A Multi-Channel Feedforward ANC System Using A Novel FXLMS . - IJEETC

International Journal of Electrical and Electronic Engineering & Telecommunications Vol. 8, No. 6, November 2019and c is the propagation speed of the sound in the ambient.ANC system is based on the superposition property ofacoustic wave, when two sound waves interfere with eachother, the sound pressure at time t can be simplified top( x, y, z, t ) p1 ( x, y, z, t ) p2 ( x, y, z, t )ANC is represented by a K J matrix W (K rows and Jcolumns) with each element of an adaptive FIR filterWkj(n) [10] [11].X (n)Unknown plant(3)PMd( n )Jwhere p1(x, y, z, t), p2(x, y, z, t) are the sound pressure ofprimary and secondary source, respectively. The soundpressure summation of the two sound waves can be madezero (silent zone), if the two sound waves are equal inmagnitude and opposite in phase [9].w(n)SKM e( n )MŚLMSMKMFig. 4. Block diagram of a multiple-reference/multiple-outputfeedforward ANC using FXLMS algorithm.B. Feedforward ANC SystemA feedforward ANC can be categorized into two types.The first one is a single-channel feedforward ANCsystem, which consists of a single reference sensor(reference microphone), a single cancelling loudspeaker(secondary source), a single error sensor (errormicrophone) and the ANC itself. The reference input ispicked up by a reference sensor. The ANC functions as asmart controller to compute and generate the estimatedsignal to the cancelling loudspeaker. The errormicrophone is then used to monitor the performance ofthe system. The main objective of the ANC is tominimize the measured error signal and thus the residualacoustic noise.Another one is a multi-channel feedforward ANCsystem, which consists of multiple reference sensors,multiple cancelling loudspeakers, multiple error sensorsand multiple ANCs. The system acts to reduce noises (tocreate silence zones) as a single-channel feedforwardANC system. But they can have more silence zone areasbecause of a greater number of cancelling loudspeakers.In this paper, a multi-channel feedforward ANCsystem is presented to increase silence zone areas in onedemonstrated KMITL classroom.The matrix S, secondary path effects, contains M Ksecondary paths defined in eq. (4), [12], [13]. s11 (n) s21 (n) s ( n) s ( n)22S(n) 12 s1K (n) s2 K (n)sM 1 ( n ) sM 2 (n) sMK (n) (4)Typical ANC systems, the S(n) matrix is not availableand will be replaced by the Ś(n) matrix, which is anestimate of S(n) using off-line modeling method.Therefore, a matrix of filtered reference signal vectors isdefined as ś11 (n) ś 21 (n) ś ( n) ś ( n)22Ś(n) 12 ś1K (n) ś 2 K (n)ś M 1 ( n) ś M 2 (n) ś MK (n) (5)Each controller in the matrix W is represented bywkj(z), where j is the reference input index and k is thesecondary source index. The secondary signal output tothe kth secondary source isIII. MULTI-CHANNEL FEEDFORWARD ANCJFrom the problem aforementioned in section I and II,we proposed the design and simulation of a multi-channelfeedforward ANC system with FXLMS algorithm toperform adaptive coefficient to reduce the aircraft noiseflying-over our KMITL classroom.y(n) yj 1kj( n ) , k 1, 2,(6),KTykj ( n ) w kj ( n ) x j ( n )x j (n) x j (n), x j (n 1), , x j (n L 1) A. Adative Filter and Its AlgorithmAs mentioned, A multi-channel feedforward ANCsystem consists of multiple references/multipleoutputs/multiple errors and multiple ANCs. ANCs are thesignificant parts of the system that compute the inputs(from reference sensors) to perform the outputs (to drivecancelling loudspeakers). Generally, an ANC composesof adaptive filter and its algorithm. In this paper, wepresent Finite Impulse Response (FIR) filter and FXLMSalgorithm to perform the ANCs.Fig. 4 shows a block diagram of a multiplereference/multiple-output feedforward ANC usingFXLMS algorithm, where the ANC filter W has Jreference input signals xj(n) that are elements of signalvector x(n). The controller generates K secondary signalsthat are elements of vector y(n). Therefore, the controller 2019 Int. J. Elec. & Elecn. Eng. & Telcomm.y (n)Adaptive Filter(7)T(8)where j 1, 2, , j and L is the length of FIR filter. Thereare M K different secondary paths Smk(z) between thesecondary sources and error microphones, which aremodeled by Smk(z) to generate an array of filteredreference signals xˈjkm(n) for multiple-channel FXLMSalgorithm. This algorithm adjusts the coefficients of theK J adaptive filters wkj(z) in the controller, which isexpressed asMw kj (n 1) w kj (n) x' jkm (n)em (n)(9)x' jkm (n) śmk (n)* x j (n)(10)m 1whereand is the step size that determines the stability andthe convergence rate of the FXLMS algorithm.322

International Journal of Electrical and Electronic Engineering & Telecommunications Vol. 8, No. 6, November 2019of our classroom such as the reverberation, the directionof sound from the cancelling loudspeakers, the location ofloudspeakers and the power of loudspeakers.In terms of acoustic domain at error sensor mth,determine dm(n) is the desired signal (noise signal in aclassroom), ym(n) is the estimated signal (cancellingsignal) computed from the adaptive filter (ANC system)and em(n) is an error signal between dm(n) and ym(n)computed as shown in Eq. (11)em ( n ) ym ( n ) d m ( n )C. 2 2 2 Multi-Channel Feedforward ANCFrom section A and B, a 2 2 2 multi-channelfeedforward ANC system is modeled in the classroom,two-reference signal, two-cancelling loudspeaker andtwo- error microphone. From (6) and (7), we can computeboth of cancelling signals, which drive cancellingloudspeakers, from the ANC system as(11)If the adaptive filter output ym(n) is identical to thedesired signal dm(n). Therefore, when dm(n) and ym(n) areacoustically combined, the residual error isem ( n ) ym ( n ) d m ( n ) 0TTTTy1 ( n ) y11 ( n ) y12 ( n ) w11 ( n ) x1 ( n ) w12 ( n ) x 2 ( n )(12)(13)y2 ( n ) y21 ( n ) y22 ( n ) w 21 ( n ) x1 ( n ) w 22 ( n ) x 2 ( n ) (14)which results in perfect cancellation of both sounds basedon the principle superposition.where the w11(n), w12(n), w21(n) and w22(n) are theimpulse responses of the adaptive filters w11(z), w12(z),w21(z) and w22(z), respectively.From (9) and (10), these four adaptive filters, whichare performed the ANC system, are updated by theFXLMS algorithm asB. Acoustic Design for a ClassroomWe have a 12-stories classroom building in theKMITL university area, which is high enough to reachthe aircraft noise and is located near the second runwayof the airport (approximately 4 km).KMITL classroom in the building is simulated asillustrated in Fig 5. ś11 ( n )x1 ( n ) e1 ( n ) ś 21 ( n ) x1 ( n ) e2 ( n ) w11 ( n 1) w11 ( n ) (15)Unknown plantP1 ( z )y2 ( n )AircraftnoiseAircraftNoised1 ( n )CancellingLoudspeakerx1 ( n )y1 ( n )ReferenceMicrophoney11 ( n ) y1 ( n ) e1 ( n )Ś11x2 ( n )Ś21e1 ( n )e2 ( n )LMS4mKMITLclassroom4mS11w11 ( n )ReferenceMicrophoneErrorMicrophonex1 ( n )Adaptive FilterAdaptive FilterŚ124mŚ22S21w21 ( n )y21 ( n )e1 ( n )e2 ( n )LMS4me1 ( n )e2 ( n )Adaptive FilterŚ11ANCŚ21S12w12 ( n )e1 ( n )e2 ( n )LMSFig. 5. KMITL classroom with a multi-channel ANC system.Adaptive FilterThe classroom is a rectangular enclosure of dimension4m 4m 8m. A multi-channel feedforward ANC systemis designed in the classroom by using two referencemicrophones to measure the aircraft noises, twocancellation loudspeakers to perform secondary sources,two error microphones to measure the residual signals,and an ANC system to compute the input signals fromreference microphones for driving secondary sources. Wecalled a 2 2 2 multi-channel ANC system.In terms of acoustic design, which are identical todevelopment and implementation of a multi-channelactive control system for the reduction of road inducedvehicle interior noise [14], acoustic devices that will beused in the system to perform silence zone areas must beoptimized. Consequently, we will use referencemicrophones and error microphones whose specificationis compatible for frequency response and sensitivity ofthe noise sources. For the cancelling loudspeakers, theymust be suitable for an acoustic design and the dimension 2019 Int. J. Elec. & Elecn. Eng. & Telcomm.Ś12x2 ( n )Ś22y12 ( n )S22w22 ( n )e1 ( n )e2 ( n )LMSy22 ( n ) y2 ( n ) e2 ( n )d 2 (n)Unknown plantP2 ( z )Fig. 6. Diagram of a proposed 2 2 2 multi-channel feedforward ANCw 21 ( n 1) w 21 ( n ) ś12 ( n )x1 ( n ) e1 ( n ) ś22 ( n )x1 ( n ) e2 ( n ) (16) ś11 (n)x2 (n) e1 (n) w 21 (n 1) w 21 (n) ś21 (n)x2 (n) e2 (n) (17) ś12 ( n ) x 2 ( n ) e1 ( n ) ś 22 ( n ) x 2 ( n ) e2 ( n ) (18)w 22 ( n 1) w 22 ( n ) 323

International Journal of Electrical and Electronic Engineering & Telecommunications Vol. 8, No. 6, November 2019From (13) to (18), we can illustrate a block diagram ofthe 2 2 2 multi-channel feedforward ANC system asshown in Fig. 6, which is demonstrated how the ANCsystem is complicated and performed.IV. SIMULATION RESULTSFor the simulations, we present results of applying thecollected noise through the 2 2 2 multi-channelfeedforward ANC system using the FXLMS algorithm tominimize the actual noise gathered from the actualdemonstrating classroom that occurred when the time ofaircraft taking off and landing.A. Aircraft NoiseThe actual noise used in this simulation, which is thesame as we used to simulate a single-channel ANC in ourpaper [15], is a random aircraft noise recorded from theoutside of university classrooms near Suvarnabhumiairport for 5 seconds at the sampling rate 16 kHz. Thekey characteristic of this noise is shown in Fig. 7. Asfollows: Fig. 7 (a) illustrates the time-domain plot of thecollected noise, Fig. 7 (b) illustrates the frequencydomain plot of such a signal, Fig. 7 (c) presents the powerspectrum of the noise in dB/Hz, and Fig. 7 (d) plots theshort time Fourier transform (STFT) of such a noise toillustrate the complexity of the interested noise. It can beseen clearly from Fig. 7 that our noise here is highly nonlinear with multiple frequencies.Fig. 8. Simulation results x1(n), d1(n), y1(n), e1(n) of the ANC systemFig. 9. Simulation results x2(n), d2(n), y2(n), e2(n) of the ANC systemFig. 7. Aircraft noise characteristics recorded outside our classroom.B. Multi-Channel Feedforward ANC Simulation ResultThe simulation results in this case were done bypassing the collected noise through the 2 2 2 multichannel feedforward ANC system previously shown inFig. 7.The aircraft noise acts as input signal x1(n) and x2(n) ofthe ANC system, which the difference of the two inputsignals is amplitude that is x2(n) 0.8x1(n). The errorsignal e1(n) and e2(n) are obtained by summation of d1(n),y1(n) and d2(n), y2(n) respectively. Fig. 8 shows thesimulation results in this case by plotting x1(n), d1(n), y1(n)and e1(n) in the same time axis. Fig. 9 identically showsx2(n), d2(n), y2(n) and e2(n). 2019 Int. J. Elec. & Elecn. Eng. & Telcomm.324A variation of the relationships between the length ofthe adaptive filter (L) and the FXLMS step size (µ) canbe concluded that the best practice for this scenario iswhen using the adaptive filter length 512 and the step size0.001, respectively.C. Noise Attenuation CapabilitiesNoise attenuation in this paper is analyzed usingfrequency-domain analysis of the residual signal e1(n)and e2(n), defined asJCem x ( ) Cem x j ( )j 1(19)where Ce x ( ) is the magnitude-squared coherencemfunction between the error signal em(n) and reference

International Journal of Electrical and Electronic Engineering & Telecommunications Vol. 8, No. 6, November 2019signal xj(n). It follows that maximum possible noisereduction by an adaptive feedforward multi-channel ANCsystem in decibels.Fig. 10 shows estimated noise attenuation at errormicrophone e1(n) and Fig. 11 shows estimated noiseattenuation at error microphone e2(n). The attenuationplots show how the system can attenuate the aircraft noisein each of frequency. For example, in Fig 10, the noiseattenuation at e1(n), at frequency 500 Hz that the multichannel ANC system can attenuate the noise level about15 dB, at frequency 1000 Hz that the multi-channel ANCsystem can also attenuate the noise level about 15 dB.Both of Fig. 10 and Fig. 11 are the final noise attenuationcapabilities of the multi-channel feedforward ANCsystem.Fig. 12. MSE convergent time of a multi-channel feedforward ANCV. CONCLUSIONThe conclusion can be made here that for thisparticular highly-nonlinear aviation-noise problem inKMITL classroom mentioned in this paper, by choosingthe optimal key parameters like FXLMS step size andadaptive filter length, the proposed multi-channelfeedforward ANC system is far superior to the singlefeedforward ANC system mentioned in [15] in terms ofnoise attenuation capabilities. Unfortunately, the MSEconvergence time performance of this proposed strategyis slower than the simpler one mentioned in [15] due tothe more complicate in FXLMS algorithm versus theprevious LMS algorithm, and also the consideration ofthe secondary-path effects makes the overall system morecomplex. The simulation results from this paper shouldbe a good guideline for any relevant decision making.However, there are always some rooms for improvementin any circumstance. For further research, different kindsof FXLMS algorithms as well as different configurationsof a multi-channel feedforward ANC system could beconsidered. It is also should be noted here that, in thispaper, we neglected some surrounding factors that mightaffect the system performance like the electromagneticinterference (EMC) and the effect of other electronicsdevices.Fig. 10. Noise attenuation e1(n) from the ANC systemACKNOWLEDGMENTThe authors would like to thank the Research andResearchers Industries Department (RRI Funding), ThaiGovernment, for fully support in beneficial informationand sponsorship. This work is under a funding contractPHD58I0087 from RRI.Fig. 11. Noise attenuation e2(n) from the ANC systemD. MSE Convergence TimeThe MSE convergence time of this ANC system isconsidered when the error signal e1(n) and e2(n) are equalto or less than 10-4. As shown in Fig. 12, the convergencetime of the multi-channel feedforward ANC system isabout in iteration 350000th for both of e1(n) and e2(n).For the reason, we can conclude that a multi-channelfeedforward ANC system generally requires longerconvergence than do a single-channel feedforward ANCsystem, which we have done in [15]. 2019 Int. J. Elec. & Elecn. Eng. & Telcomm.REFERENCES[1][2][3]325Department of Environmental Quality Promotion, “Report ofaircraft noise effects for the addition of runways in suvarnabhumiairport,” Ministry of Nature Resources and Environment.,Bangkok, Thailand, 2010.T. Pamies, J. Romeu, M. Genesca, and Robert Arcos, “Activecontrol of aircraft fly-over sound transmission through an openwindow,” Applied Acoustics, vol. 84, pp. 116-121, Oct. 2014.J. He, B. Lam, D. Shi and W. S. Gan, “Exploiting theunderdetermined system in multichannel active noise control foropen windows,” Applied Sciences, vol. 9, no. 3, p. 390, 2019.

