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Texas Instruments An Adaptive Noise Cancelling System to Enhance Sonar Receiver Performance -C31 Application notes
Disclaimer: This document was part of the First
European DSP Education and Research Conference.
It may have been written by someone whose native
language is not English. TI assumes no liability for the
quality of writing and/or the accuracy of the
information contained herein.
Implementing an Adaptive Noise
Cancelling System to Enhance Sonar
Receiver Performance Using the
TMS320C31 DSP
Authors: E. Verriest, Isen
ESIEE, Paris
September 1996
SPRA337
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Contents
Abstract ........................................................................................................................... 7
Product Support on the World Wide Web .................................................................... 8
Introduction..................................................................................................................... 9
Adaptive Noise Cancelling.......................................................................................... 9
Algorithm Selection................................................................................................... 12
The LMS Algorithm........................................................................................... 12
The "Spectrofiltre" Algorithm. ........................................................................... 13
DSP Implementation................................................................................................. 14
Real Time Validation................................................................................................. 14
Conclusion .................................................................................................................... 21
References .................................................................................................................... 22
Figures
Figure 1. The Adaptive Noise Cancelling Concept............................................................... 9
Figure 2. Program Execution Flow Diagram ...................................................................... 15
Figure 3. Power Spectrum of Hydrophone Output ............................................................. 16
Figure 4. Coherence Between Primary/Reference Input.................................................... 17
Figure 5. Results of ANC on the Primary Input Power Spectrum (Method of
Spectrofiltre)........................................................................................................ 18
Figure 6. Coherence Between Primary Input and Reference Input After/Before Noise
Cancellation ........................................................................................................ 19
Figure 7. Cancellation of Frequency Components of the Input Signal ............................... 20
Implementing an Adaptive Noise
Cancelling System to Enhance Sonar
Receiver Performance Using the
TMS320C31 DSP
Abstract
The performance of sonar receivers on board a ship are degraded
by mechanical noise. In order to improve the detection
performance of the acoustic sensors (hydrophones), we have
designed a local mechanical noise cancelling system using the
Adaptive Noise Cancelling (ANC) approach with a single noise
reference [1]. The implementation was realized and validated on
underwater acoustic signals with a PC-based Texas Instruments
(TI™) TMS320C31 floating-point digital signal processor (DSP)
system.
This document was part of the first European DSP Education and
Research Conference that took place September 26 and 27, 1996
in Paris. For information on how TI encourages students from
around the world to find innovative ways to use DSPs, see TI’s
World Wide Web site at www.ti.com.
Implementing an Adaptive Noise Cancelling System to Enhance Sonar Receiver
Performance Using the TMS320C31 DSP
7
SPRA337
Product Support on the World Wide Web
Our World Wide Web site at www.ti.com contains the most up to
date product information, revisions, and additions. Users
registering with TI&ME can build custom information pages and
receive new product updates automatically via email.
8
Implementing an Adaptive Noise Cancelling System to Enhance Sonar Receiver
Performance Using the TMS320C31 DSP
SPRA337
Introduction
In our work, we consider different adaptive methods of filter
identification [2] in order to estimate the signal from a noisy
hydrophone output. In a first approach, we have carried out
simulations to calculate the performance of each ANC method and
have demonstrated the advantage of frequential methods for
mechanical noise cancellation. Taking the numerical stability, rate
of convergence and simplicity as selection criteria, we have
selected the LMS (Least Mean Square, time method) and the
"Spectrofiltre" (frequential method) for our application.
Adaptive Noise Cancelling
We assume in this paper that we are processing real, discretetime, statistically stationary signals with zero mean. Noise
cancellation can be viewed as a problem of adaptive filter
identification
Figure 1. The Adaptive Noise Cancelling Concept
Implementing Adaptive Noise Cancelling to Enhance Sonar Receiver Performance
9
SPRA337
A signal s is transmitted over a channel to a sensor that also
receives a noise b uncorrelated with the signal. The combined
signal and noise s+b form the primary input y to the canceller. A
second sensor receives a noise r uncorrelated with the signal but
correlated in some unknown way with the noise b. We can also
find a filter W generating b from r. The classical ANC methods
estimate this filter in the class of linear filters. Two approaches are
possible: a time and a frequential approach. In order to estimate
the filter W, a FIR transversal filter structure is chosen because it
leads to a real-time adaptive implementation of the signals [3]. In
the time domain, the adaptive filter is defined by its N tap weights.
