Performance Evaluation of Adaptive Algorithms for ...

International Journal of Applied Engineering Research ISSN 0973-4562 Volume 9, Number 17 (2014) pp. 3781-3805 © Research India Publications http://www.ripublication.com

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo Cancellation: A Technical Review 1

Mahesh Chandra, 2Asutosh Kar and 3Pankaj Goel

1

Department of Electronics & Communication Engineering, BIT, Mesra, Ranchi, India 2 Department of Electronics & Telecommunication Engineering, IIIT, Bhubaneswar, India 3Department of Electronics and Communication Engineering, BIT, Mesra, Ranchi, India E-mail: [email protected], [email protected], 3 [email protected]

Abstract The problem of acoustic echo is well defined in case of hands-free communication.The presence of large acoustic coupling between the loudspeaker and microphone would produce an echo that causes a reduction in the quality of the communication.The solution to this problem is the elimination of the echo with an echo canceller which increases the speech quality and improves listening experience. In this paper, many prominent work done in relation to acoustic echo cancellation (AEC) is discussed and analysed. The existing AEC algorithms are analysed and compared based on their merits and demerits in a time varying echoed environment. It covers the basic algorithms like least mean square (LMS) , normalized least mean square (NLMS) and recursive least square algorithm as well as their modified versions like variable step size NLMS, fractional LMS, Filtered-x LMS, variable tap-length LMS algorithm, multiple sub-filter (MSF) based algorithms, variable tap-length MSF structures etc. Finally, a judicious comparison is presented towards the end of the paper in order to judge the best AEC algorithm in the present time. Keywords: adaptive filter; acoustic echo cancellation; least mean square; mean square error, convergence.

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1. Introduction Active Echo is the phenomenon in which a delayed and distorted version of the original wave is reflected back to the source. Echo depends on two parameters i.e. amplitude and time delay of reflected waves. In general, echoes with appreciable amplitude and larger delay such as 1ms are considered, but if echo generates in such a way that the delay increases more than 20ms then it becomes increasingly disturbing and objectionable. However, echo is not noticed if the delay associated with the acoustic feedback loop is small or the magnitude of the echo is below perception threshold. Echo cancellation is an important aspect in the design of modern telecommunication systems [1-3]. Mainly two types of echo are present in present communication technologies i.e. hybrid echo and acoustic echo. The network or hybrid echo, on the Public Switched Telephone Network (PSTN), is caused by the four-wire to two-wire impedance mismatch [4]. The mismatch results in unwanted reflection of transmitted energy back to the speaker or the source. Networks are equipped with echo cancellers (ECs) known as network or line ECs, to remove these unwanted reflections. The International Telecommunication Unions (ITUs) Recommendation ITU-T G.168 2002 [5] specifies the minimum requirements and test conditions for performance of network ECs in PSTN. However, the development of hands-free applications gave rise to another kind of echo known as acoustic echo which is the main area of focus in this paper. Acoustic echo is produced due to coupling of the loudspeaker and microphone and becomes more severe in digital communication. The signal interference caused by acoustic echo is disturbing to users and causes a reduction in the quality of the communication. Here along with the original required signal the attenuated, time-delayed images of this speech signal is produced which creates disturbance.When the coupling of loudspeaker and microphone takes place in an enclosure, say room, such arrangement is called Loudspeaker-Enclosure-Microphone (LEM) system [3], [6]. In LEM system model, loudspeaker emitted signal reaches the microphone not only directly but also via reflections from neighboring objects [6] as shown in Fig. 1. Therefore, the signal received at the microphone is a superposition of the delayed, attenuated, and filtered versions of the emitted signal. Thus the received signal contains a direct path plus extra paths resulting acoustic echo. The echo canceller applications are presented in Table 1 for both hybrid and acoustic systems. Acoustic echo is typically more complex than hybrid or network echo, and its impulse response is much longer. Acoustic echo is more pronounced in the case of digital wireless applications where long processing time is needed for signal compression, channel coding etc. Acoustic echo is generally modeled as the response of a linear system, the impulse response of which is of the order of a few tens to hundreds of milliseconds [7]. To overcome this problem an Acoustic Echo Canceller (AEC) is connected at each end. The AEC generates an estimate of echo signal which is received at the microphone and subtracts it from the received signal. [8-10] Classical methods for AEC rely on a studio environment or employ voice controlled switches in order to reduce the effect of acoustic echo [3]. In studio environment speakers are not allowed to move freely. In addition reflections can be prevented by using sound absorbing materials. Acoustic Echo Suppressor or voice

