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American Institute of Aeronautics and Astronautics
A Background Noise Reduction Technique using Adaptive
Noise Cancellation for Microphone Arrays
Taylor B. Spalt
1
, Christopher R. Fuller
2
Vibration and Acoustics Laboratories, Virginia Tech, Blacksburg, Virginia 24061
Thomas F. Brooks
3
, William M. Humphreys, Jr.
4
NASA Langley Research Center, Hampton, Virginia 23681
Background noise in wind tunnel environments poses a challenge to acoustic measurements due to
possible low or negative Signal to Noise Ratios (SNRs) present in the testing environment. This paper
overviews the application of time domain Adaptive Noise Cancellation (ANC) to microphone array signals
with an intended application of background noise reduction in wind tunnels. An experiment was conducted to
simulate background noise from a wind tunnel circuit measured by an out-of-flow microphone array in the
tunnel test section. A reference microphone was used to acquire a background noise signal which interfered
with the desired primary noise source signal at the array. The technique’s efficacy was investigated using
frequency spectra from the array microphones, array beamforming of the point source region, and
subsequent deconvolution using the Deconvolution Approach for the Mapping of Acoustic Sources (DAMAS)
algorithm. Comparisons were made with the conventional techniques for improving SNR of spectral and
Cross-Spectral Matrix subtraction. The method was seen to recover the primary signal level in SNRs as low
as -29 dB and outperform the conventional methods. A second processing approach using the center array
microphone as the noise reference was investigated for more general applicability of the ANC technique. It
outperformed the conventional methods at the -29 dB SNR but yielded less accurate results when coherence
over the array dropped. This approach could possibly improve conventional testing methodology but must be
investigated further under more realistic testing conditions.
Nomenclature
c
n
= Finite Impulse Response filter coefficients at step n
= steering vector for array to focus location
e
m
= component of for microphone m
f = frequency
∆f = frequency bandwidth resolution of spectra
G
mm’
= cross-spectrum between p
m
and p
m’
= matrix (CSM) of cross-spectral elements G
mm’
K = counting number of CSM averages
m = microphone identity number in array
m’ = same as m, but independently varied
M = total number of array microphones
n
0
= background noise present in primary ANC input
n
1
= background noise present in reference ANC input
N = total number of FIR filter weights
p
m
= pressure time records from microphone m
P
m
= Fourier Transform of p
m
r
c
= distance r
m
for m being the center array microphone
r
m
= coordinate distance to m
s = signal from primary sound source
____________________________
1
Student, AIAA Student Member
2
NIA Samuel P. Langley Professor, AIAA Associate Fellow
3
Senior Research Scientist, AIAA Fellow
4
Senior Research Scientist, AIAA Senior Member
2
American Institute of Aeronautics and Astronautics
= output power response of the array at focus location
T = data block length
T = complex transpose (superscript)
w
s
= data window weighting constant
x
n
= reference input at step n
y
n
= FIR filter output at step n
z
n
= ANC output at step n
= coherence
ε
n
= ANC error at step n
μ = LMS algorithm step size
τ = time delay
τ
m
= propagation time from grid point to microphone m
I. Introduction
ORMALLY designed wind tunnels are not optimal for acoustics testing because they are designed with only
aerodynamic considerations in mind. The acoustic measurements of components placed for testing in the
tunnels are often masked by background noise generated by the wind tunnel flow drive or the flow itself, resulting in
low or negative SNRs. This background noise limits the accurate measurement, identification, and quantification of
noise sources under study. Thus, reduction of background noise to improve the SNR in testing environments is of
interest.
In wind tunnels, techniques have been investigated that remove noise contamination from source noise
measurements [1]. One technique used the assumption that if the background noise at two different transducers was
uncorrelated yet statistically equal, the frequency spectrum due to only the model source could be recovered from
the difference between the two time-series. Improvements were made on the technique over the next two decades [2-
5]. In 1989, a technique for capturing model noise from turbulent boundary layer wall-pressure fluctuations was
investigated [6]. The authors postulated that acoustic disturbances propagated down the wind tunnel acting as a
waveguide. Turbulent pressure fluctuations due to local velocity disturbances were found to be uncorrelated to the
acoustic disturbances at any streamwise location. Two microphones at the same streamwise location yet separated
spanwise were used. One signal was delayed by a time constant τ then subtracted from the other signal to form a
new time-series. The true spectrum due to the model source was obtained from this time-series at frequencies 1/τ
and higher harmonics. It was concluded that some of the model source signal was cancelled along with the
contaminating noise if the microphone spacing was insufficient. This approach was extended beyond the
aforementioned frequency-domain studies to time-domain noise cancellation in 1996 [7]. The authors used an
optimizing Finite Impulse Response (FIR) filter to estimate the correlated noise between a primary and reference
signal then subtracted it from the reference signal. The turbulent pressure components in each signal were taken as
uncorrelated as long as the transducers were separated by a sufficient distance [6]. Therefore, the correlated parts
belonged to the common noise between the signals. This was then subtracted from the reference signal leaving just
the source noise time-series with magnitude and phase intact. At low frequencies part of the source signal was
cancelled along with the background noise if insufficient transducer spacing was used. It was shown that this
undesired source signal cancellation [7] was an order of magnitude smaller than that removed using the
aforementioned methods [1-6].
