9: ;<= >? @A AB CED F GIH JKML N L OQP KSR LT U K F L K F V LW R L PYX Z

(1)

!

"$# #% & '

% ( ' )*+ ,- .# # )0/ 1* *+ ) 2# 3 4#5 ) ,6/ '

% 7 8 '

+ - 8# #% *%

9: ;<= >? @A AB

CED F GIH JKML N

L OQP KSR LT U

K F

L K F V

LW R L PYX

Z [\] ^ [_ `

X

CED U F

L L Jba D

T N \

T L P c

LT d ef

X

g ^

hf f e V

LW R L PX g

L J d

K

W i

X

jk kmln o o jIpq rst rsu k

t vIw x

rwy rzt { r o

∼^y^k ^u ^z| ^u ^k ^r

k p p zty u z| u k r} s~ jp p k r su k

t vIw x rwy rzt { r

(2)

• ^%^< ⁺ ⁾ ^# ⁵ ⁷ ^- ⁾^#%

+ # 3 * ' , ) ; 5 '+ * , )# = + * 7 - )#% 9

+ + #+

< 7

*%

) - ' )#%

- ' )#%

#5 4* ) '

+ # 4

5 , )

- #5 , )- 9- .# > '% - * ' )#%

- ' )#% @

: % 4 ' ,* 7

- #5 , )-

* * 7 4 '- > '% - * ' )#%

• ⁼ ⁺ ^# ⁴^* ³ ^; ⁾ ^' ⁾^* ^3*% ⁾

; ) ' )* #

) .* '+ )

; )# - . ' , )- 1

+ ' 7 *% ) 2= 9 #+ ) . 3

>

#+ * = + # 4* 3 ;- '

% 3 45 )

% ) .* 2= 9

#+

) . 3

>#% ,* 5 *% - * , # ) .* ;- '

% 3 45 )

• ⁼ ⁺ ^# ^# ^{, *} ⁷ ^;^# ⁵ ⁾^#%

2* 5 '+

% ) .*

5 '+ '+ ' 4* , < 7

*%

) - ' )#%

5 ' 2* 5 '+ ' )#%

• ^; ⁵ ³ ^' ⁾^#% ²^* ⁵ ^, ⁾ ^,

2* 5 '+ ' )#% 8 ' )

+ >#% , )

+ 5 - )#% 5 ,

% = + #+

% # * 7 * #% ; * * - . > . '+ '-

)*+ , )- ,

; 3

5 ' )#%

9 & '

5 ' )#% # <

3+ # &* 3*% )

% >#% &*+ *% - * #

2< 2 ># * - *% ) , 9 , ) 3 ' )*

; 35 ' )#% @

9 & '

5 ' )#% # <

3+ # &* 3*% )

% - -5 + '- # " 2 ># * -

*%

) , 9 , ) 3 ' )*

• ^>^#% ^- ⁵ ^,^#% ^,

" # " $%& '( ) $+* ,- ./0 123 4 45 2+6 $78 % 9

(3)

• ¹^# ^' ⁷^*% ⁾ ^'⁺ ^# ^# ³ ³⁵ ^,* ⁺ ^* ^, ^#% ^{, *} ^2< ² F(q, t) = f₀(t) + f₁(t)q⁻¹ + . . . +

f_nF(t)q^−nF^/ ^&*% ^' ⁺ ^' ^*% ⁷ ^,^% ^' u(t) ^% ^' ⁷ ³ ^-+ ^# ^.^#% ^* ^,^% ^' y(t)^/ ^# ^, ^, ⁴ ⁷ ⁵^, ⁾⁺ ⁴^* ⁷ ⁴

) .* + * , *% - * #

'% * + '

*%

7 ,% '

v(t)

• ^* ^' ^, ⁾ ^,⁵ ⁺ ^' ^* ^, ^; ⁷^*% ⁾ ^- ^' ⁾^#%

7 ' ) ' 3# 7*

y(t) = F (q, t)u(t) + v(t)