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3783 switching techniques, are the first introduced solutions to deal with acoustic echoes [7], [8]. In the voice controlled switching, echo is suppressed by inserting loss devices between the receiving and the transmitting circuit of the communication system according to the direction of conversation. However, echo suppression is not practicable due to following deficiencies: i. The attenuation of the acoustic path from loudspeaker to microphone is not high. ii. Only half duplex communication is possible when voice controlled switching is employed. Several echo suppression methods such as frequency shift, centre-clipping, comb filtering, microphone arrays etc have not been very effective in controlling acoustic echo [1]. Increased network delay render echo suppressor technology ineffective and encouraged the development of echo cancellation equipment. In late 1960’s echo canceller was invented by J.L Kelly and B.F. Logan, presented by M.M. Sondhi [9]. This device adaptively estimates the echo path transfer function and subtracts an estimated echo from the returning signal. In present time AEC is realized by adaptive Finite Impulse Response (FIR) filters having thousands of coefficients to achieve a satisfactory echo cancellation [10], [11]. LMS algorithm is used for adaptation due to its simplicity in implementation and low computational complexity. However, LMS algorithm converges poorly when the input reference signal has large eigen value spread and when the length of adaptive filter is large [12], [13]. The echo canceller should have a fast convergence speed so that it can identify and track rapidly the changes in the unknown echo path. The convergence rate depends on the adaptive algorithm as well as the structure of adaptive filter used in AEC [14]. When two speakers talk simultaneously the echo canceller should be able to detect this double talk accurately. The echo return loss enhancement (ERLE) is used to measure the effectiveness of an echo cancellation method. If it is high then the echo canceller is considered to be good [15], [16]. A way to alleviate the effect of slow convergence and computationally intensive long adaptive filter problem is to use Multiple Sub-filter (MSF) instead of Single Long Filter (SLF) [17-20]. Moreover, the acoustic channel is time varying which leads to further degradation in performance. The high computational load of the adaptive filtering algorithm can be improved by Selective Coefficient Update (SCU) where selected coefficients are updated at each iteration resulting fewer computations [21], [22]. In this paper all these well known algorithms are analyzed based on their computational and structural complexity, mean square error, convergence and tracking capability for an AEC framework to suggest the best low complexity algorithm in a noisy time varying scenario for echo cancellation.

2. Adaptive Filter Based Acoustic Echo Cancellation Long distance telephone circuits have generally been impaired by echo effects. Echo suppressors developed at the Bell Laboratories have been perfected during past decades. Conventional echo suppression techniques were not very successful with

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satellite communication where international calls have echoes of long time delay. Earlier echo suppressors were used in half duplex mode. To permit simultaneous two way transmission (full duplex mode of communication) of voice and data, adaptive echo cancellers are found to be better replacements for echo suppressors. Table 1: Echo Canceller Applications Echo Source Application 1. Impedance Voice Communication Mismatches  Long Haul Transmission Data Communication Full Duplex Data Transmission 2. Sound-Wave Speaker/Microphone System Reflection

Example

 

Satellite Communication Automatic Call Transfer

V.32 Data Modem 

Teleconferencing

 Hands-free Telephony  Hearing Aids  Public Addressed System  Internet Telephony  Desktop Conferencing LEM

Far end LEM input signal

Near end LEM output signal

Fig. 1: Acoustic Echo Generations. Echo cancellation was developed in the early 1960s by AT&T Bell Labs and later by COMSAT TeleSystems [9]. The adaptive echo canceller tries to overcome the deficiencies of the classical methods. Adaptive echo cancellation is achieved by synthesizing the effect of echo path on voice or data and subtracting it from the echo path output. The synthesized echo is generated by passing the loudspeaker signal

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3785 through a filter whose impulse response matches with the impulse response of the acoustic channel. As echo path is time varying, an algorithm is needed which can adapt the filter to these acoustic channel impulse response changes [14]. To realize adaptive echo canceller, different possible filter structures and a variety of adaptive algorithms are available. A brief description of the adaptive filter, adaptive filter structure and adaptive algorithms are given in the subsequent subsections respectively. 2.1 Adaptive Filter Adaptive filtering constitutes one of the core technologies in digital signal processing and finds numerous applications including echo cancellation, channel equalization, adaptive noise cancellation. Adaptive filter consists of a digital filter and adaptive algorithm. The ability of an adaptive filter to operate suitably in an unknown environment and track time variation of input statistics make the adaptive filter a powerful device for signal processing and control application. Adaptive filters enable the system to adjust in a changing environment or statistical condition. So arrangements are to be made for adjusting the filter parameter to suit the changing need. The adaptive filter estimates the echo signal, and the estimated signal is subtracted from the observed signal generating an error signal e( n) . This error signal is fed back into the adaptive filter and its coefficients are changed algorithmically in order to minimize the cost function. In case of echo cancellation, the optimal output of the adaptive filter is equal to the unwanted echoed signal. A simple AEC framework both near and far end subscriber in a hands free communication is shown in Fig. 2.

Fig. 2: Acoustic Echo Cancellation in a Hands-Free Telephony. 2.1.1 Adaptive Filter Structure The adaptive filters can be implemented in a number of different structures or realizations. The choice of the structure can influence the computational complexity of the process and also the necessary number of iterations to achieve a desired performance level. Basically, there are two major classes of adaptive digital filter realizations, distinguished by the form of the impulse response, namely the FIR filter and the Infinite-duration Impulse Response (IIR) filters. FIR filters are usually

