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Digital Audio Signal Processing
Lecture 5
Acoustic Echo Cancellation
Marc Moonen Dept. E.E./ESAT-STADIUS, KU Leuven
[email protected] homes.esat.kuleuven.be/~moonen/
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 2
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
2
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 3
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 – …
Introduction
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 4
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 …
(*) International Telecommunication Union - Telecommunication Standardization Sector
3
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 5
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
Introduction
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 6
Introduction
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…
Room Acoustics (II) The linear filter model of the acoustic path between loudspeaker and microphone is represented by the acoustic impulse response
4
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 7
Introduction
Room Acoustics (III) To characterize the ‘reflectivity’ of a 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 :
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 8
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 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
5
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 9
Introduction
• 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
`Conventional’ AEC Techniques
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 10
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
6
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 11
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
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 12
Adaptive filtering algorithms for AEC
• Algorithms to be discussed
– Normalized LMS (NLMS) – Frequency-domain adaptive filter (FDAF) & partitioned block freq-domain adaptive filter (PB-FDAF) – Affine projection algorithm (APA) & fast affine projection algorithm
7
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 13
• NLMS update equations
in which
N is the adaptive filter length, µ is the adaptation stepsize,
δ is a regularization parameter and k is the discrete-time index
][
][][][][
1 ke
kykdkeky
kk
Tk
kk
kTk
xxx
ww
wx
δµ+
+=
−=
=
+
xk =x[k]
x[k − (N −1)]
"
#
$$$
%
&
''', wk =
w[0]
w[N −1]
"
#
$$$
%
&
'''
Adaptive filtering algorithms: NLMS
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 14
• 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
Adaptive filtering algorithms: NLMS
8
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 15
Adaptive Filtering Algorithms for AEC
• 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
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 16
Adaptive Filtering Algorithms: Block-LMS
• To derive the frequency-domain adaptive filter the BLMS algorithm is considered first
nnnn
nTnnn
eXwwwXdeµ+=
−=
+1
Xn =
x[nL +1] x[(n+1)L]
x[nL +1− (N −1)] x[(n+1)L − (N −1)]
"
#
$$$
%
&
''', dn =
d[nL +1]
d[(n+1)L]
"
#
$$$
%
&
''', wn =
w[0]
w[N −1]
"
#
$$$
%
&
'''
in which
N is # filter taps, L is block length, n is block time index BLMS = gradient averaging over block of samples
9
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 17
nnnn
nTnnn
eXwwwXdeµ+=
−=
+1
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 :
with
Mjnnn
mnenm
Lnx
MLnxdiag
π2)()( ),(,,
])1[(
]1)1[(−
=⎥⎦
⎤⎢⎣
⎡=
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
+
+−+
= F0w
FwFX !M-point DFT-matrix
convolution
correlation ⎥⎦
⎤⎢⎣
⎡⎥⎦
⎤⎢⎣
⎡
⎥⎦
⎤⎢⎣
⎡
−
−
−−
n
n
NM
N
nn
L
LM
e0
FXF000I
wXFI000
*)(1
)()(1
overlap-save
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 18
Adaptive Filtering Algorithms: FDAF
Overlap-save FDAF
)(*)(1)()1(
)()()(
)(
)()(1)(
)(
])1[(
]1[,
])1[(
]1)1[(
nn
NM
Nnn
nnn
nn
LMn
nn
L
LMn
n
Lnd
nLd
Lnx
MLnxdiag
FeXF000I
Fww
yde
dd0
d
wXFI000
y
FX
−
−
+
−
−−
⎥⎦
⎤⎢⎣
⎡+=
−=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
+
+
=⎥⎦
⎤⎢⎣
⎡=
⎥⎦
⎤⎢⎣
⎡=
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
+
+−+
=
µ
!
!
