An Investigation of Delayless Subband Adaptive Filtering for Multi-Input Multi-Output Active Noise Control Applications

Abstract

The broadband control of noise and vibration using multi-input, multi-output (MIMO) active control systems has a potentially wide variety of applications. However, the performance of MIMO systems is often limited in practice by high computational demand and slow convergence speeds. In the somewhat simpler context of single-input, singleoutput broadband control, these problems have been overcome through a variety of methods including subband adaptive filtering. This paper presents an extension of the subband adaptive filtering technique to the MIMO active control problem and presents a comprehensive study of both the computational requirements and control performance.The implementation of the MIMO filtered-x LMS algorithm using subband adaptive filtering is described and the details of two specific implementations are presented. The computational demands of the two MIMO subband active control algorithms are then compared to that of the standard full-band algorithm. This comparison shows that as the number of subbands employed in the subband algorithms is increased, the computational demand is significantly reduced compared to the full-band implementation provided that a restructured analysis filter-bank is employed. An analysis of the convergence of the MIMO subband adaptive algorithm is then presented and this demonstrates that although the convergence of the control filter coefficients is dependent on the eigenvalue spread of the subband Hessian matrix, which reduces as the number of subbands is increased, the convergence of the cost function is limited for large numbers of subbands due to the simultaneous increase in the weight stacking distortion. The performance of the two MIMO subband algorithms and the standard full-band algorithm has then been assessed through a series of time-domain simulations of a practical active control system and it has been shown that the subband algorithms are able to achieve a significant increase in the convergence speed compared to the full-band implementation. Index TermsActive noise control, Active vibration control, Delayless subband adaptive filtering, MIMO J. Cheer is with the Institute

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“…One can observe that the FxRLS algorithm has the fastest convergence rate and the FxLMS algorithm suffers from slow convergence. Then, a delayless SAF algorithm for multi-input multi-output (MIMO) ANC applications was developed, which is based on Milani's work [207,208] and can significantly mitigate the computational cost [209].…”

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“…The delayless SAF for the ANC system is illustrated in Fig. 2 [17]. The reference microphones record the reference signals x ( l ), whereas the error microphones record the error signals e ( l ).…”

“…Finally, the subband filter coefficients are superposed to form the filter coefficients of the full frequency band [16]. Previous research shows that the SAF method can significantly improve convergence speed and reduce computational complexity, especially for MIMO systems [17].…”

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