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implemented with non-recursive structures, whereas IIR filters utilize recursive realizations [11]. FIR filter is preferred for AEC applications for its stability during adaptation. IIR can normally achieve similar performance as FIR, with smaller amount of coefficients and less computation. However, as the complexity of the filter grows, the order of the IIR filter increases a lot and the computational advantage is less dominant. Also, IIR suffers from the instability problem. So the filters that are being used in AEC are usually of the FIR type. [12] 2.1.2 Adaptive Algorithms The algorithm is the procedure used to adjust the adaptive filter coefficients in order to minimize a prescribed criterion. The performance of an adaptive filter is critically dependent not only on its internal structure, but also on the algorithm used to recursively updates the filter weights that define the structure. There are many recursive algorithms for the adaptation of linear adaptive filtering. The choice of algorithm is determined by the performances like rate of convergence, misadjustment, tracking, robustness, computational complexity, structure. Adaptive algorithms are broadly classified as sample-by-sample adaptive and block adaptive algorithms [14], [23]. In the sample-by-sample adaptive algorithms the adaptation can take place both in time domain as well as in frequency domain. Therefore, sample-by sample adaptive algorithm will be further divided into two classes of algorithms. One class includes filter that are updated in time domain sample-by-sample, called time domain sampleby sample adaptive algorithm [13]. Algorithms belonging to this category are Least Mean Square (LMS) and Recursive Least mean Square (RLS) which are popular due to number of advantages [2], [23]. Other class includes filters that are updated in frequency domain and are known as Frequency Domain Adaptive Filter (FDAF). In FDAF the adaptation of the filter can be performed in frequency domain sample-bysample in order to exploit the advantage of Fast Fourier Transform (FFT). The use of FFT reduces the computational complexity of FDAF [23], [24]. The common algorithm belonging to this category is frequency domain adaptive algorithm based on Discrete Fourier Transform, frequency sampling methods, and sub-band technique. Sub-band technique has the advantage that it can achieve fast convergence at reduced computational complexity [12]. But the sub-band solution exists if and only if subband signals obtained are alias-free. This requires band pass filters with infinite stop band attenuations which are not realizable. Although, in this approach the reduced computational complexity is achieved but the price to be paid is a delay introduced into the signal path by the analysis and synthesis banks. Similarly the block adaptive algorithm is further divided into two classes. One class include filters those are updated in time domain, block-by-block, and is called time domain block adaptive algorithm [23]. The basic principle for time domain block adaptive algorithm is that a number (says B sample) input signal are collected before computing a block of output signals using convolution. Thus the filter is only adapted once every B th sampling instant, resulting poor tracking performance. In order to make use of FFT the filter adaptation has to be performed in the frequency domain. Thus the multiplication replaces convolution in the adaptive filter, leading to reduction

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3787 in the computational complexity. This results in another class of adaptive algorithm in which filters are updated in frequency domain and are called as block-by-block frequency domain block adaptive algorithm [24]. We will discuss only the time domain sample-by-sample adaptive algorithm and frequency domain block adaptive algorithm in the subsequent subsections respectively. 2.1.3 Time Domain Sample-by-Sample Adaptive Algorithm A brief description of different types of time domain sample-by-sample algorithm is discussed here. 2.2 Recursive Least Square Algorithm Recursive Least square (RLS) algorithm is based on the minimization of the weighted squared error sum [14]. In the RLS algorithm initialization of the inverse of the autocorrelation matrix and the choice of forgetting factor are important. The RLS algorithm must be provided with suitable initial values. The choice of the forgetting factor also influences the convergence and tracking behavior. The RLS algorithm has computational and the storage complexity O ( L2 ) [18], where L is the length of the filter. It appears quite appropriate to choose RLS algorithm for AEC application due to its high convergence speed. But RLS algorithm has high computational complexity, thus not preferred in AEC applications [2], [5]. 2.3 LMS algorithm LMS estimation algorithm was first proposed by Widrow and Hoff in 1960 through their studies of pattern recognition [12], [13]. The LMS algorithm is most commonly used algorithm for adaptive filtering applications, due to its simplicity and low implementation cost. The algorithm is defined by the equations: e(n)  d (n)  W T (n) X (n) (1) W (n  1)  W (n)   X (n)e(n) where  is adaptive step size parameter. If  is too large then the algorithm will not be convergent in a mean square algorithm. On the other hand, if  is small then the convergence of the algorithm will be slow. It can be shown that the LMS algorithm 2 0   max where  is the largest eigenvalue of the correlation matrix is stable for max

of the input data. The LMS algorithm is a most popular algorithm due to number of advantages. But it is noticed that the convergence speed is slow when LMS algorithm is used for adaptation especially for longer filter length [25], [26]. Furthermore, the adaptive filter convergence is slow due to step size restriction which depends on the characteristics of the input signal [26]. Some methods like; pre-whitening of inputs signal etc. have therefore been explored to improve the convergence speed of the LMS algorithm. Although, these methods attempt to improve convergence speed of the LMS algorithm but add some computational complexity.