In the frequency domain, it is defined by the N weights of its
complex gain. The estimation criterion is the minimization of the
system output power E[Ie(k)I2] (in an ANC system, the system
output serves as the error signal for the adaptive process [1].
Besides, this criterion leads to simple calculations [2] and
minimizing the system output power minimizes the Mean-Squared
Error (MSE) E[Ie(k)-s(k)l2] and maximizes the output signal-tonoise ratio under the fundamental assumption that the reference
input is not correlated with the signal.
4
The optimal solution in the time domain for a N tap weights
transversal filter is given by the discrete Wiener-Hopf equation [5]:
−1
Fopt [ N ] = [Γr ] • p yr
(1)
where Γr is the (N,N) correlation matrix of the reference input, and
p yr is the (N, 1) cross-correlation vector between the tapreference input and the primary input. In the frequency domain,
the optimal solution is given by:
Fopt ( v ) = (γ yr ( v )) /(γ rr (v ))
(2)
where γyr (V) is the Fourier transform of the intercorrelation function
between the primary input and the reference input, and γrr ( ) is
the Fourier transform of the reference input autocorrelation
function. These solutions require a priori knowledge about the
second order input signal statistics. Since we do not have this
information, we use deterministic estimation criteria instead of
statistic ones.
In the time domain, we use the following estimation criterion
k
k− j
C(k ) = ∑ λ
• e( j )
2
j =0
10
Implementing an Adaptive Noise Cancelling System to Enhance Sonar Receiver
Performance Using the TMS320C31 DSP
(3)
SPRA337
where λ is an exponential weighting factor. We have chosen an
exponential window because the signals we have to process are
quasi stationary. Besides, this leads to reductions in the
computation of the noise-cancelling algorithms [6]. We obtain the
corresponding deterministic solution by differentiating C(k) with
respect to the N-tap weights transversal filter [2]:
−1
k
Fˆopt [ N ] = [ Γˆ r (k )] • pˆ yr (k )
(4)
where:
k− j
k
Γˆ r (k ) = ∑ λ
• r j[ N ] • r
T
j[ N ]
(5)
• y ( j ) • r j[ N ]
(6)
j =0
k− j
k
pˆ yr (k ) = ∑ λ
In the frequency domain, (2) requires the estimation of the power
spectra of the observed signals. We use the averaged
periodogram method to estimate the power spectra with an
exponential weighting factor in order to take into account possible
slow variations of the input signals statistics
L− j
L
γˆ yr ( v ) = ∑ λ
L
• y j ( v ) • rj ( v )
(7)
• rj ( v ) • rj ( v )
(8)
j =1
L
L− j
γˆrr ( v ) = ∑ λ
L
j =1
where rj(v) is the conjugate of the N-sample j-th section DFT of
the signal r(k) and L is the number of input sections.
To conclude, the optimal Wiener filter is the solution of the
minimization of a statistic quadratic criterion. The deterministic
approach is necessary because we have no a priori information
about the second order statistics of the input signals. However,
both approaches are equivalent for ergodic signals [2] The time
and the frequency approach lead to equivalent solutions for an
infinite order of the transversal filter [2].
Implementing Adaptive Noise Cancelling to Enhance Sonar Receiver Performance
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Algorithm Selection
In a first approach, we have carried out simulations on several
wide-band noises and single tones to calculate the performances
of each ANC method and prove the advantage of frequential
methods in the processing of mechanical noise. Taking numerical
stability, convergence rate and simplicity as selection criteria for
the algorithms, we have selected the LMS (Least Mean Square), a
suboptimal time method, and the "Spectrofiltre", an optimal
frequential method.
The LMS Algorithm.
The MSE can be developed to a second-order function of the
estimation filter [5]. Accordingly, we may visualize the dependence
of the MSE on the filter weights as a bowl-shaped surface with a
unique minimum. We refer to this surface as the errorperformance surface of the transversal filter. The requirement is to
design the filter so that it operates at the bottom of this surface. At
this point, the MSE attains its minimum value, and
correspondingly, the adaptive filter attains its optimum value in the
mean-squared sense. The LMS algorithm does not require
measurement of the correlation functions, nor does it require
matrix inversion. It uses the method of steepest descent on the
error-performance surface by approximating the gradient vector in
real time with available data.
