Interference Cancellation using Different Algorithm of Adaptive Filter

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Interference Cancellation using Different Algorithm of Adaptive Filter


Department of Electronics and Communication, Guru Jambheshwar University of Science and Technology,

Hisar, India

Dr. Sanjeev Kumar Dhull

Department of Electronics and Communication, Guru Jambheshwar University of Science and Technology,

Hisar, India

Abstract This paper compares different type of adaptive algorithms such as Least mean square (LMS), Normalized least mean square (NLMS), Sign-Sign LMS, sign-error LMS. Here adaptive behavior of the algorithm is examined for the noise or interference cancellation in speech signal. Comparison of LMS variants is based on the SNR calculated. In speech signal or acoustic signal the noise can be reduced by the adaptive filtering, when mixed with the noisy signal at same frequency. So we provide implementation of variants of LMS to compare and get the better result. Various noise signals provide the different impact over the signal during any type of transmission of signal or communicating between different sources like telephonically. As in that case noise gets mixed with the signal and information get lost. To regain the actual information it is necessary to remove the unwanted signal mixed with the original signal. So to remove that adaptive filtering is best way.

Keywords: Least mean square (LMS), Normalized least mean square (NLMS), Sign-error least mean square (SELMS), Sign- sign least mean square (SSLMS).Mean square error (MSE). Power Spectral Density (PSD).


      In digital signal processing Adaptive signal is widely used in speech processing [1]. Adaptive filter is also called as self adjusting filter, as it can modify its transfer function depending upon the proposed algorithm [3]. There are numbers of distinct kind of algorithms used in Adaptive filtering that allow the filter coefficient to adjust the signal statics as mentioned in Fig 1. LMS algorithm was developed by Windrow and Hoff [2].

      RLS stand for recursive least square and FRLS is fast recursive least square. These are discovered by Gauss.

      LMS is the mostly used algorithm in Adaptive filtering because of its simple calculation and preferential performance [2]. In this paper there are different variants of LMS used to remove the noise from desired information [2]. All four variants of LMS are used and there comparison is shown on the basis of step size and SNR [3]. LMS algorithm get required filter coefficient to get the least mean square of the comparison between the required signal and the original signal to remove noise signal. During the communication by telephone or any speech communication

      Fig.1 Type of Adaptive algorithms.

      different undesired signal got mixed like transport, crowds or it can be electronically (thermal noise) also [12]. There is different type of noise that has different effect on signals according to their quantity.

      1. NOISE

        There are different type of noise which gives different effects on signal when mix with them during transmission of signal [12]. In general, there are three type of noise-

        1. Impulsive noise

        2. White noise

        3. Colored noise

          Impulsive noise: Impulsive unwanted signal introduce to abnormal bursts of undesired signal with comparatively high magnitude. It is generally considered as corrupted Gaussian noise.

          White noise: It is a signal having all detectable repetition with same strength. This type of noise range is completely uncertain at each frequency. It is having a value in between 0 to 2 and its esteem at a specific frequency is unconnected to the range at another frequency.

          Colored noise: A noise which is having any color is considered as colored noise. White noise is uniform all over the spectrum of noise, where as Colored noise has frequency within a predetermined limited area. There are various categories of the colored noise example blue, pink, brown, orange noise determined by the scale of PSD of noise signal. The relation between the power of speech signal and the noise signal is called the Signal-to-Noise ratio defined in db

          (decibels). Ideally the ratio should be greater than 0db states that the original signal is powerful instead of noise. This relationship is shown in this paper at a different value of step- size of the adaptive algorithms use to remove the noise signal. The step-size is use to compare the performance of the different variants of LMS to remove the noise. The step-size increment or decrement with the changes in Mean-Square error, so that the filter can detect the variations in the system and to generate the minimum steady-state error.MSE is defined as the difference between the desired signal and the actual signal. It is average squared comparison between the actual signal and the required signal.


        A filter is ideal if it is familiar regarding the input data. If this is unknown, the adaptive filters will be used. The adaptive filters having the characteristics of self-optimization [8]. Whenever we dont know about the characteristics of the input signal at the initial point then we use adaptive filter. The main purpose of noise cancellation is to exceed the snr. The adaptive filter have vast applications in inverse modeling, speech enhancement, speech encoding, acoustic echo cancellation, linear prediction, channel equalization, line enhancing, system identification, jammer suppression,

        y(k) from the desired signal and provide the required output. The adaptive canceller can reduce the mean-square error (MSE) of the complete output, so that output will be the ideal evaluation of the desired signal in the minimum MSE sense.


