Digital Audio Signal Processing Lecture-4: Acoustic Echo Cancellation

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Digital Audio Signal ProcessingLecture-4
Acoustic Echo Cancellation

• Marc Moonen
• Dept. E.E./ESAT-STADIUS, KU Leuven
• marc.moonen_at_esat.kuleuven.be
• homes.esat.kuleuven.be/moonen/

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Outline

• Introduction
• Acoustic echo cancellation (AEC) problem
  applications
• Acoustic channels
• Adaptive filtering algorithms for AEC
• NLMS
• Frequency domain adaptive filters
• Affine projection algorithm (APA)
• Control algorithm
• Post-processing
• Loudspeaker non-linearity
• Stereo AEC

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Introduction

• AEC problem/applications
• Suppress echo
• to guarantee normal conversation conditions
• to prevent the closed-loop system from becoming
  unstable
• Applications
• Teleconferencing
• Hands-free telephony
• Handsets

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Introduction

• AEC standardization
• ITU-T recommendations (G.167) on acoustic echo
  controllers state that
• Input/output delay of the AEC should be smaller
  than 16 ms
• Far-end signal suppression should reach 40..45 dB
  (depending on application), if no near-end signal
  is present
• In presence of near-end signals the suppression
  should be at least 25 dB
• Many other requirements

5
Introduction

• Room Acoustics (I)
• Propagation of sound waves in an acoustic
  environment results in
• signal attenuation
• spectral distortion
• Propagation can be modeled
• quite well as a linear filtering
• operation
• Non-linear distortion mainly stems from the
  loudspeakers. This is often a second order effect
  and mostly not taken into account explicitly

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Introduction
Room Acoustics (II) The linear filter model of
the acoustic path between loudspeaker and
microphone is represented by the acoustic impulse
response

• Observe that
• First there is a dead time
• Then come the direct path impulse
• and some early reflections, which
• depend on the geometry of the room
• Finally there is an exponentially decaying tail
  called reverberation, coming from multiple
  reflections on walls, objects,...
• Reverberation mainly depends on reflectivity
  (rather than geometry) of the room

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Introduction

• Room Acoustics (III)
• To characterize the reflectivity of a recording
  room the reverberation
• time RT60 is defined
• RT60 time which the sound pressure level or
  intensity needs
• to decay to -60dB of its original value
• For a typical office room RT60 is between 100
  and 400 ms, for a church RT60 can be several
  seconds
• Acoustic room impulse responses are highly
  time-varying !!!!

ESAT speech laboratory RT60 ? 120 ms
Begijnhofkerk Leuven RT60 ? 3730 ms
Original speech signal
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Introduction

• Acoustic Impulse Response FIR or IIR ?
• If the acoustic impulse response is modeled as
• an FIR filter ? many hundreds to several
  thousands of filter taps are needed
• an IIR filter ? filter order can be reduced, but
  still hundreds of filter coeffs (num. denom.)
  may be needed (sigh!)
• Hence FIR models are typically used in practice
  because...
• these are guaranteed to be stable
• in a speech comms set-up the acoustics are highly
  time-varying, hence adaptive filtering techniques
  are called for (see DSP-CIS)
• FIR adaptive filters simple adaptation rules,
  no local minima,..
• IIR adaptive filters more complex adaptation,
  local minima

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Introduction
Conventional AEC Techniques

• Directional loudspeakers and microphones
• Voice controlled switching, loss control
• Howling control stability margin improvement of
  the closed loop by
• frequency shifting
• using comb filters
• removing resonant peaks
• Non-linear post-processing, e.g. center clipping

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Outline

• Introduction
• Acoustic echo cancellation (AEC) problem appls
• Acoustic channels
• Adaptive filtering algorithms for AEC
• NLMS
• Frequency domain adaptive filters
• Affine projection algorithm (APA)
• Control algorithm
• Post-processing
• Loudspeaker non-linearity
• Stereo AEC

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Adaptive filtering algorithms for AEC

• Basic set-up
• Adaptive filter produces a model for acoustic
  room impulse response
• an estimate of the echo contribution in
  microphone signal, which is
• then subtracted from the microphone signal
• Thanks to adaptivity
• time-varying acoustics can be tracked
• performance superior to performance of
  conventional techniques

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Adaptive filtering algorithms for AEC

• Algorithms to be discussed
• Normalized LMS
• Frequency-domain adaptive filter (FDAF)
• partitioned block freq-domain adaptive
  filter (PB-FDAF)
• Affine projection algorithm (APA)
• fast affine projection algorithm

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Adaptive Filtering Algorithms NLMS

• NLMS update equations
• in which
• N is the adaptive filter length, ? is the
  adaptation stepsize,
• ? is a regularization parameter and k is the
  discrete-time index

