for k = 0,1,2,··· where gw(k) represents an estimate of gradient vector and µis the step size or convergence factor.

V. Normalized Least Mean Square (NLMS) Adaptive Filter AlgorithmThe main drawback of the “pure” LMS algorithm is its sensitive to the scaling of the input x(n). This makes it tremendously hard (if not impossible) to select a discovering rate µ that guarantees stability of the algorithm. The Normalized least mean squares filter (NLMS) is one of the variant of LMS algorithm that solves this setback by regularizing alongside the manipulation of the input [6].

(0) ( )H zeros p=

Input Signal For n= 0, 1, 2, 3...The error function is:

( ) ( ) ( ) ( )( 1) ( )

He n d n h n u nh n h n

= −+ =

If there is no interference (v (n) =0), then the optimal learning rate of the NLMS algorithm is µopt = 1 and is independent of the input u (n) and the real impulse response h(n) (unknown). In general case with the interference (v (n) 0), the optimal learning rate is:

VI. Recursive Least Square (RLS) Adaptive Filter AlgorithmThe Aim to minimize the sum of the squares of the difference amid the wanted signal and the filter output, least square (LS) algorithm might use recursive form to resolve least-squares at the moment the latest sampling worth is acquired. The weighting update equation is:

With a sequence of training data up to time, the recursive least squares algorithm estimates the weight by minimizing the following cost:

Where u (n) is the Lx1 repressors input, d (n) is the desired response and is the regularization parameter.

VII. Results

0 50 100 150 200 250 300-1.5

-1

-0.5

0

0.5

1

1.5input Signal

Fig. 3: Input Signal Before Filtering Process

0 50 100 150 200 250 300 350 400 450 500-4

-3

-2

-1

0

1

2

3

4input Signal + noise

Fig. 4: Signal After Addiction of AWGN

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Fig. 5: Impulse Response of NLMS Filter and FastLMS Filter for Speech Signal

Fig. 6: WEVN Performances of FLMS VS NLMS for Speech Signal

Fig. 7: Comparison of MSE of NLMS and FastLMS for Speech Signal

Fig. 8: Impulse responses of NLMS filter and FastLMS filter for Speech Signal + White Noise and Background Noise

Fig. 9: WEVN Performances of FLMS VS NLMS for Speech Signal + White Noise and Background Noise

Fig. 10: Comparison of MSE of NLMS and FastLMS for Speech Signal + White Noise + Background Noise

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Fig. 11: Time Complexity of NLMS vs Fast LMS Algorithm FastLMS Clearly Works Much Faster

VIII. ConclusionThis paper provides both Mean square error (MSE) and time complexity of NLMS and FastLMS algorithms estimated for speech signal, White noise and White plus background noise and it is shown in results that the performance of FastLMS algorithm is much better than NLMS algorithm.. Time Complexity of NLMS vs. Fast LMS shows that on average FLMS is 13-29 times faster than LMS Algorithm. FastLMS clearly works much faster taking only 0.0312 seconds for Echo cancelling a speech Signal. Moreovers, WEVN performance is also estimated for speech signal, White noise and White plus background noise for both NLMS and FastLMS and it is proven that FastLMS has very less power variation in comparison to NLMS filter.

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Bhupender, Department of Electronics and Communication Engineering, Guru Jambheshwar University of Science & Technology, Hisar.Qualification: B. Tech ECE from GJU, Hisar, and pursuing M. Tech from GJU, Hisar.Area of interest is Signal Processing & VLSI technology.

Dr. Sanjeev Dhull is working as an Associate Professor in the Department of ECE, GJUS&T, Hisar. His highest qualification is Ph.d in Signal Processing. He has published 43 research papers in international journals and conferences. He has 15 years of teaching experience in reputed universities and institutes.