Data storage device comprising two-dimensional data dependent noise whitening filters for two-dimensional recording
View Patent ↗A data storage device is disclosed wherein a first 2D data dependent noise whitening (DDNW) filter is configured to perform 2D DDNW of first and second 2D equalized samples to generate first 2D noise whitened samples. A second 2D DDNW filter is configured to perform 2D DDNW of the first and second 2D equalized samples to generate second 2D noise whitened samples. A 2D sequence detector is configured to detect a first data sequence recorded in a first data track from the first and second 2D noise whitened samples and to detect a second data sequence recorded in a second data track from the first and second 2D noise whitened samples.
1. A data storage device comprising:
a disk comprising a plurality of data tracks;
a head actuated over the disk, wherein the head comprises a first read element and a second read element; and
control circuitry operable to:
position the first read element over a first data track k−1 and position the second read element over a second data track k;
sample a first read signal from the first read element to generate first signal samples;
sample a second read signal from the second read element to generate second signal samples;
a first two-dimensional (2D) equalizer configured to perform 2D equalization of the first signal samples and the second signal samples to generate first 2D equalized samples;
a second 2D equalizer configured to perform 2D equalization of the first signal samples and the second signal samples to generate second 2D equalized samples;
a first 2D data dependent noise whitening (DDNW) filter configured to perform 2D DDNW of the first and second 2D equalized samples to generate first 2D noise whitened samples;
a second 2D DDNW filter configured to perform 2D DDNW of the first and second 2D equalized samples to generate second 2D noise whitened samples; and
a 2D sequence detector configured to detect a first data sequence recorded in the first data track from the first and second 2D noise whitened samples and to detect a second data sequence recorded in the second data track from the first and second 2D noise whitened samples.
2. The data storage device as recited in claim 1 , wherein:
the first 2D DDNW filter is configured to minimize a first data dependent noise prediction error e k−1,t (b) based on:
e k−1,t ( b )= n k−1,t ( b )− A 1 T ( b ) n ( b )− m 1 ( b )
the second 2D DDNW filter is configured to minimize a second data dependent noise prediction error e k,t (b) based on:
e k,t ( b )= n k,t ( b )− A 2 T ( b ) n ( b )− m 2 ( b )
where:
t represents a time index;
b represents one of a plurality of data patterns;
n(b) represents a 2D vector of past noise samples in the first and second 2D equalized samples;
n k−1,t (b) represents a noise sample in the first 2D equalized samples;
A 1 (b) represents a first data dependent noise prediction filter;
m 1 (b) represents a DC component of predicted noise in the first 2D equalized samples;
n k,t (b) represents a noise sample in the second 2D equalized samples;
A 2 (b) represents a second data dependent noise prediction filter; and
m 2 (b) represents a DC component of predicted noise in the second 2D equalized samples.
3. The data storage device as recited in claim 2 , where:
m 1 ( b )=[ E ( n k−1,t ( b ))− E T ( n k−1,t ( b ) n ( b )) R −1 ( b ) E ( n ( b ))][1− E T ( n ( b )) R −1 ( b ) E ( n ( b ))] −1
A 1 ( b )= R 1 ( b )[ E ( n k−1,t ( b ) n ( b ))− m 1 ( b ) E ( n ( b ))]
R ( b )= E ( n ( b ) n T ( b )).
4. The data storage device as recited in claim 3 , where:
m 2 ( b )=[ E ( n k,t ( b ))− E T ( n k,t ( b ) n ( b )) R −1 ( b ) E ( n ( b ))][1− E T ( n ( b )) R −1 ( b ) E ( n ( b ))] −1
A 2 ( b )= R 1 ( b )[ E ( n k,t ( b ) n ( b ))− m 2 ( b ) E ( n ( b ))]
R ( b )= E ( n ( b ) n T ( b )).
5. The data storage device as recited in claim 4 , where:
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.
6. The data storage device as recited in claim 5 , where the control circuitry is further configured to compute a covariance matrix of the form:
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.
7. The data storage device as recited in claim 5 , where the control circuitry is further configured to generate a branch metric br of the 2D sequence detector according to:
br=− 1 n (|Σ( b )|)− e t T Σ −1 ( b ) e t
where e t =[e k−1,t (b), e k,t (b)] T .
