Noise pollution becomes a pressing problem due to the development of industrial applications [1], [2]. Reducing noise continues to be a challenge to maintaining and increasing the quality of life. Feedforward active noise control (ANC) systems are based on adaptive system identification, thus, are able to control both broadband and narrowband noises. Therefore, ANC systems are widely used in many practical applications, such as heating, ventilation, and airconditioning systems [3], [4]; engine exhaust systems [5], [6]; and ANC headphones [7], [8]. However, when the acoustic/electric delays in the ANC systems exceed the acoustic delay of the primary path, the causality constraint will be violated [9]. The performance of the feedforward ANC system dramatically degrades as the degree of noncausality increases. Thus, the positions of the noise source and the reference microphone are critical for feedforward ANC system's performance.
In some ANC applications, the noise source position is known in advance, for example, electronic mufflers. Therefore, the reference microphone can be placed at the proper upstream position to make the ANC filter casual. However, in many other applications, the noise source is unknown or moving, such as the ANC system for infant incubators [10]. The ANC system may work with a degraded performance or is unable to cancel the primary noise, as shown in Section Ⅳ. Therefore, there is an increased demand for ANC systems to estimate the noise source location or direction, then one can select the reference signal to cancel unwanted noise from unknown noise source or moving noise source environment, for example, a noisy street.
Microphone array is widely used in speech signal processing for speaker direction detection [11][15]. However, the noise sound signal, especially broadband noise, is highly uncorrelated which is different from speech signal. Therefore, the conventional localization methods designed for speech signal are difficult to utilize in noise signal situations.
In this paper, we propose to integrate a microphone array technique with the feedforward ANC system. The microphone array is used to estimate the noise source location or direction by using generalized crosscorrelation (GCC) and steering response power (SRP) methods [16], [17]. The ANC system selects the microphone close to the noise source as the reference microphone, using the filteredX least mean square (FXLMS) algorithm to reduce the unwanted noise level.
The paper is organized as follows, Section Ⅱ presents the causality problem of the feedforward ANC system and analyzes the system performance. Section Ⅲ proposes the microphone array integrated ANC system and noise source localization algorithm. Section Ⅳ shows the simulation and experiment results, and Section Ⅴ concludes the paper.
Ⅱ. PROBLEM STATEMENTIn the feedforward ANC system configuration illustrated in Fig. 1, the primary noise is sensed by a reference microphone. The antinoise, which is the output of the adaptive filter, is played by the secondary loudspeaker and it passes through the acoustic path, then reaches the error sensor. The acoustic delay AD_{1} from the reference microphone to the error sensor is proportional to the distance from the reference sensor to the error sensor. AD_{2} represents another delay between the secondary loudspeaker and the error sensor. Since the adaptive filter necessarily has a causal response, we must ensure that the acoustic delay between the reference and the error microphones is greater than the electric delay ED, plus the acoustic delay from the secondary loudspeaker [9]. That is:
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Fig. 1 The block diagram of a single channel feedforward ANC system. 
Fig. 1 shows the block diagram of a single channel feedforward ANC system. The primary path
$ \begin{align} E(z) &=X(z)z^{\Delta p}X(z)W(z)z^{\Delta s} \nonumber\\ &=X(z)z^{\Delta s}(z^{\tau}W(z)) \end{align} $  (1) 
and when
$ \begin{align*} E(z) &=X(z)z^{\Delta p}X(z)W(z)z^{\Delta s} \nonumber\\ &=X(z)z^{\Delta s}(1W(z)z^{\tau}). \end{align*} $ 
In this case, adaptive filter
The primary broadband noise can be modeled as an autoregressive (AR) model [18], [19]
$ \begin{align} x(n)=\sum\limits_{i=1}^L a_i x(ni)+n(n)\end{align} $  (2) 
where
We assume that
$ \begin{align} d(n)&=x(n)=\sum\limits_{i=1}^L a_i x(ni)+n(n)\nonumber\\ &=\sum\limits_{k=0}^\infty w(k)n(nk)\end{align} $  (3) 
with
$ \begin{align} y(n)=\sum\limits_{k=0}^\infty \tilde{w}_n (k)n(nk\tau)\end{align} $  (4) 
where
$ \begin{align} E[e^2 (n)]&=\Bigg[\Bigg(\sum\limits_{k=0}^\infty w(k)n(nk)\nonumber\\ &\qquad\sum\limits_{k=0}^\infty \tilde{w}_n (k)n(nk\tau))\Bigg)^2 \Bigg] \nonumber\\ &=\sigma^2 \sum\limits_{k=0}^{\tau1}w^2 (k).\end{align} $  (5) 
Therefore, the MSE is related with
There are many factors related to causality, and the most critical one is to select the reference sensor that is close to the noise source.