Early efforts in the study of time-domain Adaptive Noise Cancellation (ANC) were made in the 1960s [8, 9]
and the technique was formalized in 1975 [10]. The method used a minimum of two channels: a reference channel
intended to receive only undesired background noise and a primary channel containing the signal plus background
noise. The reference time-series is fed into a filter which is adapted to produce a best estimate of the noise present in
the primary time-series and then subtracted from the primary signal leaving a “cleaned” result. Since its publication
the technique has been widely employed primarily for applications of noise reduction for improved speech
recognition. Note that Adaptive Noise Cancellation is an electronic, in-wire signal cancellation technique, as
opposed to Active Noise Cancellation which involves actual pressure fluctuation cancellation.
An early, simplified experiment employing ANC reported at least 20 dB noise cancellation with minimum
distortion [11]. Background noise in a fighter jet cockpit presented an important application of the technique that led
to the identification of the major challenges for successful implementation. A reference microphone attached to the
outside of the helmet was used to capture the ambient noise present in order to cancel it from the pilot’s microphone.
An ideal simulation [12] of the cockpit environment reported an 11 dB SNR improvement. An important
consideration discussed was acquisition of the desired signal by the reference channel, which would result in
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American Institute of Aeronautics and Astronautics
cancellation of the desired signal at the output. This was circumvented by adapting the filter used for cancellation
only during periods of background noise. A more realistic evaluation [13] of the cockpit environment was performed
by simulating a diffuse background noise field and it was concluded that good cancellation was not possible at
frequencies above 2 kHz. The study identified coherence between the reference and primary channels as the most
important factor in successful cancellation. Increasing the distance between the transducers was cited as the cause
for low coherence above 2 kHz. This was an effect of a diffuse sound field [14].
Experimental implementation of ANC appears to have conflicting requirements: good coherence is necessary
for noise cancellation, necessitating the reference transducer be located either close to the noise source(s) (if
localized) or close to the primary transducer(s) (if a diffuse noise field present). And if the noise source is not
localizable, locating the reference transducer close to the primary may result in cancellation of the desired signal.
In microphone array applications, background noise has been removed using a spectral subtraction technique
since 1974 [15]. The method relies on a separate acquisition of the background noise in the testing environment
from that when the noise source under study is present. Upon converting signals to the frequency domain, this
“background only” acquisition is subtracted (on a pressure-squared basis) from that of the primary acquisition
(signal plus noise). With the introduction of beamforming using microphone arrays, this same principle has been
applied to Cross-Spectral Matrices (CSMs) since the late 1990s [16-20]. Both techniques rely on the cancellation of
the noise in its statistical sense, since the background noise present will not be identical during two acquisitions
separated in time. The CSM subtraction technique allows further noise reduction beyond what spectral subtraction
can achieve on a per channel basis. This is because uncorrelated noise at distinct array microphones is already
reduced by the cross-correlation performed when forming the CSM [21]. These techniques are compared herein to
ANC in an experiment intended to provide simulated wind tunnel background noise being measured by an out-of-
flow array in a wind tunnel test section.
II. Theory
Adaptive Noise Cancellation. Noise cancellation in the time domain utilizes a reference input, ideally
containing just noise, which is passed through an adaptive filter and later subtracted from a primary input containing
both the desired signal and correlated
components of the noise present in the
reference input. The minimized output
becomes the primary signal with the noise
attenuated or cancelled altogether. The
correlation between the noise present in the
reference channel and the primary input is
important: the higher it is, the better the
cancellation [13]. A diagram of the concept is
pictured in Fig. 1.
In Fig. 1, a primary sound source (s) that
contains uncorrelated noise (n
0
) is transmitted
to the upper left channel. The bottom left
channel receives noise (n
1
) correlated with n
0
in some unknown manner. It is fed into the
adaptive filter with the goal of replicating n
0
.
The output of the adaptive filter is subtracted
from the primary input (s + n
0
) to produce z,
which also serves as the error signal to the
filter.
The interior of the dashed box of Fig. 1 is
given in Fig. 2. Success of the adaptation is
dependent on the causality of the system, i.e.
the noise reference must be present in the
system before the input. From Fig. 2, the
reference signal (x
n
) is fed to the FIR filter at
the start of the processing. The initial filter
coefficients (c
n
) and number of weights are
provided by the user. The output of the filter
Figure 1. Adaptive noise canceller concept [10].
Figure 2. Adaptive noise canceller concept with LMS
algorithm and FIR filter block diagrams included.