8. The data storage device as recited in claim 1 , wherein:
the first 2D DDNW filter is configured to minimize a first data dependent noise prediction error e k−1,t (b) based on:
e k−1,t ( b )= n k−1,t ( b )− Ā 1 T ( b ) n ( b )− m 1 ( b )
the second 2D DDNW filter is configured to minimize a second data dependent noise prediction error e k,t (b) based on:
e k,t ( b )= n k,t ( b )− Ā 2 T ( b ) n ( b )− m 2 ( b )
where:
t represents a time index;
b represents one of a plurality of data patterns;
n (b)=[n(b), 1]
n(b) represents a 2D vector of past noise samples in the first and second 2D equalized samples;
n k−1,t (b) represents a noise sample in the first 2D equalized samples;
Ā 1 (b)=[A 1 (b), m 1 (b)];
A 1 (b) represents a first data dependent noise prediction filter;
m 1 (b) represents a DC component of predicted noise in the first 2D equalized samples;
n k,t (b) represents a noise sample in the second 2D equalized samples; and
Ā 2 (b)=[A 2 (b), m 2 (b)];
A 2 (b) represents a second data dependent noise prediction filter; and
m 2 (b) represents a DC component of predicted noise in the second 2D equalized samples.
9. The data storage device as recited in claim 8 , where:
Ā 1 ( b )= R −1 ( b ) E ( n k−1 ( b ) n ( b )) R ( b )= E ( n ( b ) n T ( b ));
and
R ( b )= E ( n ( b ) n T ( b )).
10. The data storage device as recited in claim 9 , where:
Ā 2 ( b )= R −1 ( b ) E ( n k ( b ) n ( b ));
and
R ( b )= E ( n ( b ) n T ( b )).
11. The data storage device as recited in claim 9 , where:
σ 1 2 ( b )= E ( n k−1,t 2 ( b ))− E T ( n k−1,t ( b ) n ( b )) R −1 ( b ) E ( n k−1,t ( b ) n ( b ));
and
σ 2 2 ( b )= E ( n k,t 2 ( b ))− E T ( n k,t ( b ) n ( b )) R −1 ( b ) E ( n k,t ( b ) n ( b )).
12. The data storage device as recited in claim 11 , where the control circuitry is further configured to compute a covariance matrix of the form:
Σ
(
b
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=
[
σ
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2
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σ
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]
.
13. The data storage device as recited in claim 12 , where the control circuitry is further configured to generate a branch metric by br of the 2D sequence detector according to:
br=− 1 n (|Σ( b )|)− e t T Σ −1 ( b ) e t
where e t =[e k−1,t (b), e k,t (b)] T .
14. A method of operating a disk drive, the method comprising:
positioning a first read element over a first data track k−1 and position a second read element over a second data track k;
sampling a first read signal from the first read element to generate first signal samples;
sampling a second read signal from the second read element to generate second signal samples;
performing first 2D equalization of the first signal samples and the second signal samples to generate first 2D equalized samples;
performing second 2D equalization of the first signal samples and the second signal samples to generate second 2D equalized samples;
performing first 2D data dependent noise whitening (DDNW) filtering of the first and second 2D equalized samples to generate first 2D noise whitened samples;
performing second 2D DDNW filtering of the first and second 2D equalized samples to generate second 2D noise whitened samples; and
using a 2D sequence detector to detect a first data sequence recorded in the first data track from the first and second 2D noise whitened samples and to detect a second data sequence recorded in the second data track from the first and second 2D noise whitened samples.
15. The method as recited in claim 14 , wherein:
the first 2D DDNW filter is configured to minimize a first data dependent noise prediction error e k−1,t (b) based on:
e k−1,t ( b )= n k−1,t ( b )− A 1 T ( b ) n ( b )− m 1 ( b )
the second 2D DDNW filter is configured to minimize a second data dependent noise prediction error e k,t (b) based on:
e k,t ( b )= n k,t ( b )− A 2 T ( b ) n ( b )− m 2 ( b )
where:
t represents a time index;
b represents one of a plurality of data patterns;
n(b) represents a 2D vector of past noise samples in the first and second 2D equalized samples;
n k−1,t (b) represents a noise sample in the first 2D equalized samples;
A 1 (b) represents a first data dependent noise prediction filter;
m 1 (b) represents a DC component of predicted noise in the first 2D equalized samples;
n k,t (b) represents a noise sample in the second 2D equalized samples;
A 2 (b) represents a second data dependent noise prediction filter; and
m 2 (b) represents a DC component of predicted noise in the second 2D equalized samples.