Will only work if
1−+≥ LNM
(M is DFT-size)
10
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 19
Adaptive Filtering Algorithms: FDAF
¤ Typical parameter setting for the FDAF :
¤ FDAF is functionally equivalent to BLMS (!) + FDAF is significantly cheaper than (B)LMS (cfr FFT/IFFT i.o. DFT/IDFT)
for a typical parameter setting If N=1024 :
- Input/output delay is equal to 2L-1=2N-1, which may be unacceptably large for realistic parameter settings : e.g. if N=1024 and fs=8000Hz → delay is 256 ms !
costLMScost FDAF
≈ 20
∈=== pMLMLN p ,2,2,
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 20
Adaptive Filtering Algorithms: PB-FDAF
• Overlap-save PB-FDAF : N-tap filter split into (N/P) filter sections, P-taps each, then apply overlap-save to each section
(`P takes the place of N’).
1:0,
])1[(
]1[,
1:0,])1[(
]1)1[(
)(*)(1)()1(
)()()(
)(
1
0
)()(1)(
)(
−=⎥⎦
⎤⎢⎣
⎡+=
−=
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
+
+
=⎥⎦
⎤⎢⎣
⎡=
⎥⎦
⎤⎢⎣
⎡=
−=⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎥⎥
⎦
⎤
⎢⎢⎢
⎣
⎡
−+
+−−+
=
−
−
+
−
=
−− ∑
PNp
Lnd
nLd
PNp
pPLnx
MpPLnxdiag
nnp
PM
Pnp
np
nnn
nn
n
p
np
np
L
LMn
np
PN
FeXF000I
Fww
yde
dd0
d
wXFI000
y
FX
µ
!
!
Will only work if 1−+≥ LPM
11
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 21
Adaptive Filtering Algorithms: PB-FDAF
¤ Typical parameter setting : ¤ PB-FDAF is intermediate between LMS and FDAF (P/N=1) + PB-FDAF is functionally equivalent to BLMS + PB-FDAF is cheaper than LMS :
If N=1024, P=L=128, M=256 :
+ Input/output delay is 2L-1 which can be chosen small, in
the example above the delay is 32 ms, if fs=8000Hz ¤ used in commercial AECs
∈=== qMLMLP q ,2,2,
6PBFDAFcostLMScost
≈
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 22
Adaptive Filtering Algorithms: PB-FDAF
• PS: Instead of a simple stepsize µ, ‘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 removing
from the weight updating equation (=`unconstrained updating’)
1−
−⎥⎦
⎤⎢⎣
⎡F
000I
FPM
P
12
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 23
Adaptive Filtering Algorithms: APA
Affine Projection Algorithm =intermediate between RLS and NLMS, complexity- as well as performance-wise
NLMS (delta=0) :
[ ] [ ][ ]ke
kdke
kTkkkk
kTk
11 )( −+ +=
−=
xxxwwxw
µ
[ ] [ ]0
' 1
=
−= + kTkkdke xw
[ ]
kkTkkkk
kTkkk
Pkkkk
eXXXwwwXde
xxxX
11
11
)( −+
+−−
+=
−=
=
µ
!
0wXde =−= +1' kTkkk
a-posteriori error is 0 P last a-posteriori errors are 0
APA :
if µ=1
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 24
Adaptive Filtering Algorithms: APA
Problem with APA : near-end noise amplification
kkk ndd +=noisy
orthogonal Tkkkk VΣUX =
contains sorted singular values on diagonal
Solution : replace by in update formula (=`regularization’, similar to delta in NLMS-formula)
1)( −k
TkXX 1)( −+ IXX δk
Tk
kk VU ,
kΣ
, multiplied by , appears as `noise in the filter weights ’ iσ1
[ ] kTk
Pkk nVUw )1,,1,1diag(
211 σσσ
…… +=+
nk
kd
kn
is echo-signal is near-end noise
13
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 25
Adaptive Filtering Algorithms: APA
Effect on near-end noise amplification
[ ] kTk
P
Pkk nVUw ),,,diag( 22
2
221
11 δσ
σδσ
σδσ
σ+++
+=+ ……
Effect on adaptation speed
[ ]…
…
+
⎥⎦
⎤⎢⎣
⎡
+++−=+ k
Tk
P
Pkk wUUIw ),,,diag( 22
2
221
11 δσ
σδσ
σδσ
σ
Smaller if more regularization
Slower if more regularization
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 26
[ ]⎥⎦
⎤⎢⎣
⎡
−=⎥
⎦
⎤⎢⎣
⎡⇒−=
−1)1(* k
kk
Tkkk
kee
ewXde
µ
1. `Recursive ’ error vector calculation (delta=0) :
Ex: mu=1, then lower components were already nulled @ 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 k+P-1)
kkTkk eXXε 1)( −=
APA complexity, i.e.O(P.N), may be reduced to (roughly) LMS complexity, i.e. O(N) :
3. Recursive updating scheme for inverse in
Adaptive Filtering Algorithms: Fast-APA
Skip
ste
ps 2
& 3
14
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 27
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
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 28
Control Algorithm
• Adaptation speed (µ ) 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-CIS) → double-talk detection
Double talk refers to the situation where both the far-end and the near-end speaker are active.