Ⅲ. MICROPHONE ARRAY INTEGRATED ANC SYSTEMIn this section, we use an infant incubator ANC application as an example. We combine the microphone array technique with a feedforward ANC system. For an ANC application with unknown noise source/sources, The microphone array is used to estimate the noise sources' direction or location, then the proper reference sensor is selected and the ANC algorithm is conducted.
The ANC system contains
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Fig. 2 Integrated ANC system (m_{1} m_{4} are the sensors in the microphone array). 
The primary noise is sensed by a reference microphone (m_{2}) close to the noise source [1, 2]. The adaptive filters use the sensed reference signal
The noise source direction or position can be estimated by processing the signals received by the microphone array, as shown in Fig. 3.
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Fig. 3 Microphone array with 4 sensors. 
Assume that
The time difference of arrival (TDOA) method is widely used in acoustic event localization. The TDOA estimation problem is to measure the time difference between the signals received at different microphones [11], [12].
Consider an unknown noise source
$ \begin{align}T_i=\frac{1}{v_s }\sqrt{(xx_i )^2+(yy_i )^2+(zz_i )^2 }\end{align} $  (6) 
where
Then, the TDOA between m_{i} and m_{1} can be expressed as
$ \begin{align}\tau_{i1}= &T_iT_1\nonumber\\ =&\frac{1}{v_s } \Bigg(\sqrt{(xx_i )^2+(yy_i )^2+(zz_i )^2 }\nonumber\\ &\sqrt{ x^2+y^2+z^2 }\Bigg), \quad i=2, 3, 4.\end{align} $  (7) 
Equation set (7) contains three hyperboloid equations with three unknowns
1) Generalized CrossCorrelation: The generalized crosscorrelation (GCC) algorithm is one of the most popular methods for TDOA estimation [17], which is defined as the expectation of two observed signals
$ \begin{align}r_{m_i m_j}^{\rm GCC} (k)&=F^{(1)} [\Psi_{m_i m_j } (f)]\nonumber\\ &=\int_{\infty}^\infty\Psi_{m_i m_j} (f) e^{j2\pi fk} df\nonumber\\ &=\int_{\infty}^\infty v(f)\Phi_{m_i m_j} (f) e^{j2\pi fk} df\end{align} $  (8) 
where
$ \begin{align} \Phi_{m_i m_j} (f)=E[M_i (f) M_j^* (f)]. \end{align} $  (9) 
The maximum possible delay will be given where
$ \begin{align} {\hat{\tau}}_ij={\rm arg} \mathop {\rm max}\limits_k r_{m_i m_j}^{\rm GCC} (k) \end{align} $  (10) 
where
The frequencydomain weighting function
$ \begin{align} v(f)=\frac{1}{\left\Phi_{m_i m_j } (f) \right}. \end{align} $  (11) 
The amplitude has been normalized since it is not related with TDOA, the phase information which is used for calculating TDOA is left. Thus the GCC can be calculated efficiently.
2) Steered Response Power: In our system, since the noise signal is highly uncorrelated, the accuracy of TDOA we obtained from GCC is low. Therefore, the estimation accuracy of the GCC phase transform (PHAT) algorithm is not acceptable, as shown in Section Ⅳ. Therefore, in this subsection, we use the SRP [13], [14] algorithm to improve the estimation accuracy.