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Adaptive Filtering Algorithms NLMS

• Pros and cons of NLMS
• cheap algorithm O(N)
• small input/output delay ( 1 sample)
• for colored far-end signals (such as speech)
  convergence of the NLMS algorithm is slow
  
• (cfr lambda_max versus lambda_min, etc., see
  DSP-CIS)
• large N then means even slower convergence
• NLMS is thus often used for the cancellation of
  short echo paths

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Adaptive Filtering Algorithms

• As some input/output delay is acceptable in AEC
  (cfr ITU..), algorithms can be derived that are
  even cheaper than NLMS, by exchanging
  implementation cost for extra processing delay,
  sometimes even with improved performance
• Frequency-domain adaptive filtering (FDAF)
• Partitioned Block FDAF (PB-FDAF)

cost reduction optimal (stepsize) tuning for
each subband/frequency bin separately results
in improved performance
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Adaptive Filtering Algorithms Block-LMS

• To derive the frequency-domain adaptive filter
  the BLMS algorithm is considered first

in which
N is filter taps, L is block length, n is block
time index
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Adaptive Filtering Algorithms Block-LMS

• Both the BLMS convolution and correlation
  operation are computationally demanding. They can
  be implemented more efficiently in the frequency
  domain using fast convolution techniques, i.e.
  overlap-save/overlap-add

convolution
overlap-save
correlation
with
DFT matrix
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Adaptive Filtering Algorithms FDAF

• Overlap-save FDAF

Will only work if
(M is FFT-size)
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Adaptive Filtering Algorithms FDAF

• Typical parameter setting for the FDAF
• FDAF is functionally equivalent to BLMS
• FDAF is significantly cheaper than (B)LMS
• for a typical parameter settingIf N1024
  
• - Input/output delay is equal to 2L-12N-1,
  which may be unacceptably large for realistic
  parameter settings e.g. if N1024 and
  fs8000Hz ? delay is 256 ms !

(estimate only, in practice lt20)
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Adaptive Filtering Algorithms PB-FDAF

• Overlap-save PB-FDAF N-tap full-band filter
  split into (N/P) filter sections, P-taps each,
  then apply overlap-save to each section, etc. (P
  takes the place of N).

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Adaptive Filtering Algorithms PB-FDAF

• Typical parameter setting
• PB-FDAF is intermediate between LMS and FDAF
  (P/N1)
• PB-FDAF is functionally equivalent to BLMS
• PB-FDAF is cheaper than LMS If N1024,
  PL128, M256
• Input/output delay is 2L-1 which can be chosen
  small, in the example above the delay is 32 ms,
  if fs8000Hz
• used in commercial AECs

(estimate)
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Adaptive Filtering Algorithms PB-FDAF

• PS Instead of a simple stepsize ?, subband
  dependent stepsizes can be applied
• stepsizes dependent on the subband energy
  (subband normalization)
• convergence speed increased at only a small extra
  cost
• PS PB-FDAF algorithm can be simplified by
  leaving
• out of the weight updating equation
  (unconstrained updating)

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Adaptive Filtering Algorithms APA
Affine Projection Algorithm intermediate
between RLS and NLMS, complexity- as well as
performance-wise
NLMS (delta0)
APA
if ?1
P last a-posteriori errors are 0
a-posteriori error is 0
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Adaptive Filtering Algorithms APA
Problem with APA near-end noise amplification
is echo-signal
is near-end noise
orthogonal
contains sorted singular values on diagonal
, multiplied by , appears as noise in the
filter weights 
Solution replace by
in update formula
(regularization, similar to delta in
NLMS-formula)
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Adaptive Filtering Algorithms APA
Effect on near-end noise amplification
Smaller if more regularization
Effect on adaptation speed
Slower if more regularization
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Adaptive Filtering Algorithms Fast-APA
APA complexity, i.e.O(P.N), may be reduced to
(roughly) LMS complexity, i.e. O(N)
1. Recursive  error vector calculation
(delta0)
Ex mu1, then lower components were already
nulled _at_ time k-1
2. Delayed filter vector update accumulate
filter adaptations based on vector x_k, apply
only when x_k leaves  the X_k matrix (at
time kP-1)
Ignore steps 2 3
3. Recursive updating scheme for inverse in
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Outline

• Introduction
• Acoustic echo cancellation (AEC) problem appls
• Acoustic channels
• Adaptive filtering algorithms for AEC
• NLMS
• Frequency domain adaptive filters
• Affine projection algorithm (APA)
• Control algorithm
• Post-processing
• Loudspeaker non-linearity
• Stereo AEC

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Control Algorithm

• Adaptation speed (? ) should be adjusted
• to the far-end signal power, in order to avoid
  instability of the adaptive filter? stepsize
  normalization (e.g. NLMS)
• to the amount of near-end activity, in order to
  prevent the filter to move away from the optimal
  solution (see DSP-II)
• ? double-talk detection

Double talk refers to the situation where both
the far-end and the near-end speaker are active.
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Control Algorithm

• 3 modes of operation
• Near-end activity (single or double talk) (Ed
  large) ?
• No near-end activity, only far-end activity (Ex
  large, Ed small) ?
• No near-end activity, no far-end activity (Ex
  small, Ed small) ?

