Design Of Quantized Least Mean Square Adaptive Filter For Adaptive Noise Cancellation

Design Of Quantized Least Mean Square Adaptive Filter For Adaptive Noise Cancellation

Design of Quantized Least Mean Square Adaptive Filter for Adaptive Noise Cancellation

Nitesh Mudgal, Mr. Pankaj Shukla, Dr. R. S. Meena

Abstract an adaptive filter finds its application in adaptive noise cancellation where a signal corrupted from noise is ex- tracted and signal free from noise using an adaption algorithm is obtained. There are various types of adaptation algorithms for FIR filters such as least mean square (LMS) and recursive least square (RLS). The performance of these algorithms can be compared according to three parameters which are convergence speed, misadjustment and tracking capability. Convergence speed is simply the number of iterations needed for the filter to converge to its optimum state for a specific desired signal and input signal. in adaption algorithm it is not necessary to have any a priori knowledge of signal or noise characteristics that corrupt the signal. This paper proposes method of noise cancellation using quantized version of least mean square algorithm which provide better result as compared to normal least mean square algorithm. This property makes the adaptive filter has an important application in noise cancellation.

Index Terms sign function; modified sign function; least Mean Square algorithmt ; QX-Least Mean Square Algorithm.

The adaptive filters are popular owing to its simplicity but even simpler approaches are required for many real-time ap- plications. Reduction of the complexity of the Adaptive filter had received attention in the area of adaptive filter. [1]

A signal corrupted from noise is to be extracted find its applica- tion in various application fields, such as digital communications, radar, sonar and biomedical engineering, so that uncorrupted sig- nal can be used for signal processing. And less power is utilized by system. Suppressing information bearing signal from signal corrupted by a sinusoidal interference utilize a fixed notch filter tuned to the frequency of the interference in traditional method. But in this case a precise frequency of the interference is to be known, but when notch is required to be very sharp, then adap- tive noise cancellation provide solution for extracting information bearing signal from corrupted signal.

the method for filtering a information bearing signal from noise corrupted signal uses a filter that filters the noise from corrupted signal and information bearing signal remain unchanged. a fixed or adaptive filter can be utilized for filtering process.

Adaptive filters have the capability to adjust their own parame- ters automatically using an adaption algorithm. On the other hand, fixed filters design is based on prior knowledge of both the

• Nitesh Mudgal is currently pursuing master degree program in digital communication engineering in University college of engineering kota, India.

• Mr. Pankaj Shukla is Asso. Professor in Electronics Dept. in University

college of engineering kota,India.

information bearing signal and the noise.

In design of adaptive filter a priori knowledge of signal or noise characteristics is not required. In this paper we have used adap- tive filter for noise cancellation using quantized least mean square algorithm. An application of noise cancellation for adap- tive filter have highly advantageous in various fileld.It makes use of primary input supplies an information bearing signal and a that are uncorrelated with each other. Noise is the correlated ver- sion of the sinusoidal interference supplied as the reference input. Primary input contains both the signal and noise. Reference input is filtered and subtracted from a primary input so noise is atte- nuated or eliminated by subtracting the reference input from pri- mary input.

1. In order to improve signal-to noise ratio (SNR) for a system, adaptive filters find an application of adaptive noise cancellation where noise from the corrupted information bearing signal is ex- tracted. This process is known as adaptive noise cancellation. An Adaptive Noise Cancellation is typically a dual-input, closed- loop adaptive feedback system where two inputs are: the primary input signal and reference input.

   Fig. 1 Block diagram for Quantized Adaptive Noise cancellation scheme

   Block diagram for quantized adaptive noise cancellation scheme is shown in fig. 1. A signal source used to transmit signal that signal is corrupted by a noise. The combined signal and noise form the primary input to the quantized adaptive noise canceller. Input to the filter receives a noise, uncorrelated with the signal but correlated in some unknown way with the noise. Adaptive filter processes this noise input signal using QX-LMS adaption algorithm and filtered to produce an output y(n) that is approx- imated version of noise. Then the output of adaptive filter is sub- tracted from the primary input which is combination of signal and noise to produce the system output. The overall system output is the output for Quantized adaptive noise canceller.

   In the system shown in Fig. 1, FIR filter is used as a adaptive filter where the reference input (noise) is processed. This filter differs from a fixed filter in sense that this filter automatically adjusts its coefficients weight (impulse response) using an adap- tion algorithm. In this paper filter uses QX-LMS adaption algo- rithm so that the error can be minimize by adjusting the filter coefficients.