The signal picked up by the ith microphone is denoted as
$ \begin{align}P_n ({\pmb x} )=\int_{nT}^{(n+1)T}\left\sum\limits_{i=1}^M \omega_i m_i (t\tau({\pmb x}, i) )\right^2 dt\end{align} $  (12) 
where
SRP can be calculated by summing the generalized crosscorrelations of all possible microphone pairs of the microphone array [13]. Based on Parseval's theorem, the total energy contained in a waveform
$ \begin{align}P_n ({\pmb x} )= &\sum\limits_{k=1}^M \sum\limits_{l=1}^M\int_{\infty}^\infty W_k (\omega) W_l^* (\omega) M_k (\omega)M_l^* (\omega)\nonumber\\ &\times e^{j\omega(\tau({\pmb x}, l)\tau({\pmb x}, k)) } d\omega\end{align} $  (13) 
where
The maximum of
$ \begin{equation*} {\hat{\pmb x}}={{\rm arg} \mathop{\rm max}\limits_{\pmb x}} P_n ({\pmb x}) \end{equation*} $ 
$ \begin{align}P'_n ({\pmb x} )= &\sum\limits_{k=1}^M \sum\limits_{l=k+1}^M\int_{\infty}^\infty W_k (\omega) W_l^* (\omega) M_k (\omega)M_l^* (\omega)\nonumber\\ &\times e^{j\omega(\tau({\pmb x}, l)\tau({\pmb x}, k) )} d\omega.\end{align} $  (14) 
The TDOA information is conveyed in the phase instead of the amplitude of the crossspectrum [11]. Performing phase transform (PHAT), frequencydependent weights choose inverse of the magnitude of the crossspectrum as
$ \begin{align}\psi_{kl} (\omega)=W_k (\omega) W_l^* (\omega) =\frac{1}{M_k (\omega) M_l^* (\omega) } \end{align} $  (15) 
and
Searching in a restricted 3D spatial area for maximum
The basic idea of the SRC algorithm is, given an initial rectangular search volume containing the desired number of global optima and gradually, in an iterative process, decrease the search volume until a sufficiently small subvolume is reached in which the optimal
Define
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Fig. 4 3D SRC search region example. 
The SRC search algorithm can be implemented by following steps:
1) For the initial iteration
2) Calculate
3) Sort
4) Contract the search region to a smaller volume with boundary
5) If
6) Else, calculate the mean value
7) Continue searching for other
8)
3) Reference Microphone Selection and ANC Algorithm: In this paper, we simply choose the microphone close to the noise source as the reference microphone expressed as
$ \begin{align*} {{\pmb r}}=\arg \mathop{\min }\limits_{\left\ {Sm_i } \right\} {{\pmb r}}_i.\end{align*} $ 
Then, the FXLMS algorithm can be utilized to reduce the noise level, the secondary sources are driven by the adaptive filters output signals,
$ \begin{align} y_k (n)={{\pmb r}}_i^T (n){{\pmb A}}_{k, i} (n) \end{align} $  (16) 
where
The error signal vector measured by the error microphones is
$ \begin{align} {{\pmb e}}(n) &={{\pmb d}}(n)+{{\pmb y}}'(n) \nonumber\\ &={{\pmb d}}(n)+{{\pmb S}}(n)\ast \left[{{{\pmb r}}^T(n){{\pmb A}}(n)} \right] \end{align} $  (17) 
where
$ \begin{equation} {{\pmb A}}(n+1)={{\pmb A}}(n)\mu {{\pmb r}}'(n){{\pmb e}}(n) \end{equation} $  (18) 
where
$ \begin{align} {{\pmb r}}'(n)&=\left[{{\pmb S}}(n)\ast {{{\pmb r}}^T(n)} \right]^T \nonumber\\ & =\left[\begin{bmatrix} {\hat {s}_{11} (n)} & {\hat {s}_{12} (n)} & \cdots & {\hat {s}_{1K} (n)} \\ {\hat {s}_{21} (n)} & {\hat {s}_{22} (n)} & \cdots & {\hat {s}_{2K} (n)} \\ \vdots & \vdots & \ddots & \vdots \\ {\hat {s}_{M1} (n)} & {\hat {s}_{M2} (n)} & \cdots & {\hat {s}_{MK} (n)} \\ \end{bmatrix}\ast \begin{bmatrix} {\rm {\bf 0}} \\ \vdots \\ {{\pmb r}}(n) \\ \vdots \\ {\rm {\bf 0}} \\ \end{bmatrix}^T \right]^T \end{align} $  (19) 
and
In this paper, an ANC application for an infant incubator is used as an example of the proposed integrated system. In this system, the microphone array consists of four omnidirectional microphones and is placed at the four corners outside of incubator, as shown in Fig. 5. Recorded neonatal intensive care unit (NICU) noise is used as the noise source is played by a loudspeaker. The TASCAM HSP82 multitrack recorder is used to record the 4channel noise signals from the 4 microphones, sampling frequency is 48 kH, which is down sampled to 6.4 kHz.