? FILT
? FILTADAPT
? NOP

• Ex is short-time energy of
• the far-end signal (p.36)
• Ed is short-time energy of
• the desired signal

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Control Algorithm

• Double-talk Detection (DTD)
• Difficult problem detection of speech during
  speech
• Desired properties
• Limited number of false alarms
• Small delay
• Low complexity
• Different approaches exist in the literature
  which are based on
• Energy
• Correlation
• Spectral contents

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Control Algorithm

• Energy-based DTD
• Compare short-time energy of far-end and
  near-end channel Ex and Ed
• Method 1 If Ed gt ? Ex ? double talk ? is a
  well-chosen threshold
• Method 2

If ? gt 1 ? double talk
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Post-processing

• Error suppression obtained in practice will
• be limited to /- 30 dB, due to
• non-linearities in the signal path (loudspeakers)
• time-variations of the acoustic impulse responses
• finite length of the adaptive filter
• local background noise
• failing double-talk detection
• A post-processing unit is added to further reduce
  the residual signal, e.g. center clipping

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Loudspeaker Non-linearity

• If loudspeaker non-linearity is significant
  (e.g. consumer applications), then this should be
  compensated for
• Solution-1 Non-linear model (fixed) in
  cancellation path

x
Non-linear model
Adaptive filter
y
d
e
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Loudspeaker Non-linearity

• Solution-2 Inverse non-linear model in forward
  path
• Advantage if successful, also improves
  loudspeaker
• characteristic/sound
  quality..

x
Inverse non-linear model
Adaptive filter
y
d
e
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Outline

• Introduction
• Acoustic echo cancellation (AEC) problem appls
• Acoustic channels
• Adaptive filtering algorithms for AEC
• NLMS
• Frequency domain adaptive filters
• Affine projection algorithm (APA)
• Control algorithm
• Post-processing
• Loudspeaker non-linearity
• Stereo AEC

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S-AEC Problem Statement
Multi-microphone/multi-loudspeaker systems
complexity for pre- whitening (APA, RLS) of x
can be shared amongst microphone channels.
Apart from this, different microphone signals
are processed independently
Hence from now on consider S-AEC on one
microphone only. Other microphone(s)
similarly (but independently) processed
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S-AEC Problem Statement
Conditioning Problem S-AEC input vectors are
Mono autocorrelation of x-signal (e.g.
speech) has an impact on
convergence (see DSP-CIS) Stereo also
cross-correlation between signals x1 and x2
plays a role now
Large(r) eigenvalue spread (large(r) condition
number) of correlation matrix -gt large(r) impact
on convergence !
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S-AEC Problem Statement
Hence filter input data matrix X will be singular
(with null-space) -gt LS solution non-unique,
and solutions depend on (changes in)
transmission room (G1,G2) !
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S-AEC Problem Statement
In practice
Hence
So that X will be (only) ill-conditioned
(instead of rank-deficient) which however is
still bad news
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S-AEC Fixes

• -Reduce correlation between the loudspeaker
  signals by
• Complementary comb filters
• White noise insertion (naive solution - large
  distortion)
• Colored (masked) noise insertion
• Non-linear processing

• Disadvantages
• Signal distortion
• Stereo perception may be affected

-In addition use algorithms that are less
sensitive to the condition number than NLMS,
e.g. RLS, APA, ...
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S-AEC Fixes Complementary comb filters
Comb-1 for x1, comb-2 for x2 Two channels are
decorrelated, BUT stereo image is distorted if
applied below 1 kHz (psycho-acoustics) Can be
combined with another technique below 1 kHz
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S-AEC Fixes Noise insertion
Remove all signal content below the masking
threshold Fill with noise (both channels
independently)
Correlation between input channels decreases

• Poor performance for speech
• Good performance for music
• Computationally intensive

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S-AEC Fixes Non-linear processing
is often a half wave rectifier
is necessary for good performance, but audible
Good results for speech, audible artifacts in
music
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S-AEC Fixes Non-linear processing
Loudspeakers play original signal
Mismatch
Loudspeakers play processed signal
Time