; -+ )*+ #%

minˆf(t)

1 2N

Xt k=1

λ^t−k[y(k) − ˆF(q, t)u(k)]²

• ⁼ ⁺ ^* ⁷ ^- ⁾^#% ^*+ ⁺ ^#+ ⁼ ⁹ ⁷^*% ⁾ ^- ^' ⁾^#% ^% ^- ⁵ ⁷^* ^' ⁾ ^3* ^&⁺ ^' ^% ² ^" ² ^% ^* ⁺ ^' ^*% ⁷ ^,^% ^' ³^# ⁷^*

7 ' ) ' 3# 7*

y(t) = F (q, t)u(t) + 1

A(q, t)e(t)

= 9 -+ )*+ #%

ˆf(t),min^ˆ^a(t)

1 2N

Xt k=1

λ^t−k ˆ

σ_k² ˘ ˆA(q, t)[y(k) − ˆF(q, t)u(k)]¯2

" # " $%& '( ) $+* ,- ./0 123 4 45 / $ ( $

8 0 7% . $ " $% % $ 0 '%

. 7 $

8

.8 7 " $

8 % ' 7 $ ' 1 ( 7 '

8 '

3

(4)

!

#5 4* ) '

% - #5 , )- 9- .# > '% - * ' )#%

• ⁷^#5 ⁴^* ⁾ ^' ⁷^#5 ⁴^* ⁾ ^' ⁷^*

)* - )

#+

"

3 *+

* - )#% ,

% -+ * ' ,*

7#5 4* ) '

+ # 4

5 , )

% * , , # ' 7

'

) &*

)*+

% ' #+

) . 3 ,

• ⁷^#5 ⁴^* ⁾ ^' ^% ^# ^, ^% ^* ⁺ ^'

*% 7 - #% 7 )#% ,

*% ' 4* ' 7

'

) &* )*+

)# # *+ ' )* ) .#5 ) "

far-endfrom

far-endto

x(t) y(t)

Fˆ u(t)

d(t)

F room

v(t)

near-end

• ^# ⁴ ^' ^,^# ⁵ ⁾^#% ⁾^# ⁼ ⁹ ^-+ ⁾^*+ ^#% ⁵ ^% ⁷^*+ ^,^# ³^* ^- ^#% ⁷ ⁾^#% ^,

* , )

% * '

+ : % 4 ' ,* 7 9 , ) 3 ' )* : 9 #

2< 2

e

] R D P

D F

LT U GIH H F

X !

H i cIH

W F U

X " #

LT GH L R LX D P $ % %H H P L PX & `

H

W cJ

L ^ F

D J N ^

T H c

W U F aT L $K F

KH P LT T HT K $

L P F

K ' D F

KH P

D J

dH

T K F G i U (

H

T D HW U F

K L GIH D P L JJD F

KH PYX )* + + +, - ./ 021 3465 / . 78 - 9:; 0 01X R H J < <

X P H h

X a a => ?A@ = < =

X %DT

Bf fC

" # " $%& '( ) $+* ,- ./0 123 4 45 / $ ( $

8 0 7% . $ " $% % $ 0 '%

. 7 $

8

.8 7 " $

8 % ' 7 $ ' 1 ( 7 '

8 ' D

(5)

!

' ,

%

- #5 , )- * * 7 4

'-

> '% - * ' )#% >

• ^- ^# ^{, *} ⁷ ^# ^# ^,^% ^' ^- ^#+ ⁺ ^* ^' ⁾^#% ^% ^; ^2< ² ^* ^, ⁾ ³ ^' ⁾^*

• ⁼ ⁹ ⁷^*% ⁾ ^- ^' ⁾^#% ⁺ ^# ^& ⁷^* ^, ^,^% ^' ⁾ ^.^#5 ⁾ ^' ^* ^- ^%⁾ ^- ^# ^{, *} ⁷ ^# ^# ^,^% ^' ⁵ ^' ⁾ ^@

F G

x(t) y(t)

Fˆ u(t)

d(t)

near-end room

v(t)

amplifier

equalizer

control room

B !

