ABSOLUTE AVERAGE ERROR BASED ADJUSTED STEP SIZE LMS ALGORITHM FOR ADAPTIVE NOISE CANCELLER

1. ABSOLUTE AVERAGE ERROR BASED ADJUSTED STEP SIZE LMS ALGORITHM FOR ADAPTIVE NOISE CANCELLER

2. By ThamerM.Jamel And HaiderAbdalLatif University of Technology Baghdad - Iraq

3. ABSTRACT • In this paper, an Absolute Average Error-based Adjusted Step Size LMS (AAE-ASSLMS) algorithm is proposed, which overcome and avoid one of the drawbacks of the standard LMS algorithm. This drawback is convergence speed – misadjustment trade off problem. • In this proposed algorithm an appropriate time varying value of the step size is calculated based on gradually decreasing maximum step size to the minimum value.

4. This time varying step size is based on the absolute average value of the current and the previous estimation errors. • The proposed algorithm shows through a computer simulation result fast convergence time and low level of misadjustment compared with traditional LMS and another Variable Step Size LMS algorithme (VSSLMS) for adaptive noise cancellassions system.

5. Primary I/P s + + Signal Source n - + Noise path H(z) Adaptive FIR Filter Noise Source Reference I/P Filter O/P Signal • The ANC concept and Model System O/P d=S+ n Y(n) e(n) n1 Error Signal

6. Transversal FIR (nonrecurisve) Filters X(n) X(n-1) X(n-L+2) x(n-L+1) T ..... T T w1 wL-2 wL-1 w0 + + + y(n) ........

7. NEW PROPOSED ALGORITHM (AAE-ASSLMS) • AAE-ASSLMS regards as modified version of the standard LMS algorithm. • AAE-ASSLMS algorithm used variable step size that will be adjusted according to absolute average value of the current and the previous estimator errors as follows:-

9. In this new proposed algorithm the subtraction process is used to make the next step size µ(n-1) always smaller than the current step size µ(n). • Furthermore, in this algorithm the absolute value is used to get a decrease in step size in order to arrive at the minimum step size with the lower number of iterations. • In this algorithm, the average error is used to increase the ability of adaptive filter for tracking the weight coefficients of the noise path.

10. The parameter ( β) controls the convergence time as well as the level of misadjustment of the algorithm at a steady state. • If the value of the constant (β) is small, the speed of arrival to the minimum step size µ(min) is slow. • The small value of (β) is an important in the environments where the noise level is low because the step size remains large for more iterations before arrives at µ(min) , this makes the convergence time fast. • The large value of (β) is an important in the environments where the noise level is high in order to make the step size arrive at µ(min) with faster time, this makes the misadjustment low at a steady state.

11. VSSLMS ALGORITHM

12. Simulation Results • LMS algorithm • VSSLMS algorithm • AAE-ASSLMS algorithm

13. Performance of the Algorithms • Miss-adjustment • Attenuation • Error Function Z(n) • MSE • Weight coefficients Estimation

16. Corrupted speech signal

17. Attenuation performance for LMS algorithm at different (SNR)

18. Attenuation performance for VSSLMS algorithm at different (SNR)

19. Attenuation performance for AAE-ASSLMS algorithm at different (SNR)

21. Error function performance for different algorithms at SNR = -20 dB • From this figure, one can investigate that the proposed algorithm gives faster convergence time and lower misadjustment at the steady state.

22. In ANC application the adaptive filter tries to minimize the total output power in order to make the output error e(n) to be a best least-squares estimate (LSE) of the original signal s(n). This figure shows that the proposed algorithm has the best ability for estimation the original signal when a signal to noise ratio equal to (-20 dB).

23. Filter Coefficients Estimation • The ability of algorithms for tracking the noise path coefficients is investigated. • Figures below show the weight coefficients estimation performance for LMS, VSSLMS and AAEASSLMS for signal to noise ratio at the primary input equals (-20 dB) respectively.

24. Weight coefficients estimation for LMS algorithm at SNR (-20 dB)

25. Weight coefficients estimation for VSSLMS algorithm at SNR (-20 dB)

26. Weight coefficients estimation for AAE-ASSLMS algorithm at SNR (-20 dB)

27. As shown in these figures, the Adaptive FIR filter (AFIR) coefficients of ANC using AAE-ASSLMS converges fast to the noise path coefficients and has good estimation coefficients than the standard LMS and VSSLMS algorithms.

28. CONCLUSIONS • This paper focused on enhancement performance of the standard LMS using new proposed algorithm (AAEASSLMS) • This proposed algorithm used an appropriate time varying step size that is calculated based up on the absolute average value of the current and the previous estimator errors.

29. The motivation of the proposed algorithm is starting from the maximum step size to achieve fast convergence time and decreasing to the minimum step size to get a low level of misadjustment. • The proposed algorithms show fast and low level of miss-adjustment compared with LMS and VSSLMS algorithms.

30. Furthermore, the attenuation factor of ANC was enhanced using proposed algorithm compared with other algorithms. • The proposed algorithm gives high robustness to high variance noise signals compared with other algorithms.

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