15
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 29
Control Algorithm
3 modes of operation: 1. Near-end activity (single or double talk) (Ed large)
→ 2. No near-end activity, only far-end activity (Ex large, Ed small)
→ 3. No near-end activity, no far-end activity (Ex small, Ed small)
→
max, µµ =−= yde → FILT+ADAPT
0orsmall, =−= µyde → FILT
0, == µde → NOP
• Ex is short-time energy of the far-end signal • Ed is short-time energy of the desired signal
Ex = x[k − i]2i=0
L
∑
Ed = d[k − i]2i=0
L
∑
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 30
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 – …
16
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 31
Control Algorithm Energy-based DTD Compare short-time energy of far-end and near-end
channel Ex and Ed : – Method 1 :
If Ed > τ Ex → double talk τ is a well-chosen threshold
– Method 2 :
22 EyExEeEx+
=ρ
If ρ > 1 → double talk
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 32
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 – failing double-talk detection – …
• A post-processing unit is added to further reduce the residual signal, e.g. `center clipping’
⎪⎩
⎪⎨
⎧
≤ΔΔ−
Δ≤≤Δ−
Δ−<Δ+
=
inin
in
inin
out 0eee
eee
ein
eout
17
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 33
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
d e
y
Non-linear model
x
Adaptive filter
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 34
Loudspeaker Non-linearity
• Solution-2: Inverse non-linear model in forward path
Advantage = if successful, also improves loudspeaker characteristic/sound quality..
d
e y
Inverse non-linear model
x
Adaptive filter
18
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 35
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
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 36
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
19
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 37
S-AEC Problem Statement
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…
! [ ]
[ ]T
TTk
Tk
Nk
NkxkxNkxkxkx ]1[...][|]1[...]1[][ 22111
2,1,12
+−+−−=
=×
xxx
Conditioning Problem: S-AEC input vectors are
Large(r) eigenvalue spread (large(r) condition number) of correlation matrix -> large(r) impact on convergence !
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 38
S-AEC Problem Statement
Hence filter input data matrix X will be singular (with `null-space’)
-> LS solution non-unique, and solutions depend on (changes in) transmission room (G1,G2) !
[ ] 0.1
22,1, =⎥
⎦
⎤⎢⎣
⎡
−GG
xx Tk
Tk
QN =
Non-uniqueness Problem: Consider transmission room impulse responses G1,G2 (length Q)
Assume then :
explain!
20
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 39
S-AEC Problem Statement
In practice : QN <
[ ] 0.1
22,1, ≅=⎥
⎦
⎤⎢⎣
⎡
−δtruncated
truncatedTk
Tk G
Gxx
So that X will be (only) ill-conditioned (instead of rank-deficient) which however is still bad news…
Hence
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 40
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, ...
21
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 41
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
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 42
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
22
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 43
S-AEC Fixes: Non-linear processing
2..1))(()()(' =+= ikxfkxkx iiii α
is often a half wave rectifier )(•if
2)(
2)(
2
1
•−•=•
•+•=•
f
f
5.0=α is necessary for good performance, but audible
Good results for speech, audible artifacts in music
Digital Audio Signal Processing Version 2014-2015 Lecture-5: Acoustic Echo Cancellation p. 44
S-AEC Fixes: Non-linear processing
Loudspeakers play original signal
Loudspeakers play processed signal
Mismatch
Time