Summary of the LMS Algorithm.
Parameters: N = filter order;
µ = step-size parameter.
Definition : rk[N] = [r(k) r(k-1)... r(k-N+1)]T
Initialization : = r0[N]=0 ; F0[N]=0
Computation (k=1,…)
k −1
e(k ) = y (k ) − ([ F [ N ] ] • r k [ N ]
k −1
F [ N ] = F [ N ] + µ • e( k ) • r k [ N ]
k
12
Implementing an Adaptive Noise Cancelling System to Enhance Sonar Receiver
Performance Using the TMS320C31 DSP
(9)
(10)
SPRA337
The "Spectrofiltre" Algorithm.
The power spectra of the observed signals are estimated with the
averaged periodogram method [8]; the "Overlap-Save-Method"
(OSM) is used in order to avoid the effects of circular convolution
[7].
Parameters : N = filter order;
D = overlapping points;
λ = weighting factor.
Initialization : the (N/2+1) complex weights of the adaptive filter
and estimated interspectrum are zero; the (N/2+1) real weights of
the estimated autospectrum are zero.
Input signals are sectioned according to the OSM method ; the
current N-point sections are denoted as yj(k) and rj(k).
Computation (j = 1, …):
yj(k) and rjk) are transformed by FFT ; we obtain N/ 2+1 complex
points yj(v) and rj(v).
e j (v ) = y j (v ) − F
j −1
( v ) rj ( v )
(11)
ej(v) is inverse transformed by IFFT; the first D points are then
discarded (OSM). We estimate the interspectrum between the
primary and reference input:
j −1
j
γˆ yr ( v ) = λ • yˆ yr (v ) + y j (v ) • rj (v )
(12)
We estimate the power spectrum density of the reference input:
j −1
j
γˆrr ( v ) = λ • γˆrr ( v ) + rj (v ) • rj (v )
(13)
Finally, the complex gain of the adaptive filter is calculated:
j
j
j
F (v ) = (γˆ yr (v )) /(γˆrr (v ))
Implementing Adaptive Noise Cancelling to Enhance Sonar Receiver Performance
(14)
13
SPRA337
DSP Implementation
We have implemented the LMS and the Spectrofiltre algorithms
on a Texas Instruments 32 bit floating-point DSP: the
TMS320C31. Excellent real-time results have been attained, well
above the minimum required for a signal band of 1-6 KHz
(underwater acoustic signals). Hand-written assembler code was
necessary in order to optimize the real-time performance of the
algorithms. We shall now give some details about the
implementation of the OSM for the Spectrofiltre algorithm. We
know that the filtering operation, when carried out in the frequency
domain, may produce estimation errors because a multiplication of
DFTs corresponds to the circular convolution of the time
sequences [8]. The OSM is equivalent to implementing a circular
convolution and identifying the part that corresponds to a linear
convolution. For example, if we consider the circular convolution
of the M-point unit-sample response with an N-point section, the
first (M-1) points are incorrect while the remaining points are
identical to those that would be obtained had we implemented a
linear convolution. We also section the input signals y(k), r(k) into
sections of length N so that each section overlaps the preceding
one by D points. Each section is FFT’d and processed, but we
discard the first D points of each output section since this portion
is corrupted by the effects of circular convolution. The (N-D)
remaining points from successive sections are then abutted to
construct the final filtered output. Each succeeding input section
consists of (N-D) new points and D points saved from the previous
section. In our application, unfiltered signals are input to the 16 bit
parallel A/D converter via an Interrupt Service Routine which fills
two circular input buffers with fresh data y(k) and r(k). The ISR
also outputs the estimated signal (Figure 2).
While the main program processes the current section of N
samples (section j), the ISR inputs new data from the section (j+1)
and simultaneously outputs the estimated signal corresponding to
the section (j-1).
Real Time Validation
The real-time validation of the algorithms was subsequently
realized on underwater acoustic signals. The experiment used a
thin steel plate positioned at the air-water interface carrying an
accelerometer on the air side and the hydrophone directly below it
on the water side. The signal to be detected was generated by a
submerged transducer and the noise by a vibration exciter on the
plate. The sensor signals were processed by our PC-based TI
TMS320C31 floating-point DSP system.
