Faculty of science, Ibn Tofail Kenitra University, Morocco Faculty of Science, Moulay Ismail University, Meknès, Morocco

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1 Design and Simulation of an Adaptive Acoustic Echo Cancellation (AEC) for Hands-ree Communications using a Low Computational Cost Algorithm Based Circular Convolution in requency Domain 1 *Azeddine Wahbi 1 Laboratory of Electrical Engineering and Energy System aculty of science, Ibn ofail Kenitra University, Morocco wahbi_azeddine@yahoo.fr Abstract In this paper a module consisting of a ast Least Mean Square (LMS) filter is modeled and verified to eliminate acoustic echo, which is a problem for hands free communication. However the acoustic echo cancellation (AEC) is modeled using digital signal processing technique especially Simulink Blocksets. he needed algorithm code is generated in Matlab Simulink programming. At the simulation level, results of simulink implementation prove the module behavior for cancellation of echo in hands free communication using the LMS adaptive algorithm. he main scope of this paper is to implement the module, benefiting the advantage of circular convolution properties and ast ourier ransform () high computation speed in frequency domain rather adaptive algorithms Normalized Least Mean Square (NLMS) and Recursive Least Square (RLS) in time domain with high complexity. Keywords Adaptive Algorithm, AEC, Circular Convolution, ast ourier ransform (), Digital Signal Processing (DSP). I. INRODUCION Adaptive filtering technique has emerged as an important technology for hands free communication. his is why adaptative filters were developed and tested long before by the use of analog bench platforms until a digital based technique took place, the DSP. his new technique allows better signal filtering design and found its benefits in High idelity audio systems or speech networks. Acoustic echo takes place whenever a loudspeaker is placed near a microphone in a full-duplex communication application. his is the case in speaker-phones, audio and video conferencing, desktop communication, and many other communication scenarios. Especially hands-free mobile communication and car-kits are becoming increasingly important due to safety regulations introduced in many countries [1-2]. In this work, the method used to achieve echo cancellation is known as adaptive filtering. his method is frequently used to enhance communication quality by removing line echo. his is why adaptative filters were developed and tested long before on analog bench platforms until a digital based technique breakthrough emerged, the DSP. his new 2 Ahmed Roukhe and 1 Laamari Hlou 2 Laboratory of Atomic, Mechanical, Photonics and Energy aculty of Science, Moulay Ismail University, Meknès, Morocco technique allows better signal filtering design and found its benefits in High idelity audio systems or speech networks. his paper will focus on software based LMS adaptive algorithm to remove acoustic echo from hands free communication. However, the AEC is modeled in Simulink environment by using digital filters, especially adaptive ast Least Mean Square (LMS) algorithm based \I operations and circular convolution frequency domain that require approximately Nlog 2 N real multiplications and reduce the computational complexity compared to LMS adaptive algorithms modeled and implemented by A.wahbi in [3], NLMS [4-5-6] and RLS [7-8] adaptive algorithms, which deal with time domain based on a linear convolution. his algorithm requires 3N+1 real multiplication. he paper is structured as follows: section II presents digital adaptive filters for echo cancelling, section, section III presents simulation results and Section IV concludes this paper. II. DIGIAL ADAPIVE ILERS OR NOISE CANCELLING Developing a filter that is able to comply with the statistics of the signal is the main scope of adaptive filtering. Adaptive algorithm efficiency depends on three criteria that size up: he complexity of computation and the amount of computation executed at each stage. he behavior of speed adustment that permits an adaptive filter to reach Weiner solution. he estimated error generated by the dissimilarity between the actual Weiner solution and the adaptive algorithm resolution. Adaptive cancellation of noise is the main pattern of adaptive filters.

