## 1 Introduction  
Acoustic noise has become a serious problem with the increased use of industrial equipment, such as engines, manufacturing plants, air conditioners, and so forth. One of the methods used to reduce unwanted noise is passive noise control, such as ear plugs, which cannot reduce noise at low frequencies. Another approach is the use of active noise control (ANC) systems [1; 2; 3; 4]. ANC systems use an adaptive digital filter [5; 6; 7] to track the time-varying characteristics of the noise source and acoustic environment. The control structure of an ANC system is classified into feedforward [2; 8; 9] control and feedback control [10; 11; 12].  
A feedforward ANC system consists of a reference microphone, an error microphone, and a loudspeaker called the secondary source. The reference microphone and error microphone are used to pick up the unwanted noise and to sense the residual noise, respectively. Then, anti-noise is generated by the noise control filter and radiated from the secondary source. Feedforward ANC can reduce unwanted acoustic noise such as broadband noise by placing the reference microphone close to the noise source [4].  
In general, an ANC system uses the filtered-x algorithm [13; 14], which requires a secondary path model. The secondary path model is an identified secondary path between the secondary source and the error microphone. Hence, if the secondary path changes, then the performance of the ANC system deteriorates. To solve this problem, head-mounted ANC systems were proposed, in which a compact loudspeaker as the secondary source and the error microphone are located near the user's ears [15; 16; 17; 18; 19; 20; 21].  
If multiple noise sources are distributed in a wide area, the noise reduction performance of the single-channel feedforward ANC system deteriorates. Therefore, a multichannel feedforward ANC system [22; 23; 24; 25; 26; 27; 28; 29] is necessary to reduce multiple unwanted noises. For the multichannel ANC system, the locations of the reference microphones are very important because the causality constraint [30; 31] should be satisfied to maintain the noise reduction performance. The causality constraint is that the unwanted acoustic noise propagates to the control point faster than the anti-noise. If the causality constraint is violated, then the noise reduction performance of the feedforward ANC system deteriorates. This problem occurs when some reference microphones are not sufficiently close to the noise source. In particular, the noise reduction performance deteriorates if the arrival direction of the unwanted noise changes owing to the movement of the noise source.  
To solve this problem, we propose a multichannel ANC system with an optimal reference microphone selector [32]. The proposed system estimates the time difference of arrival (TDOA) between the unwanted acoustic noise at the control point and the unwanted acoustic noise at the reference microphones located around the control point. On the basis of the estimated TDOA, appropriate reference microphones that satisfy the causality constraint are selected. Then, the multichannel feedforward ANC system is operated using the selected reference microphones.  
This paper is organized as follows. In Section 2, the principle of the single-channel feedforward ANC system and its causality constraint are explained. Then, the principles of the multichannel ANC system and the proposed ANC system with the optimal reference microphone selector based on the TDOA are described in Section 3. Experimental results are given in Section 4 and a conclusion is given in Section 5.