Symmetric leakage for adaptive finite-impulse-response filters
View Patent ↗An adaptive finite-impulse-response filter includes a series of taps; each tap has a corresponding value of tap coefficient. Values of tap coefficients are calculated to minimize a system error function. The solution is under-constrained, and some values of tap coefficients can grow and cause overflow errors. Growth of tap coefficients is controlled by introducing tap leakage. Disclosed is a symmetric leakage algorithm, in which an updated value of the tap coefficient of a particular tap is based on the old value of the tap coefficient of the particular tap, on the old values of the tap coefficients of a set of taps preceding the particular tap, and on the old values of the tap coefficients of a series of taps following the particular tap.
1. A method for updating a plurality of tap coefficient values in an adaptive finite-impulse-response filter, wherein each tap coefficient value in the plurality of tap coefficient values corresponds to a tap in a series of taps, and wherein each tap coefficient value in the plurality of tap coefficient values corresponds to a first time instant, the method comprising the steps of:
receiving a first error value corresponding to the first time instant;
calculating an error update function based on the first error value; and
for each particular tap in the series of taps:
calculating a symmetric leakage update function based on:
the value of the tap coefficient corresponding to the particular tap;
a first set of tap coefficient values in the plurality of tap coefficient values; and
a second set of tap coefficient values in the plurality of tap coefficient values;
wherein:
each tap coefficient value in the first set of tap coefficient values corresponds to a tap in a first set of taps, wherein each tap in the first set of taps precedes the particular tap;
each tap coefficient value in the second set of tap coefficient values corresponds to a tap in a second set of taps, wherein each tap in the second set of taps follows the particular tap; and
the number of taps in the first set of taps is equal to the number of taps in the second set of taps; and
calculating an updated tap coefficient value based on a sum of the symmetric leakage update function and the error update function, wherein the updated tap coefficient value corresponds to the particular tap, and wherein the updated tap coefficient value corresponds to a second time instant.
2. The method of claim 1 , wherein:
the first time instant is represented by t;
the first error value is represented by e;
the error update function is represented by g(e(t));
each tap in the series of taps is represented by a tap index n, wherein:
n is an integer;
0≦n≦(N−1); and
N is a user-defined maximum integer;
the value of the tap coefficient is represented by c(n,t);
the second time instant is represented by t+1;
the updated tap coefficient value is represented by c(n,t+1);
the symmetric leakage update function is represented by ƒ(C(t); and
the updated tap coefficient value is calculated according to the algorithm:
c ( n,t+ 1)=ƒ( C ( t ))+ g ( e ( t )).
3. The method of claim 2 , wherein the symmetric leakage update function is calculated according to the algorithm:
f
(
C
(
t
)
)
=
k
·
[
∑
j
=
JMIN
JMAX
c
(
n
-
j
,
t
)
2
-
∑
j
=
JMIN
JMAX
c
(
n
+
j
,
t
)
2
]
2
·
c
(
n
,
t
)
;
wherein:
k is a user-defined constant;
j is an integer;
JMIN is a user-defined lower limit, JMIN≧1; and
JMAX is a user-defined upper limit.
4. The method of claim 3 , wherein the adaptive finite-impulse-response filter comprises an adaptive equalizer receiving sampled signals, wherein:
x(t−nT) represents a sampled signal received at a time (t−nT), wherein T is a sample period;
k=1−β, wherein β is a leakage amount;
g(t)=−α·e(t)·x(t−nT), wherein α is an adaptation size; and
the updated tap coefficient value is calculated according to the algorithm:
c
(
n
,
t
+
1
)
=
(
1
-
β
)
·
[
∑
j
=
JMIN
JMAX
c
(
n
-
j
,
t
)
2
-
∑
j
=
JMIN
JMAX
c
(
n
+
j
,
t
)
2
]
2
·
c
(
n
,
t
)
-
α
·
e
(
t
)
·
x
(
t
-
nT
)
.
5. The method of claim 1 , wherein the adaptive finite-impulse-response filter is configured to perform:
adaptive equalization;
adaptive echo cancellation;
adaptive noise cancellation;
adaptive system identification; or
adaptive linear prediction.
6. A computational system for updating a plurality of tap coefficient values in an adaptive finite-impulse-response filter, wherein each tap coefficient value in the plurality of tap coefficient values corresponds to a tap in a series of taps, and wherein each tap coefficient value in the plurality of tap coefficient values corresponds to a first time instant, the computational system configured to:
receive a first error value corresponding to the first time instant;
calculate an error update function based on the first error value; and
for each particular tap in the series of taps:
calculate a symmetric leakage update function based on:
the value of the tap coefficient corresponding to the particular tap;
a first set of tap coefficient values in the plurality of tap coefficient values; and
a second set of tap coefficient values in the plurality of tap coefficient values;
wherein:
each tap coefficient value in the first set of tap coefficient values corresponds to a tap in a first set of taps, wherein each tap in the first set of taps precedes the particular tap;
each tap coefficient value in the second set of tap coefficient values corresponds to a tap in a second set of taps, wherein each tap in the second set of taps follows the particular tap; and
the number of taps in the first set of taps is equal to the number of taps in the second set of taps; and
calculate an updated tap coefficient value based on a sum of the symmetric leakage update function and the error update function, wherein the updated tap coefficient value corresponds to the particular tap, and wherein the updated tap coefficient value corresponds to a second time instant.