H i cH

W F U

X ] R D P

D F

LT U GIH H F

X C [ F

T W R LX D P $ % %H H P L PYX &\ H

W U F

K (

L L $ cID N U

W a aT L U U

KH P (

H

T JIH P dD H

W U F

K a D F G U

W U

KP d D P H P U F

D F

KH P DT

UH

W T L iH $

L J

X )* + + +, - ./ 01 345 / . 78 - 9:; 0 01X R H J <>

X P H

X a a h> B ?A@ h> h>

X [

L a F

Bf f ?

" # " $%& '( ) $+* ,- ./0 123 4 45 / $ ( $

8 0 7% . $ " $% % $ 0 '%

. 7 $

8

.8 7 " $

8 % ' 7 $ ' 1 ( 7 '

8 '

(6)

!

• ^; ⁾ ^' ⁾^* ^# ⁾ ^.^* ⁺ ^' ⁾ ^, ⁾^# ^- ^. ^' ^, ⁾^- ⁺ ^' ⁷ ^*% ⁾ ⁼ ² ⁹ ^' ^#+ ⁾ ^. ³ ⁺ ^# ⁵ ⁷ ^- ^* ^, ^* ^, ⁾ ³ ^' ⁾^* ^, ^#

+

3 '+ & '+ ' 4* ,

2< 2 - # * - *% ) , &* - )

#+ ˆf(t) = h

fˆ₀(t) . . . fˆ_nF(t)i

'

5 '+ & '+ ' 4* , " 2 - # * - *% ) , &* - )

#+ ˆa(t) = ˆ ˆ

a₁(t) . . . ˆa_nA(t)˜

/ = 9

& '+ '% - *

ˆ σ_t²^/

• ^;^- ^'^% ^' ³ ⁴⁵ ⁾ ^,^# ³^* ^# ⁾ ^.^* ⁵ ^' ⁺ ^' ^&⁺ ^' ^' ⁴^* ^, ⁺ ^' ^* ⁺ ^* ^'- ^* ⁷ ⁴ ⁾ ^.^*⁺ ^{, -} ^' ^* ⁷ ^- ^#5 ^% ⁾^*+ ⁺ ^' ⁾ ^,

˘â(t), â(t − 1), ˆσ²_t,σˆ²_t−1, ψ_F[t, â(t − 1)], ε[t, ˆθ(t − 1)], R_A(t), R_A(t − 1)¯

↓

˘Kâ(t),Kâ(t − 1),K²σˆ_t²,K²σˆ_t−1² ,Kψ_F[t, â(t − 1)],Kε[t, ˆθ(t − 1)],K⁻²R_A(t),K⁻²R_A(t − 1)¯

'

% 7 ) .* ,- '

% '- )

#+

, '

+ * *% #5 .

K >> kˆa(t − 1)k⁻¹₂

) .*% ) .* 2= 9 ' #+ ) . 3 * 7 , ˆf(t)

" # " $%& '( ) $+* ,- ./0 123 4 45 / $ ( $

8 0 7% . $ " $% % $ 0 '%

. 7 $

8

.8 7 " $

8 % ' 7 $ ' 1 ( 7 '

8 '

(7)

!