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Fig. 5 The experimental set up of noise source direction detection. 
The position of microphone m_{2} is assigned as the origin of the coordinate system, and the microphone array locates at [(0.85, 0, 0); (0, 0, 0); (0, 0.55, 0); (0.85, 0.55, 0)]. In every quadrant, we randomly change noise source location 25 times and record 4channel synchronous signals. These recorded signals are processed using GCCPHAT and SRPPHAT algorithms.
Fig. 6 shows 2D searching result for maximum
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Fig. 6 Searching result (2D) for maximum. 
In each quadrant, the estimated position for unknown noise sources are plotted in 2D plane using different color marks as shown in Fig. 7. We find that 16 points are misestimated. For example, some green points fall in quadrant Ⅳ and some estimated locations of the noise sources are inside the range of the microphone array.
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Fig. 7 Estimation of 100 noise source positions by using GCCPHAT method. 
The detailed localization estimation results of the GCCPHAT algorithm are tabulated in Table Ⅰ. In the computer simulation, 29 of 100 recordings have no real solutions which are indicated as N/A in the table, and 55 out of 71 estimated noise source points are in the right quadrant as highlighted in shaded cells of Table Ⅰ. The correct rate of noise source localization using GCC algorithm is 55% and it is not acceptable.
For the SRP algorithm, the estimated results of the same total 100 positions are shown in the 2D plane of the microphone array in Fig. 8. It is well noticed that the quantity of the wrong estimation for unknown noise sources is reduced. For example, only 5 points fall in other quadrants.
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Fig. 8 Estimation of 100 noise source positions by using SRPPHAT method. 
The performance of the SRP algorithm is summarized in Table Ⅱ. There are 10 estimated locations inside the microphones array area, so these results are invalid and indicated as N/A. There are 5 estimated noise source locations in the wrong quadrant, thus the correct rate of noise source localization using SRP algorithm is 85%.
Based on the results obtained from SRP algorithm, we selected the microphone close to the noise source to act as reference microphone. The 1X2X2 feedforward ANC system with two error sensors and two secondary loudspeakers is used. We use the recorded NICU noise as the primary noise.
Table Ⅲ presents the experimental results of the microphonearrayintegrated ANC system's performance when the reference microphone is chosen properly and improperly. When the wrong reference microphone is chosen, the causality of the ANC system is invalid and the performance is degraded. When the ANC system is causal, the performance is improved by around 5 dB.
We proposed to develop the microphone array integrated ANC system. The performance of a feedforward ANC system is analyzed when the causality condition is violated. A microphone array with 4 microphones is used to pick up the noise signal simultaneously; the GCCT algorithm and SRP algorithm are used to estimate the noise source location and direction for selecting the proper reference sensor. The simulation and experiment results show that the proposed technique can locate the noise sources with high accuracy. The SRC search algorithm is utilized to reduce the computational complexity of the SPR algorithm. The FXLMS algorithm was conducted using the properly selected reference microphone. Our future work includes: multiple noise source detection and reference microphone signals processing for feed forward ANC systems, and conduct a case study for the moving noise source problem with real NICU.
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