Combined Adjusted Step Size Lms Algorithm and Active Tap Detection Technique for Adaptive Noise Cancellation

In this paper ,a new idea to combine Adjusted Step Size Least Mean Square (ASSLMS) algorithm with standard LMS active tap detection technique is presented .Then the combined method is used for estimating unknown time-invariant (stationary) and time varying (nonstationary) Finite Impulse Response (FIR) channel for adaptive noise cancellation (ANC) application. The focus of this paper is to improve the convergence rate and low level of the error in the steady state for the popular LMS adaptive filter. The simulation results have shown improvement on the convergence rate using the combined technique over both the ASSLMS algorithm and standard LMS active tap detection technique if they are used alone. KEYWORS: Adaptive Noise Cancellation, Active Tap Detecting Technique, Adjusted step size LMS algorithm. نازولاا فشك ةینقت عم اینمز ریغتملا ةوطخلا لماعم تاذ عیبرتلل لدعم لقا ةیمزراوخ جمد ةفیكتملا ءاضوضلا ءاغلا ةموظنمل ةلاعفلا ثحبلا صخلم : مدقی ثحبلا اذھ قت ع م ا ینمز ر یغتملا ةو طخلا لماعم تاذ عیبرتلل لدعم لقا ةیمزراوخ جمدل ةدیدج ةركف ة لاعفلا نازولاا ف شك ة ین رفص يواستلا اھتمیق نوكت يتلا . كلذكو نمزلا عم ةریغتم ریغ ةانقلو ةفیكتملا ءاضوضلا ءاغلا ةموظنم ىلع ةركفلا هذھ قیبطت مت اینمز ةریغتم نوكت ىرخا ةانق عم اھقیبطت مت . " ةعج شم جئا تن ى لع لو صحلا م ت بو ساحلا مادخت ساب ةا كاحملا جمار ب للا خ ن م جو اھدحول ركذلا ةفنا قرطلا مادختسا مت ول امیف ةصلختسملا كلت عم ةنراقم ةدی . ى لع لوصحلا للاخ نم ناك ءادلاا يف نسحتلا رارقت سا ة لاح ي ف ءا طخلا ةراشلا ىوتسم لقا ىلع لوصحلاو ءاضوضلا ءاغلا ءادا يف ةیلاع ةعرس ) وا لا ة لحرملا اھن ئ ة ی ( ل مع ةموظنملا . INTRODUCTION Adaptive Noise Cancellation (ANC) system is regarded as one of the method used for signal (speech) enhancement and attempts to reduce the additive noise which may arise from different sources. Noise canceling is an adaptive system that makes use of an auxiliary or reference input as shown in Fig.1 [Bernard Widrow, Samuel D. Strearns]. Engineering journal, no. 1 , vol. 16 , March 2010 , College of engineering, university of Baghdad. 2 In this Fig., ANC has two inputs called primary and reference inputs. The reference input (n1) is filtered using adaptive FIR filter and subtracted from a primary input which is containing both desired signal and the noise (s+no). As a result the primary noise is attenuated or eliminated by cancellation and the output signal is called error signal (e). The signal (no) represents the noise that is filtered through the noise channel path a(n) which it is considered as FIR filter in this paper. This noise path channel has impulse response which may be stationary or non-stationary time varying. Filtering and subtraction of the ANC system must be controlled by an appropriate adaptive process that uses the error signal in order to obtain noise reduction with little risk of distorting the signal or increasing the noise level [Bernard Widrow, Samuel D. Strearns]. Many algorithms are used by ANC to adjust their impulse response. The LMS algorithm is regarded as a special case of the gradient search algorithm which was developed by Widrow and Hoff in 1959 [Bernard Widrow, Samuel D. Strearns]. This algorithm is often used for the adaptation of the ANC system because it is easy to implement and requires small number of calculations. But this algorithm suffers from slow convergence since the convergence time of LMS algorithm is inversely proportional to the step size [Bernard Widrow, Samuel D. Strearns]. However if large step size is selected then fast convergence will be obtained but this selection results in deterioration of the steady state performance (i.e. increased the misadjustment (error level)). Also if the channel to be estimated is time varying the LMS algorithm fails to track this type of channel. The LMS has also been cited and worked upon by many researchers and several modifications have been applied to it in order to optimize its performance for