IMPULSE NOISE CANCELLATION ON POWER LINES

IMPULSE NOISE CANCELLATION ON POWER LINES D. T. H. FERNANDO d.fernando@jacobs-university.de Communications, Systems and Electronics School of Engineering and Science Jacobs University Bremen September 2, 213 Supervisor: Prof.Dr.-Ing.Werner Henkel

Abstract In this research we have investigated the performance of using an adaptive NLMS lter to cancel the impulse noise on powerlines. Using 93 impulses from various sources, which had measured and collected between the live-neutral channel(ln) and neutralearth channel(ne) of the powerline, we have simulated our proposed adaptive algorithm. Dierent cancellation results have obtained via changing the nature of the input to the canceler by processing the collected signals in many ways such as down sampling and interpolating the originally measured powerline signal. In order to make the decision to use the adaptive NLMS algorithm for cancellation, rst we studied the correlation between the LN and NE channels and then used the NE channel to estimate the noise on LN channel using our adaptive NLMS lter. Finally by subtracting the estimated signal by LN channel signal, the cancellation result has obtained. i

Contents 1 Introduction 1 2 Background 2 2.1 Adaptive Filters................................ 2 2.2 Least Mean Square(LMS) and Normalized Least Mean Square(NLMS) Algorithms.................................... 3 3 Design and Simulation 6 3.1 Impulse noise canceler............................ 6 3.2 Data manipulation.............................. 7 3.3 Convergence and the stability of the algorithm.............. 7 4 Results and Analysis 8 4.1 Correlation between the two powerline channels.............. 8 4.2 Comparison of the outputs obtained from the canceler for inputs processed in several ways................ 9 5 Conclusion 21 ii

List of Figures 2.1 Block diagram of the LMS adaptive lter.................. 3 2.2 Block diagram of the Transversal lter................... 4 2.3 Block diagram of the Adaptive weight control mechanism......... 4 3.1 Block diagram of the impulse noise canceler................ 6 4.1 The correlation between the two channels of the powerline........ 8 4.2 Mean Squared Error of the cancellation result against iteration...... 9 4.3 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 1 4.4 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 1 4.5 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 1 4.6 Mean Squared Error of the cancellation result against iteration...... 11 4.7 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 12 4.8 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 12 4.9 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 12 4.1 Mean Squared Error of the cancellation result against iteration...... 13 4.11 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 14 4.12 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 14 4.13 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 14 4.14 Mean Squared Error of the cancellation result against iteration...... 15 4.15 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 16 4.16 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 16 4.17 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 16 4.18 Mean Squared Error of the cancellation result against iteration...... 17 4.19 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 18 iii

4.2 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 18 4.21 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 18 4.22 Mean Squared Error of the cancellation result against iteration...... 19 4.23 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 2 4.24 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 2 4.25 LN channel response (sub gure1-red), cancellation result(sub gure1-................ 2 iv

Chapter 1 Introduction Impulse noise as one of the primary causes of errors in data communication, consists of a set of random pulses with a short duration, but relatively large amplitudes. It can be occurred due to several sources like external electromagnetic disturbances such as lightning, vehicle ignition systems, heavy-duty electrical equipment, and dropouts or surface degradation of audio recordings, etc. Impulse noise on transmission channel, can result in wrong information or low quality signals at the receiving end. Therefore, detecting and mitigating of these impulse noise on communication channels are very important for a successful communication. [4] The Power-Line-Communication (PLC) is becoming popular as a reliable, cost eective and a simplistic communication technology in the modern world. However the power line channels always dominated by several sources of noises severely impulsive noise which can come from any source connected to the grid, simply for instance, from a switched-on blender in the kitchen, or even turning on a light in anywhere at home. Many studies has taken so far for suppressing the impulse noise on telecommunication channels, but very few has taken on powerline channels. [5] As the rst phase of our research, a circuit was constructed to observe the impulse noise over the power line cables. Starting from measuring the characteristic impedance of the powerline cables, a circuit was designed, implemented and tested for observing the impulse noise between the two pairs, the live line and neutral lines(ln channel), as well as the neutral and the earth lines(ne channel). And under this report we have discussed about the second phase of our research, i.e., a study on how to cancel the impulse noise appeared on LN channel using the measured data during the rst phase of the research. Here by we have proposed a method of canceling the noise on LN channel using the correlated signal on NE channel, applying an adaptive lter which is designed with Normalized Least Mean Square(NLMS) algorithm. In a communication environment where the prior information about the statistics of data are not available, use of an adaptive mechanism in order to lter the received noisy signal would be ideal. Out of many algorithms to develop an adaptive lter, the NLMS algorithm has many advantages when the ltering process involves two inputs where one signal is used to estimate the noise added to the signal, while the second input acts as a reference signal with noise. Thereby the cancellation will be done by subtracting the reference signal from the estimated noise. 1