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There are more common variant of LMS algorithm like; Normalized LMS (NLMS) [6], Proportionate NLMS (PNLMS) [2], Affine Projection Algorithm (APA) [6]. These have their relative advantages and disadvantages when used for the long length adaptive filter adaptation. NLMS is defined as, e(n)  d (n)  W T (n) X (n)

W (n  1)  W (n) 

 X (n) e(n) 2   X ( n)

(2)

where  is the controlling factor which prohibits the weight updation equation to go into infinite when X (n) is equals to zero. The stability and convergence properties of NLMS are determined by the step-size parameter  . The NLMS algorithm is stable for 0    2 and the stability of NLMS is thereby independent of the properties of the input signal. Furthermore, NLMS exhibits faster convergence compared to LMS for both correlated and uncorrelated data. Both the LMS and NLMS algorithm are computationally efficient and having computational complexity O ( L ) . Although, the computational complexity of both the LMS and NLMS are same, but NLMS require extra computation for obtaining the input vector norm and further used normalization of the adaptation step size. PNLMS algorithm exploit the structure of the impulse response of the acoustic echo path and assigning different step size to different sections of the echo acoustic path impulse response [2]. The idea is that, ideally, the impulse response samples with large values are adapted with large step size while those with small size get a small step size. But this method depends on the a priori knowledge concerning the current echo path impulse response and the ability to adjust the step size accordingly. FLMS is based on the concept of fractional order calculus. Fractional derivative equation, is used in the FLMS concept [27]. Estimation error of the FLMS converges earlier than the LMS, whereas the LMS consumes more number of iterations. The mean square error of the FLMS algorithm is also improved as compared to LMS algorithm. It also stabilizes the MSE quicker than the LMS algorithm. 2.2 1Frequency Domain Block Adaptive Algorithm Frequency domain techniques are implemented in order to handle the long impulse response system. An approach to reduce computation complexity of large adaptive FIR filter is to incorporate block updating strategies. In this method, blocks of input samples are transformed and processed in frequency domain using Fast Fourier Transform (FFT). This method reduces the computational complexity at the expense of delay [24]. The delay problem can be alleviated by partitioning the filter vector. A small filter length results in large number of parallel branches and vice versa. Obtaining too many branches of small length increases the steady state error but using less number of branches with large block length reduces the convergence speed. From the above discussion, it can be seen that based on the performance criteria, LMS is suitable for AEC application.

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3789 3. Dynamic Structure Acoustic Echo Cancellers The overall performance and complexity of linear adaptive filter in a time varying scenario largely depend on its structure. The filter order or the number of weights/taps is one of the most important structural parameters of the linear adaptive filter. Most current adaptive filters fix the filter order at some compromise value which makes it less effective in time varying scenarios. Too few filter coefficients results in undermodelling and too many results in adaptation noise and slow convergence due to mismatch of extra coefficients [28-30]. The optimum filter order that best balances the complexity and steady state performance of the adaptive filter has grabbed attention due to its applicability in field like acoustic echo cancellation(AEC), adaptive equalizers, system modeling etc [28-30]. As the length of adaptive filter used for echo cancellation setup is very long so it increases the overall complexity of the system. So the optimum order estimation algorithm can be applied to the echo cancellation frame work to find out the optimum length of the adaptive filter being used for echo cancellation without affecting the overall performance of the system [29]. In case of fixed filter length it results in so called too short and too long filter as discussed below. Type-1 (Too short order filter): Too few filter coefficients results in under modeling .Suppose there is a typical impulse response from an acoustic arrangement as shown in Figure.1 where the intension is to identify the long non-sparse system. A too short filter will result in degraded echo cancellation performance and demonstrates the problem of insufficient modeling. Type-2 (Too large order filter): The obvious drawback of a too long filter is slow convergence .It is not suitable to have a too long filter as it increase the filter design complexity and introduce adaptation noise due to extra coefficients .Suppose there are two filters of different length to model a acoustic echo cancellation arrangement shown in Fig.2, where the too long filter converges slower than the filter which has same number of coefficient as the acoustic system to be identified. Due to the mismatch of tap-length the error spreads all over the filter and the adaptive filter itself introduce echo in this case. The first variable filter order algorithm [1] proved that shorter filters has faster convergence than the larger ones and adjusting the filter order can improve the convergence of the LMS algorithm[28],[31]. In [29] a variable filter order algorithm is proposed by comparing the current MSE to the previous estimated MMSE and in [1] by using the time constant concept where step size is constant and calculated in advance. In both [25], [29] order can only be increased in one direction from lower to optimum value of tap-length which motivated further research. Further an algorithm was proposed in [25] which was efficient than the previous ones. All these algorithms aim more at improving the convergence rather than finding the optimum filter order. But the step size control has less effect on filter length control[28].More relevant work was proposed in [31] where the filter is partitioned into segments and order is adjusted by one segment either being added or removed from the filter according to the difference of the output errors from the last two segments. This algorithm suffers from the drawback of carefully selecting the segments and use of simple errors rather than MSE i.e. to solve the problem of optimum filter order estimation it creates another issue of selecting the proper length of the segment. Based on gradient descent

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approach another algorithm is proposed [32] in which the filter length is adjusted dynamically along the negative direction of the squared estimation error signal. This algorithm was proved to be more flexible than [29] but it created the wandering problem. 3.1 The fractional variable tap-length learning algorithm The pseudo fractional tap-length that automatically does the structure adaptation in a dynamic time varying situation was first obtained efficiently by following the adaptation proposed [31] (3) Lnf (n 1)  Lnf (n)  [(eLL(n) (n))2  (eL (n))2 ] L ( n )L ( n )