14
Implementing an Adaptive Noise Cancelling System to Enhance Sonar Receiver
Performance Using the TMS320C31 DSP
SPRA337
Figure 2. Program Execution Flow Diagram
We have attained excellent real-time results for the subtraction of
noise spectral components and reduction of coherence between
the sensor signals, especially with the Spectrofiltre algorithm. The
parallel operations instructions group makes a high degree of
parallelism possible and allowed a sampling frequency of 32 KHz
for this algorithm. The computational requirements for the
Spectrofiltre with N=1024 are about 115000 machine cycles for
the processing of a 1024 section. We can also use an overlapping
rate of 90% with a sampling frequency of 16KHz.
Assembly language programming for the LMS algorithm has
produced a computational complexity of 3N+100 machine cycles
for the processing of a couple of samples y(k), r(k). This allows us
to use a 360 tap-weight adaptive transversal filter with a sampling
frequency of 16 KHz.
The submerged hydrophone measures an additive noise
corresponding to the plate vibrations ; the power spectrum of the
hydrophone output with and without the noise is shown in Figure
3.
Implementing Adaptive Noise Cancelling to Enhance Sonar Receiver Performance
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SPRA337
Figure 3. Power Spectrum of Hydrophone Output
We observe an excellent correlation between the primary and the
reference input on the noise, but the coherence function is
degraded due to the correlation between the reference input and
the signal to be detected (Figure 4):
16
Implementing an Adaptive Noise Cancelling System to Enhance Sonar Receiver
Performance Using the TMS320C31 DSP
SPRA337
Figure 4. Coherence Between Primary/Reference Input
Implementing Adaptive Noise Cancelling to Enhance Sonar Receiver Performance
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Figure 5. Results of ANC on the Primary Input Power Spectrum (Method of
Spectrofiltre)
The Spectrofiltre achieves excellent cancellation of the noise
spectral components (N=1024, D=512) (see Figure 5).
Further, we have a coherence reduction between the reference
input and the estimated signal, which corresponds to an effective
cancellation of the noise spectral components [2] (see Figure 6).
However, the correlation between the reference input and the
signal to be detected induces some distortion of the signal after
noise cancellation (Figure 7). We have also shown that it is
absolutely necessary for the reference input to be decor-related
with the signal to detect, if we want to obtain good noise
cancelling performance. The LMS algorithm has not reached the
performance of the Spectrofiltre method, which confirms the
advantage of frequential ANC methods over time ANC methods.
18
Implementing an Adaptive Noise Cancelling System to Enhance Sonar Receiver
Performance Using the TMS320C31 DSP
SPRA337
Figure 6. Coherence Between Primary Input and Reference Input After/Before
Noise Cancellation
Implementing Adaptive Noise Cancelling to Enhance Sonar Receiver Performance
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SPRA337
Figure 7. Cancellation of Frequency Components of the Input Signal
20
Implementing an Adaptive Noise Cancelling System to Enhance Sonar Receiver
Performance Using the TMS320C31 DSP
SPRA337
Conclusion
To our knowledge, no real-time validation of frequential ANC
methods has yet been done. The Spectrofiltre method has proved
efficient in floating-point implementation for the reduction of
mechanical noise on a sonar receiver. A real-time implementation
and validation of the fast RLS algorithms is being conducted.
Implementing Adaptive Noise Cancelling to Enhance Sonar Receiver Performance
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References
[1] B. Widrow et al., "Adaptive noise cancelling : principles and
applications”, Proc. Of the IEEE, 1975
[2] C. Servière, "Eléments de comparaison entre différentes méthodes
de Soustraction de Bruit”, Thèse de Doctorat, 1989
[3] F. Michaut, "Méthodes adaptatives pour le signal", 1992
[4] J.F. Guerre-Chaley, "Etude de différentes structures de soustracteurs
de bruit adaptatifs multiréférences", Thèse de Doctorat,
1990
[5] S. Haykin, "Adaptive Filter theory", 1986
[6] J. Cioffi, T. Kailath, “Windowed Fast Transversal Filters Adaptive
Algorithms with Normalization”, IEEE Trans. On ASSP,
1985
[7] C. Servière, “Comparison between two estimation methods of the
complex gain of an optimal Wiener filter”, Traitement du
Signal, 1989
[8] A. V. Oppenheim, R. W. Schafer, “Digital Signal Processing”, 1975
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Implementing an Adaptive Noise Cancelling System to Enhance Sonar Receiver
Performance Using the TMS320C31 DSP
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