• ^>^#% ^,* ⁵ ^*% ^- ^* ^,

% 3 '% 2= 9 , 35 ' )#% ,/

) .* '5 '+ & '+ ' 4* ,5 % 7*+ #

'

%

/ 5 % ) % 5 3*+ - ' # &*+

# # - -5 + ,

) . , *

* - )+ *%

7*+ , ) .* 2= 9 '

#+

) . 3

• ⁹ ^' ³ ^* ^# ^{, -} ^' ^* ^# ⁾ ^# ⁾ ^.^* ^,⁵ ⁺ ^' ^* ⁷

% #+ 3 # )

# '5 '+ & '+ ' 4* ,

#+ % '

> , 35 ' )#%

" 2 - # * -

*%

) ,

%

#+

3

kˆa(t)k²₂

+ * 7 - )#% *+ + #+ &+ ' % ' - *

ˆ σ_t²

0 1 2 3 4 5 6 7

x 10⁴

−200 0 200 400 600 800 1000 1200 1400 1600

t (iterations)

dB

RPE 20 log₁₀kˆa(t)k2

RPE 10 log₁₀σˆ_t²

" # " $%& '( ) $+* ,- ./0 123 4 45 / $ ( $

8 0 7% . $ " $% % $ 0 '%

. 7 $

8

.8 7 " $

8 % ' 7 $ ' 1 ( 7 '

8 '

(8)

• ⁼ ⁺ ^# ^# ^{, *} ⁷ ^,^#⁵ ⁾^#% ⁺ ^* ⁵ ⁺ ^' ^* ⁾ ^.^* ⁷^*% ⁾ ^- ^' ⁾^#% ^# ^#% ^* ^# ⁾ ^.^* ⁵ ^' ⁺ ^' ^&⁺ ^' ^' ⁴^* ^,^/ ^* ^/ ⁾ ^.^* ^" ²

- # * - *% ) , 7

*%

) - ' )#%

• ^" ^.^#% ^# ^& ²^* ⁵ ⁺ ^' ^' ⁾^#% ^% ^- ⁵ ⁷^* ^, ^' ^%³ ⁵ ³ ³^% ^#+ ³ ^- ^#% ⁺^, ⁾ ^%^' ⁾^% ⁾ ^.^* ⁼ ⁹ ^-+ ⁾^*+ ^#% ^/ ^* ^'⁵ ⁾⁺ ^% ^#% ^*

+ * 5 '+ ' )#% '+ ' 3* )*+

β

ˆf(t),min^ˆ^a(t)

1 2N

Xt k=1

λ^t−k ˆ σ_k²

˘ ˆA(q, t)[y(k) − ˆF(q, t)u(k)]¯2

+βkˆa(t)k²₂

• ^' ^* ^,^% ^' ²^* ⁵ ⁺ ^' ^' ⁾^#% ^' ⁷ ⁷ ^, ^' ³^#+ ^* ^* ⁴^* ⁺ ^* ⁵ ⁺ ^' ^' ⁾^#% ⁾^*+ ³^% ⁾ ^.^* ⁼ ⁹ ^-+ ⁾^*+ ^#%

ˆf(t),min^ˆ^a(t)

1 2N

 ^t X

k=1

λ^t−k ˆ σ_k²

˘ ˆA(q, t)[y(k)− ˆF(q, t)u(k)]¯2

+[ˆa(t) − a⁰]^TR_a⁻¹[ˆa(t) − a⁰] ff

. - . 3 '

% - #+ #+ ' )* +

#+

% # * 7 * #% )

+ 5 * " 2

+ # - * , , *% *+ ' )

% ) .* % * '+ *% 7 ,% '

a₀ , E{a}, R^a , ^- ^# ^&{a} = E˘

(a − a⁰)(a − a⁰)^T¯

" # " $%& '( ) $+* ,- ./0 123 4 45 / $ ( $

8 0 7% . $ " $% % $ 0 '%

. 7 $

8

.8 7 " $

8 % ' 7 $ ' 1 ( 7 '

8 ' 5

9: ;&lt;= &gt;? @A AB CED F GIH JKML N L OQP KSR LT U K F L K F V LW R L PYX Z

9: ;<= >? @A AB CED F GIH JKML N L OQP KSR LT U K F L K F V LW R L PYX Z