7. The computational system of claim 6 , wherein:
the first time instant is represented by t;
the first error value is represented by e;
the error update function is represented by g(e(t));
each tap in the series of taps is represented by a tap index n, wherein:
n is an integer;
0≦n≦(N−1); and
N is a user-defined maximum integer;
the value of the tap coefficient is represented by c(n,t);
the second time instant is represented by t+1;
the updated tap coefficient value is represented by c(n,t+1);
the symmetric leakage update function is represented by ƒ(C(t)); and
the updated tap coefficient value is calculated according to the algorithm:
c ( n,t+ 1)=ƒ( C ( t ))+ g ( e ( t )).
8. The computational system of claim 7 , wherein the symmetric leakage update function is calculated according to the algorithm:
f
(
C
(
t
)
)
=
k
·
[
∑
j
=
JMIN
JMAX
c
(
n
-
j
,
t
)
2
-
∑
j
=
JMIN
JMAX
c
(
n
+
j
,
t
)
2
]
2
·
c
(
n
,
t
)
;
wherein:
k is a user-defined constant;
j is an integer;
JMIN is a user-defined lower limit, JMIN≧1; and
JMAX is a user-defined upper limit.
9. The computational system of claim 8 , wherein the adaptive finite-impulse-response filter comprises an adaptive equalizer configured to receive sampled signals, wherein:
x(t−nT) represents a sampled signal received at a time (t−nT), wherein T is a sample period;
k=1−β, wherein β is a leakage amount;
g(t)=−α·e(t)·x(t−nT), wherein α is an adaptation size; and
the updated tap coefficient value is calculated according to the algorithm:
c
(
n
,
t
+
1
)
=
(
1
-
β
)
·
[
∑
j
=
JMIN
JMAX
c
(
n
-
j
,
t
)
2
-
∑
j
=
JMIN
JMAX
c
(
n
+
j
,
t
)
2
]
2
·
c
(
n
,
t
)
-
α
·
e
(
t
)
·
x
(
t
-
nT
)
.
10. The computational system of claim 6 , wherein the adaptive finite-impulse-response filter is configured to perform:
adaptive equalization;
adaptive echo cancellation;
adaptive noise cancellation;
adaptive system identification; or
adaptive linear prediction.
11. A non-transitory computer readable medium storing computer program instructions for updating a plurality of tap coefficient values in an adaptive finite-impulse-response filter, wherein each tap coefficient value in the plurality of tap coefficient values corresponds to a tap in a series of taps, and wherein each tap coefficient value in the plurality of tap coefficient values corresponds to a first time instant, the computer program instructions defining the steps of:
receiving a first error value corresponding to the first time instant;
calculating an error update function based on the first error value; and
for each particular tap in the series of taps:
calculating a symmetric leakage update function based on:
the value of the tap coefficient corresponding to the particular tap;
a first set of tap coefficient values in the plurality of tap coefficient values; and
a second set of tap coefficient values in the plurality of tap coefficient values;
wherein:
each tap coefficient value in the first set of tap coefficient values corresponds to a tap in a first set of taps, wherein each tap in the first set of taps precedes the particular tap;
each tap coefficient value in the second set of tap coefficient values corresponds to a tap in a second set of taps, wherein each tap in the second set of taps follows the particular tap; and
the number of taps in the first set of taps is equal to the number of taps in the second set of taps; and
calculating an updated tap coefficient value based on a sum of the symmetric leakage update function and the error update function, wherein the updated tap coefficient value corresponds to the particular tap, and wherein the updated tap coefficient value corresponds to a second time instant.
12. The non-transitory computer readable medium of claim 11 , wherein:
the first time instant is represented by t;
the first error value is represented by e;
the error update function is represented by g(e(t));
each tap in the series of taps is represented by a tap index n, wherein:
n is an integer;
0≦n≦(N−1); and
N is a user-defined maximum integer;
the value of the tap coefficient is represented by c(n,t);
the second time instant is represented by t+1;
the updated tap coefficient value is represented by c(n,t+1);
the symmetric leakage update function is represented by ƒ(C(t)); and
the updated tap coefficient value is calculated according to the algorithm:
c ( n,t+ 1)=ƒ( C ( t ))+ g ( e ( t )).
13. The non-transitory computer readable medium of claim 12 , wherein the symmetric leakage update function is calculated according to the algorithm:
f
(
C
(
t
)
)
=
k
·
[
∑
j
=
JMIN
JMAX
c
(
n
-
j
,
t
)
2
-
∑
j
=
JMIN
JMAX
c
(
n
+
j
,
t
)
2
]
2
·
c
(
n
,
t
)
;
wherein:
k is a user-defined constant;
j is an integer;
JMIN is a user-defined lower limit, JMIN≧1; and
JMAX is a user-defined upper limit.
14. The non-transitory computer readable medium of claim 13 , wherein the adaptive finite-impulse-response filter comprises an adaptive equalizer configured to receive sampled signals, wherein:
x(t−nT) represents a sampled signal received at a time (t−nT), wherein T is a sample period;
k=1−β, wherein β is a leakage amount;
g(t)=−α·e(t)·x(t−nT), wherein α is an adaptation size; and
the updated tap coefficient value is calculated according to the algorithm:
c
(
n
,
t
+
1
)
=
(
1
-
β
)
·
[
∑
j
=
JMIN
JMAX
c
(
n
-
j
,
t
)
2
-
∑
j
=
JMIN
JMAX
c
(
n
+
j
,
t
)
2
]
2
·
c
(
n
,
t
)
-
α
·
e
(
t
)
·
x
(
t
-
nT
)
.
15. The non-transitory computer readable medium of claim 11 , wherein the adaptive finite-impulse-response filter is configured to perform:
adaptive equalization;
adaptive echo cancellation;
adaptive noise cancellation;
adaptive system identification; or
adaptive linear prediction.