2 A. Adaptive ilters In this section we first go through an examination of the filter structure with an emphasis on inite Impulse Reponses (IR) filters. his is followed by a review of the Wiener filter leading to the development of the ast Least Mean Squares (LMS) algorithm. An acoustic echo canceller is a closed loop linear adaptive filter used for direct system modeling. here are many different combinations of filters and algorithms, depending on the particular application requirements. or noise cancellation, there is a classical standard adaptive filter formation. he filter part is made up of the most commonly used structure: a IR filter which is also known as a tapped delay line, nonrecursive or feed-forward transversal filter, as shown in ig 1. during the inverse transformation). o make it simple, we assume here that we choose M=N+L-1 in order to give an implementation example with values of M greater than N+L-1. Let W be the D matrix having M (M N) in size and the following coefficients: kl W k, l exp( 2 ) (2) M and W 1 the inverse transform matrix: 1 1 kl W k, l exp(2 ) (3) M M ig. 2. Block diagram of N-point algorithm ig. 1. IR filter structure in time domain. he IR filter consists of a series of delays, multipliers and adders; has one input, x, and one output, y. he output is expressed as a linear combination of the delayed input samples: Where y x. h (1) herefore h are the filter coefficients and L is the filter length. vectors h and y is the convolution (inner product) of the two x. In this paper we will only consider LMS filters for echo cancellation. B. ast ourier ransform or calculating the (ig. 2), M is to be chosen as a power of 2. In general, we choose N+L-1 if this value is suitable. Otherwise, we choose the nearest power of 2 that is greater than the latter value (in which case we have to complement the vectors by the number of zero coefficients necessary and discard the last vector components introduced C. ast adaptive algorithm in the frequency domain One of the adaptive filter applications is the adaptive echo canceller. ig. 3 describes its structure where the desired response is composed of an original signal plus the echoed, which is uncorrelated with the signal. he filter input is a sequence of an original signal which is correlated with the echoed signal in the desired signal. By using the LMS algorithm inside the adaptive filter, the error term e produced by this system is then the original signal with the echo signal cancelled. ig. 3. ast adaptive filter structure

3 D. ast Convolution in the ourier transform domain Echoed signal values y are estimated, as shown above, by means of a linear convolution represented by the equation (1). his calculation is very consuming regarding computation. he main idea emerging in terms of fast convolution algorithms is to fulfill convolution in the ourier transform domain according to the principle of duality. Indeed, circular convolution in the time domain is equivalent to a term to term multiplication in the D frequency domain and hence quick calculation algorithms of the D are then used to perform this operation with reduced complexity he filter is implemented in the circular convolution frequency domain between vectors and respectively defined by: h et x, both having length N+L-1, h [ h (0) h (1)... h ( L 1) (4) h Let and h 0 1 ( N 1) y be the product of the circular convolution between h : y x h x (5) where represents the circular convolution product between two vectors. he length of vector y is N+L-1, and its last N components correspond to the linear convolution of equation (4), that is to say to Y components. he first L-1 components result from circular convolution and should be excluded. In a formal way, we exclude these first L 1 components by considering the truncation matrix N having N (N+L-1) in size and defined by: O I (6) N N ( L 1) N hen we have: Y y. N Y. x h (7) N he circular convolution completion is done in the frequency domain using the respective D of noted therefore X and x and H plus having M in length: h, X W. x (8) H W h. (9) he calculation of the linear convolution is then performed according to the following expression: Y W X H 1. ( ) (10) N Where represents the scalar Schur product, or the component to component product of the vectors. Returning to the equation (11) for the error signal, we then obtain: e d Y 1 N e d. W ( X H ) (11) hrough the use of, the calculation of the error generated by each block in this manner is less resource consuming than the block-based temporal LMS. E. Adaptive filter update As for the calculation of the error, the update of the filter can be performed in the frequency domain with a lower computational cost. he update equation (13) in the time domain can be expressed quite simply in the frequency domain. or this purpose, we define the D of the error sequence, E, as follows: E W 0 L 1 h.... (12) e at each iteration, the update of the adaptive filter is then performed according to the equation: * H H 1 X E ) (13) Where is the adaptation step that controls the speed of convergence of the algorithm.

4 . LMS Algorithm Block LMS (BLMS) algorithm can be made less computation time consuming if the temporal convolution is achieved in the frequency domain. Doing so, it is therefore possible to take advantage of D (Discrete ourier transform) circular convolution properties and ast ourier ransform () high computation speed. he LMS ilter block shown in ig 4 implements an adaptive ast least Mean square (LMS) filter, where the adaptation of filter weights occurs once for every block of samples. he block estimates the filter weights, or coefficients, needed to convert the input signal into the desired signal. Connect the signal you want to filter to the Input port. his input signal can be a sample-based scalar or a single-channel frame-based signal. Connect the signal you want to model to the Desired port. he desired signal must have the same data type, frame status, complexity, and dimensions as the input signal. he Output port outputs the filtered input signal, which can be sample or frame based. he Error port outputs the result of subtracting the output signal from the desired signal. H. Simulink Results In the following graphics (figs. 6, 7, and 8), we observe the input signal (the original signal with echo) and how this echo is removed from the original signal after crossing by the echo cancellation ast adaptive ilter in frequency domain module, knowing the echoed signal has less amplitude than the original signal. It is also demonstrating how the signal is filtered, and the result is an output signal with less amplitude than the input signal and without echo. ig. 6. Result obtained using Simulink simulation (Original signal) ig. 4. LMS ilter block [9] III. SIMULAION RESULS G. Echo Canceller Modeling Under Simulink In this work we modeled the system shown in fig. 5 under Simulink Blockset. he delay of time is approximately 20 ms and the number of samples for each read from file (rom Wave ile) length is 128 samples per frame at 8000 Hz sampling rate. AEC implementation is setup with filter length=128 and block size of =128. he step size is chosen as λ = ig. 7. Result obtained using Simulink simulation (Echoed signal) ig. 5. Block diagram of the acoustic echo canceller

5 REERENCES ig. 8. Result obtained using Simulink simulation (Output filtered) he effect of modifying the step-size, the filter length, the delay value on the convergence rate and obtainable performance is tested. However, the convergence rate of the AEC to find the optimal value of the LMS filter to cancel the echo depends on various factors such as the step size parameter. It should be verified that a shorter filter length is required to obtain the desired cancellation while using the input signal, a wav file. Unofficial hearing tests should prove that the system is working properly: the periodic signal is almost cancelled whereas the speech maintains its natural quality. IV. CONCLUSION In this paper, we have tried to modeling and implement an adaptive filter module in frequency domain based \I operations and circular convolution with low complexity rather than algorithms in time domain with low computation speed. his module, consisting of software blocks, was specifically designed to provide echo cancellation in hands-free communications system to achieve ideal sound reproduction as in high-fidelity systems. In the future work we will implement a combined module AEC-Noise Acoustic Cancellation (ANC) in real time onboard an autonomous DSK C6713, benefiting the low computational cost and the simplicity of the implementation using simulink programming. [1]. Ykhlef and al, Acoustic Echo Cancellation and Suppression of Noise for hands-free communications, 5th International Conference: Sciences of Electronic, echnologies of Information and elecommunication in unisia, March 2009, pp [2] S. Goetze and all, Hands-ree elecommunication for Elderly Persons Suffering from Hearing Deficiencies, IEEE Healthcom, [3] A.Wahbi and all, "Real-ime acoustic echo cancellation for hand-free communication by implementing a LMS algorithm onboard an autonomous DSK C6713 ", 3rd International Conference on Systems, Modeling and Design, Kenitra (MIC- SMD 2013), [4] R. Chinaboina and al, Adaptive algorithms for acoustic echo cancellation in speech processing, International Journal of Research and Reviews in Applied Sciences, Vol. 7, No. 1, April 2011, pp [5] P.Raesh, A.Sumalatha, A Novel Approach of Acoustic Echo Cancellation Using Adaptive iltering, International Journal of Engineering Research & echnology (IJER), vol. 1, 2012, PP [6] M. Alam and all, Performance Comparison of S, W, LMS and RLS Adaptive Algorithms in Denoising of Speech Signal, IACSI International Journal of Engineering and echnology, Vol.3, No.3, June 2011, pp [7] A. Munal and all, "RLS Algorithm or Acoustic Echo Cancellation", Proceedings of 2nd National Conference on Challenges & Opportunities in Information echnology (COI), 2008, PP [8] A. Kourav and all, RLS Algorithm for Adaptive Echo Cancellation, International Journal on Emerging echnologies, vo. 2(1), 2011, pp [9] he Mathworks Inc., Matlab and Simulink User s Guide, 2012