Finally the tap-length L ( n  1) in the adaptation of filter weights for next iteration is formulated as follows, [33], [34] L (n  1)  Lnf ( n) if L (n )  Lnf ( n )   L (n )

 

(4)

otherwise

Lnf (n) , is the tap-length which can take fractional values. (eLL(n) (n))2  (eLL(n ) (n) (n)) is L

the MSE difference with an error spacing of  L ( n ) [31].The actual order of the adaptive filter Lnf ( n ) is rounded to the nearest integer value to get the optimum tap-length. In (3) the factor  is the leakage factor which prevents the order to be increased to an unexpectedly large value and  is the step size for tap-length adaptation. It follows simple LMS algorithm for weight update. An improved FT-LMS with a novel methodology to decide variable  is presented in [35]. 3.2 The VT-VSLMS algorithm Based on the FT-LMS many algorithms are proposed. One of the recently proposed methods is VT-VSLMS. The dynamic tap-length that can take fractional value is obtained by the proposed adaptation based on constrained selection of predefined leaky factor l f and a variable error spacing (n) as defined in [19], [20], [36],  l  1 Lnf (n)  Lnf (n 1)  f  [(eLL(n) (n))2  (eLL(n)(n) (n))2 ] 1 l f  (log10 l f )2 

(5)

The tap-length L n f is rounded to the nearest integer value to get the dynamic structure where lf 1   (6)  1  l f and (log10 l f ) 2 The error spacing (n) is obtained as the adaptation, [36]

(n)  max(min , max S )

(7)

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3791 where S is smoothing parameter which changes as per the variation in the error spacing and the maximum and minimum value of  . log 10 (  ( n )) S (8) (  max   min ) If S changes from (0, 0.5) the error spacing varies from (  m in , 0 .5  m ax ) . The variable tap-length LMS algorithm is used for weight updating and this type of taplength selection is useful basically for echo cancellation applications [19].

4. Low Complexity Multiple Sub Filter Approach to AEC An acoustic echo canceller generates an estimate of echo signal which is received at the microphone and subtracts it from the received signal. Acoustic echo cancellers are realized by adaptive FIR filters having thousands of coefficients [6]. LMS algorithm is used frequently for adaptation due to its simplicity in implementation and low computational complexity. However, LMS algorithm converges poorly when the input reference signal has large eigen value spread and when the length of adaptive filter is large [5], [37]. It is generally found that adaptive LMS algorithm with lower order has faster convergence [25]. Moreover, the acoustic channel is time varying which leads to further degradation in performance. There are different methods available to alleviate this problem. Several methods have been reported in the literature to improve the convergence speed of adaptive filters [21], [22]. One solution to this complexity problem is to use adaptive IIR filters, such that an effectively long impulse response can be achieved with relatively few filter coefficients. But they are unstable [5]. Another method is to adapt the filter in transform domain. But the transformation in frequency domain and inverse transformation requires additional computations. Another way to mitigate the slowly convergent and computationally intensive long adaptive filter problem itself in time domain is to use decomposition or MSF instead of using SLF [18]. The idea is based on partitioning the SLF into MSF. The decomposition technique allows efficient use of parallel processing which achieves increase in speed of the convergence rate. The idea is that signal realized by each branch of the multiple sub-filter cancels the signal in the corresponding echo path which results in fast convergence because the order of each sub-filter in MSF is much smaller as compared to order of SLF. Various methods of MSF based echo cancellation are shown in Fig. 3.

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Monophonic

MSF

SLF

FU

Stereophonic

SLF

SCU

FU

SCU

MSF

Different Error Algorithm

Combined Algorithm

Different Error Algorithm

Common Error Algorithm

Common Error Algorithm

Fig. 3: Different adaptation algorithms for MSF based AEC.

4.1 Different Error Algorithm for MSF In different error algorithm, each sub-filter uses different error signals in its updation equation which provides reduced coupling between sub-filters and consequent improvement in convergence speed. The error signals in this case are independent on each other. In this case the convergence improves but the steady state error also increases as the number of sub-filter increases. The output of the multiple sub-filters is given as [17] M 1

y ( n)   Wi T ( n ) X i ( n);

n  0,1,.......M  1

(9)

i 1

where W (n)  [w1(n), w2 (n),......wL (n)]T and X i ( n )  [ x ( n ), x ( n  1), x ( n  2),.....]T . The error signal in this case can be obtained as, [17-20]

e0 (n)  d (n)  y0 (n)

(10)

M 1

ei (n )  ei 1 ( n)   yi ( n) ;

i  1, 2,..., M  1

i 1

where d ( n ) the desired signal and M is the total number of sub-filters. The LMS adaptation of each sub-filter is expressed as:

(11)

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3793 Wi ( n  1)  Wi (n )  i X i (n )ei (n );

i  0,1,......M  1

(12)

