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Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 4 / 34
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 2017-2018 Lecture-5: Acoustic Echo Cancellation 5 / 34
Outline
• Introduction : Acoustic Echo Cancellation (AEC)
• Acoustic channels
• Adaptive filters for AEC
• Control Algorithm
• Stereo AEC
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 6 / 34
• Propagation of sound waves in an acoustic environment results in – Signal attenuation – Spectral distortion
• Propagation can be modeled with sufficient accuracy 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
Acoustic Channels
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Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 7 / 34
Acoustic Channels
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…
The linear filter model of the acoustic path between loudspeaker and microphone is represented by the acoustic impulse response
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 8 / 34
Acoustic Channels
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
PS: 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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Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 9 / 34
Acoustic Channels
Acoustic Impulse Response : FIR or IIR ? • If the acoustic impulse response is modeled as an..
– FIR filter → hundreds/thousands of filter taps are needed – 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… – 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
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 10 / 34
Outline
• Introduction : Acoustic Echo Cancellation (AEC)
• Acoustic channels
• Adaptive filters for AEC
• Control Algorithm
• Stereo AEC
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Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 11 / 34
Adaptive filters 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
(e.g. voice controlled switching, loss control, etc.)
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 12 / 34
• 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 filters for AEC: NLMS
7
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 13 / 34
• 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 λmax versus λmin, etc…., see DSP-CIS) – large N then means even slower convergence
¤ NLMS is thus often used for the cancellation of short echo paths
Adaptive filters for AEC: NLMS
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 14 / 34
Adaptive filters 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
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Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 15 / 34
Adaptive filters for AEC: 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
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 16 / 34
nnnn
nTnnn
eXwwwXdeµ+=
−=
+1
Adaptive filters for AEC: 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
9
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 17 / 34
Adaptive filters for AEC: 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)
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 18 / 34
Adaptive filters for AEC: 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,
10
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 19 / 34
Adaptive filters for AEC: 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
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 20 / 34
Adaptive filters for AEC: 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 è + Input/output delay is 2L-1 which can be chosen small, in
the example above the delay is 32 ms, if fs=8000Hz + Instead of a simple stepsize µ, ‘subband’ dependent
stepsizes µi can be applied to increase convergence speed ¤ used in commercial AECs
∈=== qMLMLP q ,2,2,
6PBFDAFcostLMScost
≈
11
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 21 / 34
Adaptive filters for AEC: Kalman Filter
• Time-invariant echo path model
Echo path is assumed to be wk (=regression/state vector) xk takes the place of C[k] in state space (‘A-B-C-D’) model (!) e[k] is near-end speech, noise, modeling error,..
Kalman Filter (details omitted, see DSP-CIS)
then reduces to (standard/QRD) RLS
wk+1 = I.wk + 0+ 0
d[k]= xkTwk + 0+ e[k]
!"#
$#
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 22 / 34
Adaptive filters for AEC: Kalman Filter
• Random walk model
• ‘Leaky’ random Walk Model
• Frequency domain version •
wk+1 = I.wk + 0+ v[k]d[k]= xk
Twk + 0+ e[k]
!"#
$#
wk+1 =αI.wk + 0+ v[k] (α<1)
d[k]= xkTwk + 0+ e[k]
!"#
$#
wk+1 =αI.wk + 0+ v[k] (α<1)d[k]= xk
Twk + 0+ e[k]
!"#
$#
12
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 23 / 34
Outline
• Introduction : Acoustic Echo Cancellation (AEC)
• Acoustic channels
• Adaptive filters for AEC
• Control Algorithm
• Stereo AEC
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 24 / 34
Control Algorithm
• Adaptation speed (µ ) in LMS-type algorithms should be adjusted… – to the far-end signal power, in order to avoid instability
of the adaptive filter (see DSP-CIS) → 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 on ‘excess MSE’) → 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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Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 25 / 34
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 (loudspeaker) • Ed is short-time energy of the desired signal (microphone)
Ex = x[k − i]2i=0
L
∑
Ed = d[k − i]2i=0
L
∑
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 26 / 34
Control Algorithm
Double-talk Detection (DTD)
• Problem: detection of (near-end) speech during (far-end) 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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Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 27 / 34
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 2017-2018 Lecture-5: Acoustic Echo Cancellation 28 / 34
Outline
• Introduction : Acoustic Echo Cancellation (AEC)
• Acoustic channels
• Adaptive filters for AEC
• Control Algorithm
• Stereo AEC
15
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 29 / 34
Stereo-AEC
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
Stereo-AEC Conditioning Problem:
S-AEC input vectors are
è Large(r) eigenvalue spread (λmax>> λmin,, i.e. large(r) condition number)
of correlation matrix -> large(r) impact on convergence !
Digital Audio Signal Processing Version 2017-2018 Lecture-5: Acoustic Echo Cancellation 30 / 34
Stereo-AEC
Hence filter input data matrix X will be rank-deficient (with `null-space’, λmin=0)
-> LS solution non-unique, and solutions depend on (changes in) transmission room (G1,G2) !