2. The LMS algorithm is a widely used algorithm for adaptive filter- ing. The algorithm is described by the

   Following equations:

   Fig. 2 : Modified Sign Function

   +1, x (i)

   M 1

   y(n) wk (n) x(n i) (1)

   mgsn .

   n

   0,- <xn (i)<

   i0

   -1,x (i)

   n

   e(n) d(n) y(n) . (2)

   wk (n 1) wk (n) 2 e(n) x(n i) …. (3)

   In these equations, the tap inputs

   x(n), x(n 1), x(n 2),…………., x(n M 1) form the elements of the reference signal x(n) , where M 1 is the number of delay elements. d (n) denotes the primary input sig- nal, e(n) denotes the error signal and constitutes the overall sys-

   tem output. wk (n) denotes the tap weight at the nth iteration. In

   equation (3), the tap weights update in accordance with the esti- mation error. And the scaling factor is the step-size parame-

   ter. controls the stability and convergence speed of the LMS algorithm..[2]

   The LMS algorithm is convergent in the mean square if and only if satisfies the condition: 0<<2/tap-input power

   M 1

   Where tap-input power = E[| u(n k) |2 ]

   k 0

3. The Modified Sign Function is three level quantization scheme whose value is dependent on the value of and is given as,[3]

   Where msgn{.} is the modified sign function defined as:[1]

   It should be noted that the implementation of such an adap- tive filter has potentially greater throughput because for those times when the tap input signal, xn (i) , is less than the speci-

   fied threshold, , then xn (i) will be equal to zero and no coef-

   ficient adaptation for the corresponding weight needs to be

   performed. This means that some of the time-consuming op- erations in the weight update formula can be omitted, thereby leading to a reduction of the computational load on the pro- cessor. Whether this potential can be realized depends on the architeture used in the processor and also in applications

   For this three level Quantization Scheme, Adaptive LMS algo- rithm can be written as, [4]

   w(n 1) w(n) e(n)x(n)

   Where x(n) is the three levels Quantized input signal,

4. MATLAB results for the normal LMS and Quantized LMS are shown below, in normal LMS, primary input is the combina- tion of information bearing signal and sinusoidal interference, input to the adaptive filter is the correlated version of the si- nusoidal interference

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   tions. In this paper, Quantized LMS is used for noise cancellation which is better as compared as normal LMS algorithm and results are compared on MATLAB.

   00

   REFERENCES

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   iterationn

   1. H. Sadoghi Yazdi, M. Fathy, Car tracking by quantized input LMS, QX-

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5

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error Signal

LMS algorithm in traffic scenes, IEE Proc.-Vis. Image Signal Process., Vol. 153, No. 1, February 2006,pp. 37-45.

00 [2] Mamta M.Mahajan,S.S. Godbole,Design of Least Mean Square Algorithm for adaptive noise canceller, (ijaest) international journal of advanced engineering sciences and technologies vol no. 5, issue no. 2, 172 – 176

amplitude

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1. Xiaochun Guan,Xiaojing Chen,Guichu Wu,QX- LMS Adaptive FIR Filters For System Identification, College of Physics & Electronics Information

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   Fig. 3 Noise cancellation using LMS

   Fig. 3 Noise cancellation using LMS

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   error Signal

   Engineering, Wenzhou University,Zhejia- ng China, 2009 IEEE.

2. B.Widrow and S. D. Steams,Adaptive Signal Proce- ssing,China

   00 Machine Press, Beijing, May 2008.

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3. Lei Zhang, Jin Bi and Lianying Guo, The Practical Textbook of MATLAB,Post & Telecom press, Beijing, December 2008

4. Jun, B.-E., Park, D.-J., and Kim, Y.-W, Convergence analysis of sign-sign LMS algorithm for adaptive filters with correlated gaussian data, Proc. ICASSP95, vol. 2, 1995, pp.13801383.

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Fig.4 Noise cancellation using modified clipped QX-

LMS

Adaptive noise cancelling is a method of adaptive filtering that can be applied whenever a suitable reference input is available. The principal advantages of the method are its adaptive capability, its low output noise, and its low signal distortion. The adaptive capability allows the processing of inputs whose properties are unknown. Output noise and signal distortion are generally lower than can be achieved with conventional optimal filter configure