particular applications. Numerous modifications of the LMS algorithm have been reported [,S.K., G. Zeng, J.J. Chen, R.R. Priemer , Bozo K. ,Zdravko U. , and Ljubisa S., and R.H.Kang, E.W.Johnstone]. In these works, the optimization issue concerning the step size is discussed, and several methods of varying the step size to improve performance of the LMS algorithm especially in time varying environments are proposed. One of these modifications is to use adjusted step size LMS algorithm as proposed by [M.J. Al-Kindi , A.K. Al-Samarrie, and Th.M. Al-Anbakee ]. Our proposed algorithm is called ASSLMS algorithm which is used for ANC application . Another modification of LMS algorithm is proposed by Dr.J. Homer [J. Homer] .He proposed active tap detection LMS technique for white inputs and invariant time channel .Then several improvements of this technique (i.e. active tap detection technique) are reported in order to improve the performance of this technique especially in non-stationary environments [Charles Q.Hoang, Boon L.Chock , Vanessa Edward , and Long Le, Ozgu Ozun, and Phiipp Steurer]. This paper is organized as follows; first the concept of active tap detection LMS algorithm will be present, then ASSLMS algorithm will be present. After that, simulation results with different conditions will be present. Then this paper will enclose by the conclusions. Engineering journal, no. 1 , vol. 16 , March 2010 , College of engineering, university of Baghdad. 3 FUNDAMENTAL OF THE LMS ALGORITHM Basically, the idea for the adaptive transversal filter (or FIR) is to model the noise path channel and attempt to match it. The tap delay line structure for the unknown modeled channel, which gives the desired response, is shown below in Fig.2. The weights or the impulse response of the noise path is given as: Wk=[wo w1 w2 w3 .......wn-1 ] (1) where n is the tap length, k is the time index. There is also the estimator ( or adaptive filter) that has a similar structure: Wk=[w o w 1 w 2 w 3 .......w m-1 ] (2) where m is the tap length. The adaptive filter has zero initial conditions as is done in practice. In general, the length of the filter (m) may be different from the length (n) of the channel. For simplicity in this paper, only the case of n=m was considered. Another important aspect is that the weights or coefficients of the FIR estimator will be adjusted using the LMS algorithm to reduce mean squared error (MSE) which is a measure of the accuracy of the estimated channel. However, since the MSE requires a large amount of memory, the instantaneous squared error is used, which gives an estimate of the gradient of the MSE surface [Bernard Widrow, Samuel D. Strearns]. The estimation error can be found as: ek= (dk + nk) –yk (3) Where noise or additive disturbance (nk ) is added to the desired signal dk (not shown in the Fig. (2)). From equation 3, the adaptive filter output is yk=Wk * Nk (4) where nk is the input noise signal and * denotes convolution operation. Engineering journal, no. 1 , vol. 16 , March 2010 , College of engineering, university of Baghdad. 4 The LMS algorithm adapts the adaptive filter’s vector Wk according to [Bernard Widrow, Samuel D. Strearns], Wk+1= Wk + μ Nk ek (5) Where Nk=[ nk nk-1 nk-2 ......... nk-m+1] ,which represents the input noise signal to the taps of the adaptive FIR filter, and μ is fixed step size 0<μ<1. CONCEPT OF LMS ACTIVE TAP DETECTION ALGORITHM In adaptive estimation applications, the channel is characterized by a time domain impulse response. Using the LMS algorithm alone, extended regions of negligible response or “inactivity" may be included in the calculation of this response [Charles Q.Hoang]. The idea proposed by Dr John Homer is to apply a consistent LMS algorithm that performs estimation of nonzero or “active" taps only. This will improve the channel estimation performance (accuracy) and convergence rate. In order to detect a tap, a formula known as the least squares (LS) activity measure is used [J. Homer]: