Simultaneous Variable Perturbation Method for the Active Noise Control System with a Wireless Error Microphone

Proceedings, APSIPA Annual Summit and Conference 2020 7-10 December 2020, Auckland, New Zealand

Chuang Shi, Zhongxing Yuan, Rong Xie, and Huiyong Li University of Electronic Science and Technology of China, Chengdu, China Corresponding E-mail: [email protected]

d() n e() n Abstract—This paper proposes the use of a wireless error x() n P microphone in active noise control (ANC) systems. There are + 

several practical advantages of doing so. The target zone of + quiet (ZoQ) is allowed to be reconfigured by simply moving y() n  y'( n ) the wireless error microphone. When the target ZoQ is large, W S many error microphones have to be placed. Using the wireless error microphone eases the deployment and maintenance work.  S However, the drawback of using wireless error microphones is e'( n ) due to the jitter effect of the wireless communication. The error NLMS Wireless signal samples arrive at the ANC controller at random time r() n intervals, which sometimes are greater than the sampling interval. To solve this problem, this paper investigates the simultaneous Fig. 1. Block diagram of the feedforward ANC system with a wireless error perturbation (SP) method and proposes the simultaneous variable microphone. perturbation (SVP) method. Simulations of the ANC system with a wireless error microphone are carried out with acoustic paths measured in an actual setup. Simulation results demonstrate that when the SVP method reduces the broadband noise effectively the reference and error signals are fed to the ANC controller even when the jitter effect is severe. in a non-stop sample by sample manner. However, the noise canceling headphone, one of the most I.INTRODUCTION successful ANC applications, adopts a fixed-filter structure [9]. The ANC has gained rapid development in the last three The reference signal is still crucial to generate the control decades to tackle problems resulting from the noise. It serves signal in real time, but the error signal is abandoned since as a complementary technique to the passive noise control no adaption is implemented. This fact inspires us to make the (PNC), which can become relatively less efficient in terms transmission of the error signal to be wireless. In Fig. 1, we of size, weight, volume and cost when the noise frequency propose to use a wireless error microphone in the ANC system. is lower [1], [2]. The principle of the ANC is the acoustic The proposed system design has several practical advantages. wave superposition. The ANC system transmits an anti-noise Since the ZoQ is formed around the error microphone, the wave that has the same amplitude and opposite phase as the target ZoQ is allowed to be reconfigured by simply moving the noise wave. The anti-noise wave interferes with the noise wireless error microphone around [10], [11], [12]. Moreover, wave. Together, they result in a trivial residual noise level. when the target ZoQ is large, more than one error microphones This procedure is readily extended to a 3D space, where the have to be placed. Using the wireless error microphone eases ANC constructs an anti-noise sound field and results in a large the deployment and maintenance work. ZoQ [3], [4], [5]. With the emerging technology, such as 5G, latency is no ANC systems are categorized by their control structures longer a concern with the wireless communication [13], [14]. and number of electro-acoustic devices involved [6]. The The drawback of the wireless error microphone lies in the jitter single-channel feedforward ANC system includes a reference effect. The error signal samples arrive at the ANC controller microphone, a control source and an error microphone, which at random time intervals, which are likely to be greater than can be imaged based on Fig. 1 by replacing the wireless the sampling interval. Buffering the error signal samples and channel with a connecting wire. The reference microphone adopting the delay FxLMS algorithm can only deal with a mild provides the reference signal to the ANC controller. The error jitter effect. Therefore, this paper investigates the SP method microphone inputs the error signal for the controller to adapt and proposes the SVP method. The SP method requires no its control filter coefficients. The control source transmits the secondary path model, which is more suitable to be used control signal, which is the output of the control filter. The with the wireless error microphone than the FxLMS algorithm FxLMS algorithm is widely-recognized as the standard ANC [15]. By introducing a time-varying perturbation magnitude, algorithm [7], [8]. In order for the FxLMS algorithm to work, the SVP method can converge to a lower noise level than the

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xN (n) = [x (n) , x (n − 1) , . . . , x (n − N + 1)] , (1) o N where N is the memory size, depending on the length of the control filter Nw and the length of the secondary path model T Nsˆ; denotes the transpose. Fig. 3. Comparison of the SP and SVP methods when µ = 1.0 × 10−6, The error signal e (n) is resultant from the acoustic wave α = 0.9965 and γ = 5.0 × 10−9. superposition of the noise and anti-noise wave, i.e. e (n) = d (n) + y0 (n) , (2) update the control filter coefficients in a block by block where d (n) is the disturbance signal; and y0 (n) is the anti- manner. Supposing the block size is given by the length of noise signal. The imaginary system taking the reference signal the control filter Nw, the updating equation is written as as the input and generating the disturbance signal as the output J (n + Nw) − J (n) is modeled as the primary path p. Another imaginary system w (n + Nw) = w (n) − µ q (n) , (6) taking the control signal as the input and generating the anti- c noise signal as the output is modeled as the secondary path s. where n X Both the primary and secondary paths are not just the acoustic J (n) = e2 (k); (7)

paths. They also include the effects of the electro-acoustic k=n−Nw+1 devices. In order for the ANC controller to implement the T FxLMS algorithm, a secondary path model ˆs is trained either q (n) = [q (n) , q (n − 1) , . . . , q (n − Nw + 1)] (8) off-line or on-line [17], [18]. The adaption of the control filter and q (n) is generated by the M sequence. q (n) serves as the coefficients w (n) is written as perturbation filter coefficients, which are changing in every r (n) e (n) block. The output of the perturbation filter is denoted as o (n), w (n + 1) = w (n) − µ , (3) rT (n) r (n) which is further written as where µ is the step size; the filtered reference signal vector is o (n) = cq (n) ∗ x (n) . (9) provided by c is the perturbation magnitude in both (6) and (9). T r (n) = [r (n) , r (n − 1) , . . . , r (n − Nw + 1)] , (4) Previous studies show that the convergence speed becomes slower as the perturbation is made smaller. Therefore, in this in which paper, we propose the SVP method, whereby the constant c r (n) = ˆs ∗ x (n) (5) Nsˆ in (4) and (7) is replaced by a time-varying c (n) as and ∗ denotes the convolution. c (n + N ) = αc (n) + γJ 2 (n). (10) Figure 2 shows an alternative adaptation, namely the time- w domain time-difference SP (TDTDSP) method [19]. The SP α and γ are two hyper parameters to ensure that the perturba- method adds perturbation to the control filter coefficients and tion magnitude decreases as the noise level reduces. Last but

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V C IV. ONCLUSIONS 286 C h,N in,R i,adH i Asmlto netgto of investigation simulation “A Li, H. and Xie, R. Jiang, N. LMS Shi, error multiple C. “A [8] Nelson, A. P. and Stothers, M. I. Elliott, multiple-input J. “Understanding S. Gan, [7] S. W. and Shi, D. Li, H. Shi, incident “Controlling C. Gan, S. [6] W. and Shi, active C. Lam, on B. Cheer, advances J. “Recent Elliott, S. Kuo, M. [5] S. and Gan, S. W. Kajikawa, Y. [4] Elliott, J. S. [3] Hansen, H. C. Morgan, [2] R. D. and Kuo M. S. [1] 2019YJ0182 No. Sichuan (Project and 2018JY0218). Program 61671137), and Technology and and 61701090 Foundation No. Science Science (Grant (Joint Natural China China National of of U1933127), Administration No. Aviation Grant Civil by supported effect jitter the under methods SVP and FxLMS the of Comparison ( 7. Fig. λ hsmnsrp speae ae ntersac work research the on based prepared is manuscript This 6) = 09ASP nu umtConf. control,” Summit noise Annu. active APSIPA feedforward 2019 for algorithms FxLMS modiﬁed vibration,” and 1987. sound 1434, Process. of Sig. control Speech active Acoust. Trans. the IEEE to application its and algorithm and sampling 2017. of Malaysia, perspective a from reconstruction,” control noise in apertures,” active through multiple-output and Vib. space Sound free Congr. in Int. arrays 24th source Proc. with ﬁelds sound applications,” innovative Process. and Inf. issues Sig. Open control: noise 2000. London, 2001. London, Implementations DSP and Noise Power Level (dB) Normalized Amplitude Normalized Amplitude hnteei udncag ftescnaypath. secondary the of change sudden a is there when

inlpoesn o ciecontrol active for processing Signal 7-10 December2020, Auckland, NewZealand rc 07ASP nu umtConf. Summit Annu. APSIPA 2017 Proc. nesadn cieniecancellation noise active Understanding o.1 o 3 p –1 2012. 1–21, pp. e3, no. 1, vol. , A CKNOWLEDGMENT R ie:NwYr,1996. York, New Wiley: . EFERENCES cieNieCnrlSses Algorithms Systems: Control Noise Active odn K uy2017. July UK, London, , azo,Cia 2019. China, Lanzhou, , o.AS-5 o 0 pp.1423– 10, no. ASSP-35, vol. , cdmcPress: Academic . ul Lumpur, Kuala , PIATrans. APSIPA pnPress: Spon . Proc. Proceedings, APSIPA Annual Summit and Conference 2020 7-10 December 2020, Auckland, New Zealand

[9] C. Shi, T. Murao, D. Shi, B. Lam, and W. S. Gan, “Open loop active control of noise through open windows,” Proc. Meetings Acoust., vol. 29, no. 1, 2016. [10] S. J. Elliott and J. Cheer, “Modeling local active sound control with remote sensors in spatially random pressure ﬁelds,” J. Acoust. Soc. Am., vol. 137, no. 4, pp. 1936-1946, 2015. [11] C. Shi, R. Xie, N. Jiang, H. Li, and Y. Kajikawa, “Selective virtual sensing technique for multi-channel feedforward active noise control systems,” Proc. 2019 Int. Conf. Acoust. Speech Sig. Process., Brighton, UK, 2019. [12] C. Shi, Z. Jia, R. Xie, and H. Li, “An active noise control casing using the multi-channel feedforward control system and the relative path based virtual sensing method,” Mech. Syst. Sig. Process., vol. 144, 2020. [13] L. Sujbert, K. Molnar, G. Orosz, and L. Lajko, “Wireless sensing for active noise control,” Proc. 2006 IEEE Instrum. Meas. Tech. Conf., Sorrento, Italy, 2006. [14] S. Shen, N. Roy, J. Guan, H. Hassanieh, and R. R. Choudhury, “MUTE: Bringing IoT to noise cancellation,” Proc. SIGCOMM’18, Budapest, Hungary, 2018. [15] Y. Kajikawa and Y. Nomura, “Active noise control system without secondary path model,” Proc. 2000 IEEE. Symp. Circuits Syst., Geneva, Switzerland, 2000. [16] Y. Kajikawa and Y. Nomura, “Active noise control without a secondary path model by using a frequency-domain simultaneous perturbation method with variable perturbation,” Proc. 2003 Int. Conf. Acoust. Speech Sig. Process., Hong Kong, China, 2003. [17] L. J. Eriksson and M. A. Allie, “Use of random noise for on-line transducer modeling in an adaptive active attenuation system,” J. Acoust. Soc. Am., vol. 85, no. 2, pp. 797–802, 1989. [18] M. T. Akhtar, M. Abe, and M. Kawamata, “A new variable step size LMS algorithm-based method for improved online secondary path modeling in active noise control systems,” IEEE Trans. Audio Speech Lang. Process., vol. 14, no. 2, pp. 720–726, 2006. [19] T. Shimizu and Y. Kajikawa, “Online secondary-path-modeling ANC system with simultaneous perturbation method,” Proc. 2016 APSIPA Annu. Summit Conf., Jeju, Korea, 2016. [20] C. Shi, N. Jiang, H. Li, D. Shi, and W. S. Gan, “On algorithms and implementations of a 4-channel active noise canceling window,” Proc. 2017 IEEE Int. Symp. Intell. Sig. Process. Commun. Syst., Xiamen, China, 2017.

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