Thus splitting the burden of adjusting a single long length weight vector over M sub-filters of smaller lengths leads to faster convergence speed of each sub-filter, and will bring about improvement in the convergence of the system error to its steady state value. 4.2 Common Error Algorithm for MSF The common error adaptation algorithm for MSF has ability to overcome the high steady state error problem but with a sacrifice in convergence speed due to the coupling of each weight update equations. The error signal in this case is dependent on all other errors. Each sub-filter is updated by an individual algorithm by this common error. The steady state error is less in this case. The error in this case can be obtained as, [17-20] M 1

e( n )  d ( n)   Wi T ( n )X i ( n) ;

i  0,1, 2,..., M  1

(13)

i 0

where d ( n ) is the desired signal and M is total number of sub-filters. Where W (n)  [ w1 (n), w2 (n),...wL (n)]T and X i ( n )  [ x ( n ), x ( n  1), x ( n  2),.....]T Here L is the length of the sub-filter. The LMS adaptation of each sub-filter is expressed here as,

Wi (n  1)  Wi (n)   X i (n)e(n);

i  0,1,2....., M  1

(14)

4.3 Combined Algorithm for AEC A designer always looks for a good echo cancellation algorithm which gives better result for both convergence as well as steady state error. But practically it is not possible; a combination of different error and common error algorithm can be obtained which can provide a trade-off between the convergence rate and the steady state error according to requirement. A parameter alpha (  ) is chosen appropriately to achieve the desired performance. The parameter alpha will decide which algorithm will dominate in overall result. LMS adaptation of Combined Algorithm is given as [17] Wi (n  1)  Wi ( n)  X i ( n)  i ei ( n)  1     e( n)  ; 0    1 (15) where  will lie in the range 0    1 . 4.4 SCU based AEC The motivation of the selective coefficient adaptive algorithm can be explained by considering the high computational load of adaptive algorithm with several thousands of coefficients. The cancellation of acoustic echo needs the update of filters up to

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several thousands of coefficients. The computational complexity of adaptation algorithm is proportional to the number of filter coefficients. Updating the entire coefficient vector is costly in terms of memory and computation. So we need to reduce the computational complexity. A procedure to this is to update selected coefficients at a time. The computational complexity can be reduced by dividing the adaptive filter into smaller blocks and updating the number of these blocks rather than the entire filter at each iteration which is referred to partial updating. Several algorithms were proposed to reduce the computational cost of the NLMS algorithm. Such algorithms include the periodic NLMS algorithm and the partial update algorithms [38-41] where only a predetermined subset of the coefficients are updated at every iteration. The resulting algorithm needs fewer arithmetic operations compared to its full-update counterpart, which makes it amenable for applications involving long filters. These algorithms shows methods to reduce the computational complexity and memory resource by updating selected block of filter coefficients at each iteration either in sequential or periodic manner or by any selection criteria [42],[43]. It has been seen that the number of coefficients updated per iteration is reduced but there is an expense of some performance loss. So the selective tap algorithm should find ways in which it reduces number of coefficients updated per iteration with the performance degradation as little as possible. SCU enables the computational complexity of updating the coefficients of an adaptive filter to be reduced without necessarily reducing the order of the filter [21], [22]. In SCU, Let Q weights out of N weights are updated. Out of N  by  N selection matrix A is chosen such that only Q values will have 1’s on its diagonal element where weights are need to be updated. W (n  1)  W (n)  A X (n)e(n); n  0,1,2...N 1 (16) The selection criterion is based on [22]. The above equation shows SCU for SLF. The same can be done for the MSF.

5. Analysis of AEC Algorithms This section deals with the analysis and comparison of existing AEC algorithms as shown in Table 2. In Table 3 the adaptive algorithms are compared based on several parameters like the computational and structural complexity, convergence, steady state error, robustness, stability and field of application which facilitate the best selection of an algorithm for a particular echo cancellation application.

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3795 Table 2: Comparison of existing AEC algorithms. Sl AEC No. Algorith ms 1 AEC using LMS algorith m [15], [44]

Proposed Model

Results

Remarks

LMS algorithm is developed to reduce echo and a hardware real time implementation of the algorithm is done.

The LMS algorithm provides good numerical stability and its hardware requirements are low, therefore being the best choice on the available hardware platform. A disadvantage of this algorithm is its weak convergence. The Coded Error-LMS (CE-LMS) algorithm lets an easy digital design due to reduction of floating point operations, because input and error signals are integer numbers. The simulation results show that MSE and ERLE performance of CELMS is better than LMS, NLMS. Test result shows that the processing time needed for one frame by the sliding widow block NLMS adaptive filter is 9ms, while 35ms by the conventional NLMS adaptive filter and computational complexity of NLMS adaptive filter is reduced significantly by this new method without degrading performance.

This paper mainly focuses on the LMS algorithm & its use to cancel echo.

2

AEC using a modified LMS algorith m [16]

An echo canceller is presented, using an adaptive filter with a modified LMS algorithm, where this modification is achieved coding error on conventional LMS algorithm.

3

Echo cancellati on based on improved NLMS [45]

A novel implementation method for NLMS adaptive filter is presented based on sliding window structure and algorithm delay control technique.

This paper focuses on the modified LMS algorithm using Coding Error which does not affect the filter structure and is compatible with the existent digital adaptive filters.

This paper gives importance on increasing the processing efficiency of real time systems by proposing the improved NLMS algorithm

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4

An improved proportio nate NLMS (IPNLM S) algorith m based on l0 norm[46]

IPNLMS algorithm based on the l0 norm is developed, which represents a better measure of sparseness than the l1 norm.