Chapter 2 Background 2.1 Adaptive Filters Digital communication systems always result in noise added data at the receiving end, there by proper extraction of information from noise is needed. A lter as the name implies, is designed to extract these information from noise under such communication environment. Filters can be classied into two namely, linear and non linear lters. If the output of the lter is a linear function of the input given to the lter, then it is called a linear lter and vise versa. In order to design a lter with minimum noise at the output, some statistical criterion should be satised. Therefore, in order to obtain an optimum lter performance, the target is to minimize the mean square value of the dierence between the desired response and the lter output. In an environment with stationary inputs, when this condition is satised, it is called a Wiener lter [1]. How ever, the Wiener lter requires some prior information about the statistics (mean, correlation, etc.) of the input, otherwise it is impossible to achieve the optimum solution. Therefore, in an environment where the statistics of the input data are not known, a technique which can be referred as "estimate and plug" is used. That means, starting from a set of initial conditions, the lter rst do an estimation and then plug into the system in a way that the system adapts the output according to the estimation. This process will continue recursively until it meets the condition which is as close as possible to the Wiener solution. When the lter is designed in this way it is called an Adaptive lter. In a stationary environment of the input, the adaptive lter converges to its Wiener solution after successive iterations, where in a non stationary environment, achieving the optimum solution depends on the tracking performance of the adaptive algorithm [1]. There are several ways which can develop adaptive lters and for our research purpose we have chosen Normalized Least Mean Square(NLMS) Algorithm. The target of our research was to apply an adaptive lter to subtract the impulse noise from a powerline signal in an adaptively controlled mechanism, while improving the signal to noise (SNR) ratio of the system. 2

2.2 Least Mean Square(LMS) and Normalized Least Mean Square(NLMS) Algorithms Originated by Widrow and Ho (196), the LMS is an algorithm derived from the stochastic gradient method. The structure of the LMS adaptive lter has two main processes namely [1], Transversal lter - Computes a current linear estimate of an output according to the given set of elements of the input and tap weights, hence generates the error between the estimate and a desired output. Adaptive weight control mechanism - Starting from an initial guess, this process updates the tap weight vector depending on previously computed error by the transversal lter and feeds back to the transversal lter for the next estimation of the output. Altogether the block diagram of the LMS adaptive lter is illustrated in gure 2.1. In the gure, U(n) represents the M by 1 tap input vector at time n, where M is the number of taps of the lter also can be identied as the lter length. The tap weight vector is given by W(n) which will be initialized as W() =, if prior knowledge of W(n) is not known. d(n) is denoted as the desired output at time n, where d(n u n ) is the estimate of the desired output. Finally the error is represented by e(n) [1]. The gure 2.2 and gure 2.3 illustrate the detailed representation of the transversal lter and the weight control mechanism. U(n) Transversal filter Ŵ(n) d (n U n ) - Adaptive weight control mechanism e(n) + d(n) Figure 2.1: Block diagram of the LMS adaptive lter 3