International Journal of Electrical and Electronic Engineering & Telecommunications Vol. 8, No. 6, November 2019[4][5][6][7][8][9][10][11][12][13][14]B. Lam, C. Shi, D. Shi, and W. S. Gan, “Active control of soundthrough full-sized open windows,” Building and Environment, vol.141, pp. 16-17, Aug. 2018.K. Iwai, S. Hase, and Y. Kajikawa, “Multichannel feedforwardactive noise control system with optimal reference microphoneselector based on time difference of arrival,” Applied Sciences, vol.8, p. 2291, Oct. 2018,S. Wang, J. Yu, X. Qiu, M. Pawelczyk, A. Shaid, and L. Wang,“Active sound radiation control with secondary sources at the edgeof the opening,” Applied Acoustics, vol. 117, pp. 173-179, Feb.2017.P. Leug, “Process of silencing sound oscillations,” U.S. Patent2043416, 1936.B. Widrow, J. Glover, J. McCool, J. Kaunitz, C. Williams, R.Hearn, et al., “Adaptive noise cancelling; Principles andapplications,” Proc. of the IEEE, vol. 63, no. 12, pp. 1692-1716,Dec. 1975.I. T. Ardekani and W. H. Abdulla, “FxLMS-based active noisecontrol: A quick review,” presented at APSIPA ASC 2011, Xi’an,China, 2011.M. Moazzam and M. S. Rabbani, “Performance evaluation ofdifferent active noise control (ANC) algorithms for attenuatingnoise in a duct,” Master thesis, Dept. of Applied Signal Processing,Blekinge Institute of Technology., Karlskrona, Sweden, 2013.P. A. Nelson and S. J. Elliot, Active Control of Sound, AcademicPress Inc., CA: San Diego, 1992.S. M. Kuo and D. R. Morgan, Active Noise Control Systems:Algorithm and DSP Implementations, NY: John Wiley & SonsInc., 1996.S. M. Kuo and D. R. Morgan, “Active noise control: A tutorialreview,” Proc. of IEEE, vol. 87, no. 6, pp. 943-973, June 1999.G. Gabel, J. Millitzer, H. Atzrodt, and S. Herold, “Developmentand implementation of a multi-channel active control system forthe reduction of road induced vehicle interior noise,” Actuators,vol. 7, no. 3, Aug. 2018. 2019 Int. J. Elec. & Elecn. Eng. & Telcomm.326[15] C. Sookpuwong and C. Chompoo-Inwai, “Performancecomparisons between a single-channel feedforward ANC systemand a single-channel feedback ANC system in a noisyenvironment classroom,” presented at the 8th Annu. ISEIM Conf.International Symposium on Electrical Insulation Materials,Toyohashi, Japan, 2017.Chadaporn Sookpuwong received her B.Eng.in telecommunication engineering and M.Eng.in electrical engineering from King Mongkut'sInstitute of Technology Ladkrabang, Thailand.Currently, she is pursuing her Ph.D. inelectrical engineering in the same University.Her research interests are advanced on and power engineering,noise cancellation and reduction techniquesand also acoustic engineering.Chow Chompoo-inwai (IEEE Member since1998) received both of his B.Eng (hons.) andM.Eng degrees in Electrical Engineering fromthe King Mongkut's Institute of TechnologyLadkrabang (KMITL), BKK, Thailand. Hegot his Ph.D. degree in Electrical andComputer engineering from ClarksonUniversity, NY, USA. He joined KMITL as afaculty member since 1998. He currentlyworks an assistant professor in the EnergySystem and Illumination Research Center (ESIRC), EE. Department,Faculty of Engineering, KMITL, BKK, Thailand. His research interestsare on various fields in Power Engineering i.e., High voltage, PowerSystem, Renewable Energy, Energy Efficient Economics andManagement, Digital signal processing in Power and medicalapplications and Illumination Engineering.

A Multi-Channel Feedforward ANC System Using a Novel FXLMS Algorithm in Solving Classroom Aviation-Noise Problems . Chadaporn Sookpuwong. NEF EPNL 10log ( 16.67 ) 88 . is the propagation speed of the sound in the ambient. ANC system is based on the superposition property of acoustic wave, when two sound waves interfere with each .