IP-NLMS algorithm uses the l0 norm to exploit the sparseness of the system that needs to be identified.

5

RLS algorith m for AEC[47] , [48]

An RLS algorithm to reduce unwanted echo, is proposed which increases communication quality but with cost of extra complexity brought by the least square algorithm itself.

The RLS algorithm directly considers the values of previous error estimations. RLS algorithms are known for excellent performance when working in time varying environments and converge much faster than the LMS algorithm in stationary environment.

6

Filteredx LMS (FXLMS) algorith m [49]

This paper presents an analysis of the FX-LMS algorithm using stochastic methods. The influence of off-line and on-line estimation of the error-path filter on the algorithm is also investigated along with the bound values.

It is shown that for large errors in the error path model the on-line estimation is more robust than the off-line estimation. It is proved that for a special case of delay in the coefficient update, it puts a minor effect on stability and steady state error. The bounds for a narrowband input are much smaller than those for a broadband input.

This paper gives a new proportionatetype NLMS algorithm but The main challenge in AEC application associated with the IPNLMS-l0 algorithm is to find a practical way to choose the value of the parameter  This work focuses on the least square values of error. It has the greatest attenuation of any algorithm, and converges much faster than the LMS algorithm. But then this performance comes at the cost of computational complexity. FxLMS algorithm is stable. Though it has simple real time realization and low computational complexity but on the other hand it has slow convergence which is a major drawback. Again this paper does not emphasize much on the AEC application of FXLMS.

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3797 7

8

9

Modified FX-LMS algorith m with improved converge nce performa nce.[50]

This paper proposes two modifications of the FX-LMS algorithm with improved convergence behavior at the same computational cost of 2M operations per time step as the original FX-LMS update. An optimal choice of the stepsize parameter in order to guarantee faster convergence, and conditions for robustness, are also derived. Leaky This article presents FX-LMS a stochastic analysis algorith of the leaky FXm LMS (LFXLMS) [51] algorithm.

In modification -1 the optimal choice is approximated. The time variant coefficient is replaced by constant approximation. In modification-02 instead of directly using the error, an estimation of the error is used. Computational complexity of Modification-01and Modification-02 becomes 2M+2Mf & 2M+3Mf respectively where Mf represents length of the error filter.

Due to modification-01 the convergence rate of FxLMS algorithm increases whereas due to modification-02 convergence rate becomes reasonable. Modification-01 shows greater stability and performance. But the application in AEC framework is doubtful in this proposed method.

Performs well for both white as well as colored noise input. The simplifying assumptions used are experimentally verified exhibiting a reasonably good accuracy. On the other hand, by setting the leakage factor equal to zero the model equations become those of the FX-LMS algorithm.

MSF based AEC [10], [18]

The DEA has better convergence whereas CEA has better steady state performance for the same echo cancellation application. Hence they have their own advantages and drawback.

The model is derived under the assumption that the estimate of the secondary path is not perfect. So there is a lot of scope for improvement. Also stability becomes a major issue as stability decreases though convergence decreases. It failed to propose an algorithm which carries the advantages of the DEA and CEA. The length of adaptive filter is also kept fixed which restricts its application in time varying scenarios.

The proposed model introduces the DEA and CEA for AEC. It uses simple LMS algorithm rater than any advanced version of it.

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10 MSF based COEA for AEC [17]

Along with the DEA and CEA explanation it presents a new algorithm which tries to maintain the trade-off between them.

The proposed algorithm depicts better results in both convergence and MSE compared to DEA and CEA. Whereas it employ a fixed trade-off parameter  which limits its applicability for all type of AEC applications.

11 Selective Coefficie nt Update based AEC [37], [38]

The complexity reduction of adaptive filter is carried out by finding those coefficients only which contributes to the overall performance improvement.

The design suggests a procedure to select few coefficients out of thousands of filter weights which mainly does the job of echo cancellation and steady state performance adaptation for the filter.

12 Variable taplength adaptive filter for AEC [30], [31]

A dynamic filter structure is proposed in this paper where the filter length varies like the weights of filter.

The echoed environment is not known prior to the cancellation process always. Hence it is not possible to engage the adaptive filter of best fit length to identify the unknown impulse response. In this paper this issue of AEC was addressed with a variable tap-length adaptive filter.

This work is based on a fixed structure analysis. For time varying dynamic scenarios this may fail to depict the same performance improvement. Scope of improvement is there in finding out a variable  based on the error performance. The matrix used for selection purpose is system dependent. It definitely recedes the complexity but fails to produce better performance rather degrades it due to reduced coefficient. The proposed algorithm is based on the comparison of MSE for two consecutive tap fixing a threshold value. Whereas deciding the threshold correctly for each application is a difficult task.

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3799 13 Variable taplength MSF based AEC [19], [20]

The length of each sub-filter in the MSF structure of AEC is varied as per the dynamic structure algorithm.

It retains the advantage of both MSF approach which increases the convergence with less computational complexity and the variable tap-length algorithm for reducing the structural complexity.

A well known approach for deciding the time varying threshold parameter is fixed. The dynamic parameters which depends on both the time and length variation makes the analysis mathematically complex.

