prediction-error-method-based adaptive feedback cancellation in hearing aids using pitch estimation
Kim Ngo 1 , Toon van Waterschoot 1 , Mads Græsbøll Christensen 2 , Marc Moonen 1 , Søren Holdt Jensen 3 and Jan Wouters 4
1 Katholieke Universiteit Leuven, ESAT-SCD, Leuven, Belgium
2 Aalborg University, Dept. of Media Technology, Aalborg, Denmark
3 Aalborg University, Dept. Electronic Systems, Aalborg, Denmark
4 Katholieke Universiteit Leuven, ExpORL, O. & N2, Leuven, Belgium
Adaptive Feedback Cancellation (1)
Concept:
• Adaptively model the feedback path and estimate the feedback signal.
• Subtract estimated feedback signal from the microphone signal.
forward path
feedback cancellation
path
acoustic feedback path
+ + − u(t)
G F
ˆ
y [t|ˆf(t)]
x (t) y(t) v(t)
F ˆ
d[t , ˆf(t)]
u(t)=loudspeaker signal x(t)=feedback signal v(t)=near-end signal
ˆf(t)=Feedback path estimate
y[t|ˆf(t)]=predicted feedback signal ˆ
Microphone signal: y(t) = v(t) + x(t) = v(t) + F (q, t)u(t)
Feedback-compensated signal: d(t) = v(t) + [F (q, t) − ˆ F (q, t)]u(t).
Problem:
• Standard adaptive filtering results in a biased solution.
• Correlation between near-end signal and loudspeaker signal caused by closed signal loop.
Current solutions:
• Prediction error method (PEM)-based AFC with linear prediction (LP) model [1].
• PEM-based AFC with cascaded near-end signal model [2].
Proposed solution:
• PEM-based AFC with cascaded near-end signal model using pitch estimation [3][4].
Near-End Signal Model (3)
Harmonic sinusoidal near-end signal model:
Near-end signal: v(t) =
P
X
n=1
a n cos(nω 0 t + φ n ) + r(t)
• ω 0 is the fundamental frequency, a n the amplitude, and φ n the phase
• r(t) is the noise which is assumed to be autoregressive (AR)
• r(t) = C (q,t) 1 e(n) with C(q, t) = 1 + P n
Ci=1 c (i) (t)q −i
Near-end signal model parameter estimation:
Fundamental frequency: ω ˆ 0 = arg max ω
0E{|h H d ˜ (t)| 2 }
• where h is the optimal filter.
Amplitude: ˆ a =
Z H Z −1
Z H d
• where Z is the Vandermonde matrix containing the sinusoids Order: P ˆ = arg min
P M log ˆ σ P 2 + P log M + 3
2 log M
• The AR parameters of the noise component r(t) can be estimated using LP
Experimental Results (5)
Performance measures:
Maximum Stable Gain: MSG(t) = −20 log 10
"
max ω∈P |J(ω, t)[F (ω, t) − ˆ F (ω, t)]|
#
Misadjustment: MA F = 20 log 10 ||ˆf(t) − f|| 2
||f|| 2 .
0 5 10 15 20 25 30
10 12 14 16 18 20 22 24 26 28 30
t(s)
MSG(dB)
20 log10K(t) MSG F (q)
AFC-optfilt (variable amplitude) AFC-optfilt (variable order)
0 5 10 15 20 25 30
10 12 14 16 18 20 22 24 26 28 30
t(s)
MSG(dB)
20 log10K(t) MSG F (q)
AFC-optfilt (P =15) AFC-optfilt (P =10) AFC-optfilt (P =5)
0 5 10 15 20 25 30
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t(s)
MSG(dB)
20 log10K(t) MSG F (q)
AFC-CPZLP (P =15) AFC-CPZLP (P =10) AFC-CPZLP (P =5)
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−16
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−2 0
t (s) MAF(dB)
AFC-optfilt (variable amplitude) AFC-optfilt (variable order)
0 5 10 15 20 25 30
−16
−14
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−8
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−4
−2 0
t (s) MAF(dB)
AFC-optfilt (P =15) AFC-optfilt (P =10) AFC-optfilt (P =5)
0 5 10 15 20 25 30
−16
−14
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−10
−8
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−4
−2 0
t (s) MAF(dB)
AFC-CPZLP (P =15) AFC-CPZLP (P =10) AFC-CPZLP (P =5)
Prediction Error Method based AFC (2)
Concept:
• Reduce the correlation between the near-end signal and the loudspeaker signal
• Prefiltering of loudspeaker and microphone signals with inverse near-end signal model
+ +− forward
path
+−
feedback cancellation
path
acoustic feedback path
decorrelating
source signal model prefilter
G Fˆ
y[t|ˆf(t)]ˆ
x(t)
H e(t) y(t) v(t)
y[t, ˆh(t)]˜ ˆf(t)
u(t)
Hˆ−1
u[t, ˆh(t)]˜
Hˆ−1 Fˆ
ε[t, ˆh(t), ˆf(t − 1)]
F
d[t, ˆf(t)]
• Single all-pole model (Short-term predictor) fails to remove the periodicity
• A cascade of near-end signal models removes the coloring and periodicity
• PEM delivers an unbiased estimate of the feedback path coefficient vector f (t) Cascaded near-end signal model: H 1 (q, t)H 2 (q, t) = B (q, t)
A(q, t)
1 C (q, t) Minimize prediction error: min
f (t) t
X
k=1
ε 2 (k)
Prediction error: ε[t, ξ(t)] = H 1 −1 (q, t)H 2 −1 (q, t)[y(t) − F (q, t)u(t)]
Prediction Error Filter (4)
PEF for sinusoidal components:
• A sum of P sinusoids can be described using an all-pole model of order 2P
• When noise is added a pole-zero model of order 2P should be used
Cascade of second-order sections: H 1 −1 (q, t) =
P
Y
n=1
1 − 2ν n cos nω 0 z −1 + ν n 2 z −2 1 − 2ρ n cos nω 0 z −1 + ρ 2 n z −2 (1)
• The poles and zeros are on the same radial lines
• the poles are positioned between the zeros and the unit circle, i.e., 0 ≪ ρ n < ν n ≤ 1.
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