U(n) z -1 U(n-1) z -1 U(n-2) U(n-M+2) z -1 U(n-M+2) Ŵ *(n) Ŵ1*(n) Ŵ2*(n) ŴM-2*(n) ŴM-1*(n) e(n) d (n Un) - + d(n) Figure 2.2: Block diagram of the Transversal lter U(n) δŵ(n) U(n-1) δŵ 1(n) U(n-2) δŵ2(n) µ e * (n) δŵm-2(n) U(n-M+2) δŵm-1(n) U(n-M+1) Figure 2.3: Block diagram of the Adaptive weight control mechanism The following equations describe the algorithm for the LMS adaptive lter. W(n + 1) = W(n) + µe (n)u(n), (2.1) Where, e(n) = d(n) W H (n) u(n), (2.2) u(n) = [u(n) u(n 1)... u(n M + 1)] T (2.3) 4

and, W(n+1) is the estimate of tap weight vector at time n+1, while µ is called the step size parameter. As seen in the above equations, the adaptation of the tap weight vector is directly proportional to the tap input vector u(n), which results in a gradient noise amplication problem when u(n) is large. This is a major drawback of the LMS lter and therefore the NLMS algorithm is proposed. The NLMS algorithm is obtained by normalizing the tap weight vector at time n+1 with respect to the squared Euclidean norm of the tap-input vector u(n), at time n. Therefore, the Eq. 2.1 will now change as given in the Eq. 2.4 while the other equations remain same, in order to obtain the NLMS algorithm from the standard LMS algorithm [1]. W(n + 1) = W(n) + µe (n)u(n) u H (n)u(n) (2.4) However, in both LMS and NLMS algorithms the selection of the step size parameter µ needs more concentration. If the step size is chosen to be too small, then the algorithm will suer from slow convergence, and on the other hand, if the µ is too large, then the lter will no longer stable [2]. Therefore, one has to be very careful when choosing a value for the step size parameter. Several researches has been carried out so far in order to nd a best estimation for an optimum µ [3]. Finally for the purpose of our research, we have modied the NLMS lter to be used as a noise canceler. Using our measured signal on LN channel of the powerline as the desired output, while the measured signal on NE channel using as the tap input vector, we have designed a NLMS lter. 5

Chapter 3 Design and Simulation 3.1 Impulse noise canceler With slight modications to the NLMS lter, the impulse noise canceler has obtained as illustrated in gure 3.1. According to the gure 3.1, the lter structure is a dual input adaptive noise canceler. In order to perform better cancellation, the reference input has to be a correlated version of the noise on the primary input, which needs to be canceled [1]. Therefore, as the rst step, we studied the correlation between the measured signals on two channels of the powerline. After gured out that the two channels, LN and NE are nicely correlated, the NLMS noise canceler was developed choosing the LN signal as the primary input and the NE signal as the reference input. Then the algorithm was developed in order to compute the tap weights of the FIR lter corresponding to the normalized tap input vector obtained from NE signal and thereby obtain an estimation for the LN signal. Finally the algorithm computes the output (error) with reduced noise by subtracting the LN signal from the estimation. The error is then feed backs to the adaptive lter to calculate the new tap weight vector. For initialization, tap weight vector and the error has set to zero [2]. Primary input LN signal Delay + e(n) - Reference input NE signal Adaptive filter Figure 3.1: Block diagram of the impulse noise canceler 6

3.2 Data manipulation Before feeding the input to the noise canceler, the raw signals measured on powerline were processed in several ways. Our simulation had taken place for dierent versions of the processed powerline signals as listed below. First we used the original wide band raw signals of LN and NE channels for the canceler. Removing the high frequency components of the canceler results obtained for the original signal, another comparison has made. However originally measured signal composed of a wider frequency range which is out of range of interest for powerline communication. Therefore the higher frequency components of the original signal was chopped o to make a narrow band signal of 3MHz bandwidth corresponding to the powerline frequency band. In order to obtain further cancellation results, another attempt was taken by interpolating the narrow band signal in order to increase sample size, as a result number of iterations within one impulse has increased. As another method, while keeping the narrow band signal without interpolating, but running the LMS adaptation over multiple times within one impulse, the cancellation performance has studied. 3.3 Convergence and the stability of the algorithm The same algorithm described above has used in the literature [2] to eliminate the impulse noise from the dierential mode signal, using the interference coupling in common mode signal, on twisted pairs. Under the literature [2], the algorithm is tested for its stability and the convergence with respect to the variation of step size parameter also with number of iterations. Therefore based on the conclusions made in [2], the algorithm developed for our research has used the highest step size possible while varying the number of iterations in several ways to achieve fast convergence and the stability. 7

Chapter 4 Results and Analysis 4.1 Correlation between the two powerline channels By using 93 samples of measured data over on each of the two channels of the powerline, the correlation was computed as illustrated in the gure 4.1a. For the standard range of powerline communication frequencies, considerably high correlation coecient could observe between the two channels as shown in gure 4.1b. 1 The correlation between LN and NE channels 1 The correlation between LN and NE channels at lower frequencies.9.9.8.8.7.7.6.6 ρ.5 ρ.5.4.4.3.3.2.2.1.1 1 2 3 4 5 6 7 freq / MHz 5 1 15 2 25 3 freq / MHz (a) The correlation coecient between the two channels of the powerline as a function of frequency (b) The correlation coecient between the two channels of the powerline for low frequencies Figure 4.1: The correlation between the two channels of the powerline 8

4.2 Comparison of the outputs obtained from the canceler for inputs processed in several ways In order to obtain the results shown under this section, the algorithm has used the step size as 1 which could be the highest possible step size achieved by the algorithm. Number of iterations within one impulse were changed in each stage, processing the input by changing the number of samples accordingly. Since the measured signals on the powerline channels had various shapes of impulses, training of the canceler over many impulses were not possible. Instead, the training had to take place by increasing the number of iterations within one impulse. Out of selected 212 impulses, the cancellation results have shown for 12 th, 29 th, and 167 th impulse at dierent processing stages of the input. When the originally measured signal was fed into the canceler as input, a perfect cancellation obtained for almost all signals which contained impulse noise. The gure 4.2 illustrates how the mean squared error(mse) varies throughout 212 impulses. Figures 4.3-4.5 shows the cancellation results at this stage for dierent kinds of impulses..16 Mean Squared Error of the cancellation output.14.12.1 MSE/ mv.8.6.4.2 5 1 15 2 25 iteration Figure 4.2: Mean Squared Error of the cancellation result against iteration 9

5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 9 segment 8 5 2 4 6 8 1 12 14 x 1 4 Channel response NE, loop 1, block 9 segment 8 5 5 2 4 6 8 1 12 14 x 1 4 Figure 4.3: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 16 segment 9 5 2 4 6 8 1 12 14 x 1 4 Channel response NE, loop 1, block 16 segment 9 5 5 2 4 6 8 1 12 14 x 1 4 Figure 4.4: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 79 segment 1 5 2 4 6 8 1 12 14 x 1 4 Channel response NE, loop 1, block 79 segment 1 5 5 2 4 6 8 1 12 14 x 1 4 Figure 4.5: LN channel response (sub gure1-red), cancellation result(sub gure1-1

After removing the high frequency components of the cancellation results of original signal, far better cancellation could be seen. The gure 4.6 illustrates how the mean squared error(mse) of the cancellation varies throughout 212 impulses and it can be seen that the MSE at this stage is further reduced than the original signal. Figures 4.7-4.9 shows the cancellation results at this stage for dierent kinds of impulses..16 Mean Squared Error of the cancellation output.14.12.1 MSE/ mv.8.6.4.2 5 1 15 2 25 iteration Figure 4.6: Mean Squared Error of the cancellation result against iteration 11

5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 9 segment 8 5 2 4 6 8 1 12 14 x 1 4 Channel response NE, loop 1, block 9 segment 8 5 5 2 4 6 8 1 12 14 x 1 4 Figure 4.7: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 16 segment 9 5 2 4 6 8 1 12 14 x 1 4 Channel response NE, loop 1, block 16 segment 9 5 5 2 4 6 8 1 12 14 x 1 4 Figure 4.8: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 79 segment 1 5 2 4 6 8 1 12 14 x 1 4 Channel response NE, loop 1, block 79 segment 1 5 5 2 4 6 8 1 12 14 x 1 4 Figure 4.9: LN channel response (sub gure1-red), cancellation result(sub gure1-12

In the next stage, the high frequency components of the original signal was removed and as a result it also reduced the number of samples of the input signal, hence the results obtained for the cancellation at this stage was less than earlier stages. The gure 4.1 illustrates how the mean squared error(mse) of the cancellation varies throughout 212 impulses and it can be seen that the MSE is also reduced with the number of iterations, but signicantly in less factor. Figures 4.11-4.13 shows the cancellation results at this stage for dierent kinds of impulses..16 Mean Squared Error of the cancellation output.14.12.1 MSE/ mv.8.6.4.2 5 1 15 2 25 iteration Figure 4.1: Mean Squared Error of the cancellation result against iteration 13

5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 9 segment 8 5 1 2 3 4 5 6 7 5 Channel response NE, loop 1, block 9 segment 8 5 1 2 3 4 5 6 7 Figure 4.11: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 16 segment 9 5 1 2 3 4 5 6 7 5 Channel response NE, loop 1, block 16 segment 9 5 1 2 3 4 5 6 7 Figure 4.12: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 79 segment 1 5 1 2 3 4 5 6 7 5 Channel response NE, loop 1, block 79 segment 1 5 1 2 3 4 5 6 7 Figure 4.13: LN channel response (sub gure1-red), cancellation result(sub gure1-14

Another comparison had done with multiple iterations(2) in NLMS steps of algorithm in each sample of the ltered version of the impulse. As the gure 4.14 illustrates, the mean squared error(mse) of the cancellation at this stage has varied randomly, compared to the MSE curve obtained under previous section. Figures 4.15-4.17 shows the cancellation results at this stage for dierent kinds of impulses..16 Mean Squared Error of the cancellation output.14.12.1 MSE/ mv.8.6.4.2 5 1 15 2 25 iteration Figure 4.14: Mean Squared Error of the cancellation result against iteration 15

5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 9 segment 8 5 1 2 3 4 5 6 7 5 Channel response NE, loop 1, block 9 segment 8 5 1 2 3 4 5 6 7 Figure 4.15: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 16 segment 9 5 1 2 3 4 5 6 7 5 Channel response NE, loop 1, block 16 segment 9 5 1 2 3 4 5 6 7 Figure 4.16: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 79 segment 1 5 1 2 3 4 5 6 7 5 Channel response NE, loop 1, block 79 segment 1 5 1 2 3 4 5 6 7 Figure 4.17: LN channel response (sub gure1-red), cancellation result(sub gure1-16

The next attempt was using the ltered signal as the input to the canceler after interpolating by 2. The gure 4.18 illustrates the mean squared error(mse) of the cancellation obtained at this stage. It can be clearly seen, when the ltered signal is interpolated, the MSE has signicantly reduced than the MSE curve obtained under the previous sections with ltered version of the input. Figures 4.19-4.21 shows the cancellation results at this stage for dierent kinds of impulses..16 Mean Squared Error of the cancellation output.14.12.1 MSE/ mv.8.6.4.2 5 1 15 2 25 iteration Figure 4.18: Mean Squared Error of the cancellation result against iteration 17

5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 9 segment 8 5 2 4 6 8 1 12 14 5 Channel response NE, loop 1, block 9 segment 8 5 2 4 6 8 1 12 14 Figure 4.19: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 16 segment 9 5 2 4 6 8 1 12 14 5 Channel response NE, loop 1, block 16 segment 9 5 2 4 6 8 1 12 14 Figure 4.2: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 79 segment 1 5 2 4 6 8 1 12 14 5 Channel response NE, loop 1, block 79 segment 1 5 2 4 6 8 1 12 14 Figure 4.21: LN channel response (sub gure1-red), cancellation result(sub gure1-18

With the ltered version of the input, the following stage where the ltered signal interpolated by 2, showed the best cancellation of all kinds of ltered inputs. The gure 4.22 illustrates the mean squared error(mse) of the cancellation obtained at this stage where the sample size is increased to be equal with the length of the original signal. Figures 4.23-4.25 shows the cancellation results at this stage for dierent kinds of impulses..16 Mean Squared Error of the cancellation output.14.12.1 MSE/ mv.8.6.4.2 5 1 15 2 25 iteration Figure 4.22: Mean Squared Error of the cancellation result against iteration 19

5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 9 segment 8 5 2 4 6 8 1 12 14 x 1 4 Channel response NE, loop 1, block 9 segment 8 5 5 2 4 6 8 1 12 14 x 1 4 Figure 4.23: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 16 segment 9 5 2 4 6 8 1 12 14 x 1 4 Channel response NE, loop 1, block 16 segment 9 5 5 2 4 6 8 1 12 14 x 1 4 Figure 4.24: LN channel response (sub gure1-red), cancellation result(sub gure1-5 Impulse noise cancellation(blue), Channel response LN(red), loop 1, block 79 segment 1 5 2 4 6 8 1 12 14 x 1 4 Channel response NE, loop 1, block 79 segment 1 5 5 2 4 6 8 1 12 14 x 1 4 Figure 4.25: LN channel response (sub gure1-red), cancellation result(sub gure1-2

Chapter 5 Conclusion Our study was carried out for investigating the use of an adaptive NLMS lter to cancel the impulse noise on powerline. In order to design an NLMS noise lter, we rst needed two input channels which the noise on both channels has to be correlated. There by, as the rst phase of this research we constructed a coupling circuit to measure the noise on live-neutral(ln) channel and neutral-earth(ne) channel simultaneously. Then as the second phase of the research, throughout this study we have designed an NLMS adaptive lter and used that to cancel the impulse noise on measured signals at the rst phase. We have simulated our algorithm developed for NLMS adaptive lter using matlab, and have analyzed the results obtained for dierent kinds of inputs fed into the lter. Of ve types of inputs fed into the lter, we have obtained the optimum results when the originally measured signal is fed into the canceler. However, the originally measured signal contained high frequency components which is out of range of interest in powerline communication, hence we removed all unwanted high frequencies and tried to cancel the noise on the ltered signal. Then, as the number of samples in the input got also reduced, sample size was not enough to do a perfect cancellation. Again, by increasing the sample size of the ltered signal by interpolating, we could achieve better cancellation which was very close to the result obtain for the original signal. Even though the two channels were nicely correlated, the autocorrelation between the inputs on same channel could observe to be very poor. Therefore it was impossible to expect far better cancellation when running the simulation through many impulses, rather the cancellation was successful with increasing the number of iterations by increasing the sample size of one impulse. Unfortunately, increasing sample size leads towards the higher complexity. In order to achieve further cancellation with reduced sample size, a further analysis is proposed with collecting more data from each type of impulses and run the simulation separately. 21

Bibliography [1] S. Haykin, Adaptive Filter Theory, Englewood Clis, Prentince Hall, 1986. [2] Oana Graur, Impulse Noise Cancelation based on the Common Mode Signal, http://trsys.faculty.jacobs-university.de, Spring 29. [3] Hyun-Chool Shin, Ali H. Sayed, Fellow, IEEE, and Woo-Jin Song, Member, IEEE, Variable Step-Size NLMS and Ane Projection Algorithms, IEEE SIGNAL PRO- CESSING LETTERS, VOL. 11, NO. 2, pp. 132-135, FEBRUARY 24. [4] Christopher J. Wells, Telecommunications Principles Noise, http : //www.technologyuk.net/telecommunications/telecom_principles/noise.shtml, Feb. 213. [5] Gassara H., Bali M.C., Duval F., Rouissi F., and Ghazel A. i, Coupling interface circuit design for experimental characterization of the narrowband power line communication channel, Electromagnetic Compatibility (EMC), 212 IEEE International Symposium, pp. 1-6, Aug 212. 22