Causality study on a feedforward active noise control headset with different noise coming directions in free field

Abstract

A systematic analysis is proposed to predict the performance of a typical feedforward single channel ANC headset in terms of the delay, especially the non-causal delay caused by different noise coming directions. First, the performance of a non-causal feedforward system for a band-limited noise is analyzed by using a simplified pure delay model, where it is found that the noise reduction bandwidth is narrowed and the maximum noise reduction is decreased with the increase of the non-causal delay. Second, a systematic method is developed, which can be used to predict the system performance with measured primary and secondary path transfer functions in most practical sound fields and to study the effects of the control filter length and the path delay on the performance. Then, the causality of a typical feedforward active noise control headset with the primary source at 0° and 90° positions in an anechoic chamber is analyzed, and the performance for the two locations predicted by the systematic analysis is shown in good agreements with the experiment results. Finally, an experiment of a typical feedforward active noise control headset in a reverberation chamber is carried out, which shows the validity of the proposed systematic analysis for other more practical sound fields.

Introduction

Active noise control (ANC) headsets apply active control technique to reduce low frequency noise in headsets [1], where many methods have been used, such as analog feedback controller [2], digital feedforward controller [3], and the hybrid controller combining the digital feedforward technique with feedback technique [4]. This paper is focused on a typical feedforward active headset composed by an external reference microphone, an internal error microphone and a secondary source in the earmuff [3], where the reference microphone senses the reference signal, the filtered-x least mean square (FXLMS) algorithm is used to adapt the digital filter driving the secondary source to minimize the mean square of the noise at the error microphone.

The FXLMS algorithm is a popular ANC algorithm due to its robust performance, low computational complexity and ease of implementation. However, the performance depends on many factors, such as the degree of the coherence between the reference signal and the noise signal [5], [6], [7], acoustic feedback [7], [8], the time-varying property of the primary noise [4], [9], the estimation error between the modeling and practical secondary path [10], and the causality caused by the system delay [5]. For feedforward ANC systems, the primary path contains the acoustic delay from the reference microphone to the error microphone, and the secondary path contains the same kind of acoustic delay from the secondary source to the error microphone and the total electrical system delay from the antialiasing filter, analog to digital (AD) converter, digital to analog (DA) converter, reconstruction filter, one sampling period for processing, etc. The primary path delay should be larger than the total secondary path delay to guarantee a feedforward control filter have a causal response. This condition is called the causality constraint [11]. For stationary noise cancellation with good coherence between the reference signal and the noise signal and good secondary path modeling, the causality or the system delay becomes the dominate factor for the control performance [3], [12].

Several studies have demonstrated the effects of the system delay on the performance of feedforward ANC headsets. For example, Rafaely pointed out that the performance of the feedforward ANC headset relied on the timely detection of the reference signal and the delay of the digital system [12]. Brammer et al. showed that shorter distance between the reference and error microphones of feedforward ANC headsets resulted in a correspondingly shorter time available to the controller for executing ANC algorithm [3], so they used a dual-rate sampling system to reduce the delay of the digital system, which involved oversampling the acoustic signals from the reference and error microphones, and updating the control signal to the secondary source at a decimated rate of the external sampling frequency.

Rafaely and Jones have studied the performance of the feedforward ANC headset as functions of the primary source positions in a reverberant chamber and a laboratory room [13]. They pointed out that the performance of the feedforward ANC headset under different head positions was significantly different in the laboratory room and was similar in the reverberant chamber. The significant variation in the attenuation with the head position was qualitatively analyzed as the acoustical delay variation between the reference and the error microphones.

Using the simulation of arbitrary signal delay, such as 5, 0, and −6 samples respectively, which might be caused by AD and DA converters, Kruger et al. showed that broadband feedforward approaches in the ANC headset were strongly influenced by the delay [14], and they also pointed out that the lack of causality caused by the delay was a problem in digital realizations. In the above studies, it is clear that the delay, such as the electrical delay and the acoustical delay, affects the performance of feedforward ANC headsets. However, there is a lack of systematic analytical method to quantitatively describe the change of the noise attenuation performance with the delay.

For feedforward ANC systems using the LMS optimization technique, several studies have investigated the effects of the causality constraint. Burdisso et al. carried out causality analysis of feedforward systems subjected to broadband excitations in frequency-domain and predicted the performance of such system in terms of system parameters such as the delay time, damping, spectral content of the input, and filter size [15]. The analysis showed that the deterioration in the control performance due to the delay in the control path could be at least partially compensated by increasing the filter order.

Janocha and Liu showed in a simulation that the performance was deteriorated as increasing the delay and active noise control systems required a considerable causality margin to perform well, which was explained by an example of the delayed inverse modeling of a non-minimum phase system [16]. Kong and Kuo showed theoretically and numerically that the noise canceling efficiency decreased as the degree of non-causal delay increased and the bandwidth of the noise increased [17].

Tseng et al. studied the performance of a feedforward ANC system as a function of primary source locations in a room [18]. When the primary source reached the bounds of a causal configuration, performance started to decline and declined further as the configuration grew more non-causal. Anderson and Wright compared the performance of an ANC system canceling a periodic disturbance under both causal and non-causal conditions and demonstrated that the computation time for the inverse signal in the non-causal condition was much longer than that in a causal system [19].

Boudier et al. showed the results of a local single channel feedforward control of uncorrelated broadband noise sources (stationary and non-stationary), with various reference configurations (single close reference, single remote reference, and multiple remote references) and in three types room (an anechoic room, a call center with the reverberation time about 0.3 s and a work office with the reverberation time about 1 s) [20]. The influences of the reverberation and of the multiple sources on the coherence and the causality constraints were analyzed by the unconstrained frequency-domain controls and causality constrained time-domain (LMS) controls.

In the existing literatures, the theoretical deteriorated performance is described mainly by the overall noise reduction in a simplified pure delay model of the secondary path. For the noise with a specific bandwidth, the changes of the maximum noise reduction and attenuation bandwidth with the non-causal delay have not been studied. Some literatures have given the performance of a real system by simulations. However, there is a lack of the theoretical analysis on the non-causal performance with both practical primary and secondary paths, which is important for ANC applications.

The application background of this study is to explore whether putting more reference microphones on the earmuff for noise coming from different directions can increase the performance of current ANC headsets, so the aim of this paper is to propose a systematic analysis to predict the performance of the typical feedforward ANC headset in terms of the delay, especially the non-causal delay caused by different noise coming directions. Acoustic delay may be different in various sound fields, as pointed out in Ref. [13], where two sound fields, the laboratory room and reverberant lab, are discussed. This paper will not discuss the different non-causal delay caused by different acoustic fields, but rather focus on the non-causal performance analysis. To make the analysis clear, the free field is adopted as an example to study the system causality with different noise coming directions. First, the performance as a function of the non-causal delay in a simplified pure delay model is illustrated for a band-limited noise. Second, a systematic method is developed to predict the system performance with measured primary and secondary path transfer functions in most practical sound fields and to study the effects of the control filter length and the path delay on the performance. Then, experiments with a feedforward ANC headset in an anechoic chamber are carried out to verify the developed formula by analyzing the causality of two different primary noise source locations. Finally, an experiment with a feedforward ANC headset in a reverberation chamber is carried out to illustrate the validity of the proposed systematic method for other more practical sound fields.