        1. LMS Algorithm

          In LMS, the coefficients of adaptive filter are adjusted from sample to sample to reduce MSE. The aim of operating under varying condition and regulate itself to reduce the error is fulfilled by the LMS algorithm [3].

          2 ( )

          2 ( )

          w(k + 1) = w(k) + ( e k ) (1)


          e(k) = error signal (input signal-adaptive output signal).

          e(k) = d(k) wT(k)x(m) (2)

          Where d(k)= desired signal x(k)= original signal.

        2. Normalized LMS Algorithm

          It is an improved form of standard LMS. Both the equation of LMS and NLMS are same except the NLMS has a time- varying µ. The speed of filter can be improved by this.

          frequency tracking, noise cancellation and image encoding [9-10] etc. Adaptive filtering consists of two different parts-

          ( + 1) = () + µ





          +1 2(km)

          ()() (3)

          first one is digital filter which can regulate the coefficient and secondly there are adaptive algorithms which can modify the same. Two inputs are given to the filter, one is the original signal x(k) and second is the corrupted signal d(k)+n(k) together.

          e(k)= error signal, i.e. e(k)= d(k) – y(k) x(k) = Input signal,

          y(k) = Output signal d(k)= Desired signal

          An adaptive filter is a non-linear filter and time-variant parameters. It can adjust its parameter according to the needs. The block diagram adaptive noise canceller is shown in Fig 2. The adaptive filter finds an approximate of the noise and that is subtracted from the result of the adaptive filter. Adaptive filter get the feedback from its algorithms used and calculate the difference between the error signal produced by subtracting the

          2(k m) is the input signal energy


          Where P is filter length.

          µ control the step size.

          a is he minor fixed value added to ignore the denominator of the new term becoming zero during input is zero.

          The main disadvantage of the standard LMS is, it can be easily affected by the scaling of the input signal.

        3. Sign-Error Algorithm

          In standard LMS and NLMS algorithms, we can get the coefficient of adaptive filter by calculating the MSE between the desired and the output signal and applying the result to the current filter coefficient [4].

          Using sign-error algorithm, it restore the MSE by the sign of error to change the filter coefficient.

          When the error is positive:

          New coefficient is equal to the pervious one multiplied by the step size µ.

          Whereas, in negative error, the new coefficient is equal to the previous one minus the error multiply by the µ [4].

          ( + 1) = () + () µ sgn[()] (4)

          Where sgn(.) = sign function sgn[e(k)] = ||, 0

          Fig 2. Schematic of adaptive noise cancellation.

        4. Sign-Sign Algorithm

          Similarly in the signsign LMS, the MSE is replaced by the sign of the input to change the filter coefficient.

          Depending upon the sign of the error, the value of new coefficient remains the same as in the case of sign-error.

          w(k+1) = w(k) + sgn[x(k)] µ sgn[e(k)] (5) Where sgn(.) = sign function.



          1. for step-size 0.01




            Fig 3. For step size 0.01 (a) NLMS waveform, (b) LMS waveform, (c) Sign- error LMS, (d) Sign-Sign LMS.

          2. for step-size 0.001:





        Fig 4. Waveform for step size 0.001 (a) NLMS, (b) LMS, (c) Sign-error LMS, (d) Sign-Sign LMS.

        C. for step-size 0.03





        Fig 5. For step size 0.03 (a) NLMS waveform, (b) LMS waveform, (c) Sign- error LMS, (d) Sign-Sign LMS.

        D. for step-size 0.003





        Fig 6. For step size 0.003 (a) NLMS waveform, (b) LMS waveform, (c) Sign-error LMS, (d) Sign-Sign LMS.

        E. for step-size 0.06:





        Fig 7. For step size 0.06 (a) NLMS waveform, (b) LMS waveform, (c) Sign- error LMS, (d) Sign-Sign LMS.

        F. for step-size 0.006:





        Fig 8. For step size 0.006 (a) NLMS waveform, (b) LMS waveform, (c) Sign-error LMS, (d) Sign-Sign LMS.


Here is the comparison between the different algorithms used for the speech interference cancellation. The SNR values are mentioned in the table below at different step-size. It concludes that Normalized least square mean algorithm is best according to the SNR value for speech noise removal.


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