Table 3: Selection of proper Adaptive Algorithm for AEC Algorith m

Computational/ Speed of Stabil Robustn Application Structural converge ity ess complexity nce LMS Low Slow Stable Less Channel equalization, echo cancellation, noise reduction in communication NLMS More than LMS Fast More Less Audio systems, biothan medical equipment LMS Variable High Depends Stable More Same as LMS step LMS on (VLMS) Error Width FLMS More Faster More Moderat VOIP & than LMS than e Teleconferencing LMS FX-LMS Less Slower Stable Less All modern real time than LMS equipment RLS High Fast Unsta More Modified Laser ble Interferometer, Control Systems FT-LMS

Moderate/ structural complexity

less Faster Stable Moderat Almost all type of than LMS e adaptive system modeling and identification

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VTVSLMS / VT-SLF VT-MSFDEA

Moderate / less structural complexity Less than VTVSLMS / very less structural complexity VT-MSF- Less than VTCEA VSLMS / very less structural complexity VT-MSF Lower than the Modified past two variants

SCU based AEC

Least than discussed approaches

Faster Stable More than FTthan FTLMS LMS Very fast Less More stable than FTLMS Slow

Fast

Acoustic Echo Cancellation and Channel equalization Acoustic Echo Cancellation and noise suppression

More More Acoustic Echo stable than FT- Cancellation and noise LMS suppression

Stable More than VTDEA and VTCEA all Moderate Mode Less rate

All types of adaptive filter system identification applications Acoustic Cancellation

Echo

From the computational complexity point of view, we see that LMS algorithm requires 2N+1 multiplications and additions, NLMS algorithm requires 3M+1 multiplications the RLS algorithm requires 4N2 multiplication operations and 3N2 additions. So we see that RLS algorithm is the most computationally complex among the other algorithms. From the convergence point of view, LMS algorithm has weak convergence rate. NLMS, FLMS, RLS have a better convergence rate, whereas the FXLMS algorithm’s convergence rate depends on the phase error. If the phase error is greater than 90 degrees then rate falls down. Similarly for VLMS convergence rate depends on the error width. From the stability point of view, the NLMS, VLMS, FLMS & FX-LMS are found to be more stable than LMS algorithm and RLS is found to be the most unstable of the lot. Finally as far as robustness is concerned, except RLS and VLMS all others are less robust comparatively. The LMS, VLMS, NLMS, RLS, FLMS algorithms fail to perform well in the Active Noise Canceller framework as well when there is non-linear echo, & double talk detector case. So in these situations the most useful algorithm which can be used is FXLMS Algorithm. Also this algorithm has favourable parameters which make it popular to be used in all the modern real time equipment. The FX-LMS solution is by far the most widely used due to its stable predictable operation. The MSF approach does not decrease the length requirement of the adaptive filter but results in a new way to find out the segmented error signal which results in two different type of algorithms with reduced computational complexity. Similarly as discussed earlier the variable taplength approach reduced the structural complexity and being used with the MSF approach can be regarded as the best AEC methodology. Echo Return Loss Enhancement (ERLE)

Performance Evaluation of Adaptive Algorithms for Monophonic Acoustic Echo 3801 It is measure of amount of echo suppressed by the echo canceller. It can be defined as the ratio of power of original echo over the power of the residual echo signal after cancellation. [2]

ERLE dB  10log10

powerof microphonesignal powerof residual acousticechosignal

The higher the ERLE, better the SAEC performs. Here it is assumed that there is no near end signal and only echo signal present for ERLE measurement. The maximum, minimum and average ERLE is presented in Table 4 which clearly shows that the variable tap-length MSF based combined error scheme is the best choice among all the algorithms in the family. Table 4: Comparison of ERLE in dB for AEC of all discussed algorithms. Algorithm LMS NLMS VLMS IPNLMS FLMS FX-LMS RLS FT-LMS VT-DEA VT-CEA VT-COEA SCU

Maximum ERLE(dB) 34.4 36.7 36.0 38.6 33.1 38.6 30.3 35.5 38.5 41.7 46.4 39.0

Minimum ERLE(dB) -34 -30.2 -29.7 -21.6 -31.6 -23.1 -27.7 -35 -20.2 -10.8 -10 -16.9

Average ERLE(dB) 12.5 13.2 13.7 15.6 12.7 16.8 11.1 11.8 18.6 21.2 24.5 20.7

6. Conclusion The robust acoustic echo cancellation and speech enhancement technique has wide range of application in day today life in wireless and mobile systems. There are several number of adaptive algorithms which have different properties which are discussed in this paper, but aim is to minimize the mean square error, higher convergence rate with decreased computational complexity. Almost all effective proposed AEC algorithms are analyzed to find the area of application, tracking capability, computational and structural complexity etc. The variable tap-length MSF based algorithms discussed in this paper and the SCU variant has lower complexity, faster convergence rate and good tracking capabilities. The combined error variable structure algorithm has shown superior performance over the existing different error and common error designs in terms of convergence speed, steady state error and tracking. This has been achieved with a minimized structural complexity and less number of optimized selected coefficients. Hence this article provides a way to find out the best presently used acoustic echo suppression techniques for the perfect application to result in best

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possible system performance while reducing the design cost to the minimum.

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