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American Institute of Aeronautics and Astronautics
(y
n
) is subtracted from the primary input signal (s + n
0
, an array microphone) which contains a correlated version of
the noise present in the reference signal from an earlier time. The error (ε
n
) is then fed into the Least Mean Squares
(LMS) algorithm [10] and multiplied with the reference input (x
n
) and the step size (µ) to produce the next set of
filter coefficients (c
n+1
). The order of the FIR filter is the number of weights or “taps” used. FIR filters are always
stable and have linear phase response given that the coefficients are symmetrical.
The difference equation defining the output of the filter is
(1)
where N is the number of filter weights specified. As the noise to be cancelled is present in the reference signal
before it is in the primary signal, the system is causal and successful adaptation will be achieved. This is seen in Eq.
(1). As long as the number of filter weights is sufficient to encompass the time delay between the reference and
primary signal (in number of samples), the noise present in the primary signal will be related to that seen in an
earlier sample still present in y
n
. For proof of the concept see [10].
ANC will be implemented by removing the noise from each microphone array channel in the time domain.
These “cleaned” signals will then be used in frequency domain processing to assess the effectiveness of the noise
removal.
Beamforming. Beamforming in the frequency domain utilizes phase shifts between the microphone array
signals to “steer” the focus of the array and thus obtain more detailed sound pressure magnitude information at
defined points in space.
The first step in beamforming is to compute the Cross Spectral Matrix (CSM) for the data set to be analyzed
[22]. The CSM is formed from the Fast Fourier Transforms (FFTs) of the data set. The FFTs of two microphones, m
and m’, are denoted
and
and are formed from the microphones’ time records
and
.
The frequencies, f, at which the transforms are defined are determined by the bandwidth, ∆f = 1/T (Hz), where T is
the data block length. A CSM element, as a function of frequency, is defined
(2)
The total record length is T
tot
= TK. The summation is multiplied by two because it is a one-sided cross-spectrum. It
is then divided by the data block length T to normalize the FFT output and the number of block averages K to get a
mean value across the data blocks. The term w
s
is a weighting constant used when a weighted window is
implemented. The star on the first transform denotes the complex conjugate. The CSM element is a complex
spectrum. The full CSM for M array microphones is a Hermitian matrix and is given as
(3)
The beamforming uses the CSM to electronically “steer” to positions in space defined by the user. For the work
done here, the array was one dimensional and the grid points were located along a line that bisected the sound
source. In order to steer to grid points on the line, vectors must be calculated between each array microphone and the
grid point being steered to. The steering vector for microphone m is
(4)
where r
m
is the straight line distance from microphone m to the grid point, r
c
denotes the straight line distance from
the center microphone to the grid point, and τ
m
is the propagation time for sound to travel between microphone m
and the grid point. The term
is included to normalize the distance dependent amplitude of the steering vector to
that of the center array microphone. The steering vector matrix, size Mx1, is
(5)
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American Institute of Aeronautics and Astronautics
The steering vectors, being complex, will phase shift the contributions from each microphone in the array to allow
for constructive summing at the chosen grid point.
Finally, the array’s response is given as an output power spectrum
(6)
The response has units of mean-pressure-squared vs. frequency bandwidth. Dividing by the total number of
microphones squared normalizes the response to that of a single microphone level. The superscript T is taking the
complex transpose of the steering vector matrix.
DAMAS. The Deconvolution for the Mapping of Acoustic Sources [22] will be used to provide further detail of
the sound source under study in the presence of noise. This technique uses the beamform response as a precursor
and removes microphone array characteristics (point spread function) to provide an estimation of only the sound
source strength that exists in the scanning region. The technique uses an iterative relaxation-type solver to provide
non-ambiguous, enhanced resolution presentations of sound sources and is discussed in more detail in [22].
III. Experimental Setup
A small anechoic chamber housed at NASA Langley Research Center (LaRC) was used for the test area.
Approximate dimensions of the room are 97x77x81 inches (length/width/height), wedge tip-to-tip.
Nine B&K quarter-inch
free-field microphones were
used to construct a linear
array using metal support
rods with base stands, as
shown in Fig. 3a. The
desired microphone spacing
was 1” between diaphragm
centers; actual spacing
differed slightly due to equipment
limitations (see Fig. 3b for exact
dimensions).
Since the microphone array is
linear and configured broadside
towards the primary source, its
sensing ability lies only along a line
parallel with the array at the same
vertical height. Thus, the array,
source speaker, and background
speaker were all placed in the same
plane parallel to the floor, at a
distance of 46.5” above the floor to
ensure that the speaker was high
enough above the wedges to avoid
low frequency near-field reflections.
Refer to Fig. 4 for a diagram of the
setup. The source speaker was
perpendicular to the array at a
distance of 67”. The background
speaker was at an angle of 59 (top
view) to the array and a distance of
43” from microphone 1. A reference
microphone, labeled 10, was situated
a distance of 5” away from the diaphragm center of the background speaker with its rear facing the source speaker to
limit the source speaker’s influence on the microphone diaphragm.
Figure 3. (a) Linear microphone array, and (b) Microphone spacing.
b
a
b
Figure 4. ANC test setup.