16. The method as recited in claim 15 , where:
m 1 ( b )=[ E ( n k−1,t ( b ))− E T ( n k−1,t ( b ) n ( b )) R −1 ( b ) E ( n ( b ))][1− E T ( n ( b )) R −1 ( b ) E ( n ( b ))] −1
A 1 ( b )= R 1 ( b )[ E ( n k−1,t ( b ) n ( b ))− m 1 ( b ) E ( n ( b ))]
R ( b )= E ( n ( b ) n T ( b )).
17. The method as recited in claim 16 , where:
m 2 ( b )=[ E ( n k,t ( b ))− E T ( n k,t ( b ) n ( b )) R −1 ( b ) E ( n ( b ))][1− E T ( n ( b )) R −1 ( b ) E ( n ( b ))] −1
A 2 ( b )= R 1 ( b )[ E ( n k,t ( b ) n ( b ))− m 2 ( b ) E ( n ( b ))]
R ( b )= E ( n ( b ) n T ( b )).
18. The method as recited in claim 17 , where:
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.
19. The method as recited in claim 18 , further comprising computing a covariance matrix of the form:
Σ
(
b
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=
[
σ
1
2
(
b
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(
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k
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(
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)
σ
2
2
(
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]
.
20. The method as recited in claim 18 , further comprising generating a branch metric br of the 2D sequence detector according to:
br=− 1 n (|Σ( b )|)− e t T Σ −1 ( b ) e t
where e t =[e k−1,t (b), e k,t (b)] T .
21. The method as recited in claim 14 , wherein:
the first 2D DDNW filtering minimizes a first data dependent noise prediction error e k−1,t (b) based on:
e k−1,t ( b )= n k−1,t ( b )− Ā 1 T ( b ) n ( b )− m 1 ( b )
the second 2D DDNW filtering minimizes a second data dependent noise prediction error e k,t (b) based on:
e k,t ( b )= n k,t ( b )− Ā 2 T ( b ) n ( b )− m 2 ( b )
where:
t represents a time index;
b represents one of a plurality of data patterns;
n (b)=[n(b), 1]
n(b) represents a 2D vector of past noise samples in the first and second 2D equalized samples;
n k−1,t (b) represents a noise sample in the first 2D equalized samples;
Ā 1 (b)=[A 1 (b), m 1 (b)];
A 1 (b) represents a first data dependent noise prediction filter;
m 1 (b) represents a DC component of predicted noise in the first 2D equalized samples;
n k,t (b) represents a noise sample in the second signal samples; and
Ā 2 (b)=[A 2 (b), m 2 (b)];
A 2 (b) represents a second data dependent noise prediction filter; and
m 2 b represents a DC component of predicted noise in the second 2D equalized samples.
22. The method as recited in claim 21 , where:
Ā 1 ( b )= R −1 ( b ) E ( n k−1 ( b ) n ( b )) R ( b )= E ( n ( b ) n T ( b ));
and
R ( b )= E ( n ( b ) n T ( b )).
23. The method as recited in claim 22 , where:
Ā 2 ( b )= R −1 ( b ) E ( n k ( b ) n ( b ));
and
R ( b )= E ( n ( b ) n T ( b )).
24. The method as recited in claim 23 , where:
σ 1 2 ( b )= E ( n k−1,t 2 ( b ))− E T ( n k−1,t ( b ) n ( b )) R −1 ( b ) E ( n k−1,t ( b ) n ( b ));
and
σ 2 2 ( b )= E ( n k,t 2 ( b ))− E T ( n k,t ( b ) n ( b )) R −1 ( b ) E ( n k,t ( b ) n ( b )).
25. The method as recited in claim 24 , further comprising computing a covariance matrix of the form:
Σ
(
b
)
=
[
σ
1
2
(
b
)
E
(
e
k
-
1
,
t
(
b
)
e
k
,
t
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k
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t
(
b
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e
k
-
1
,
t
(
b
)
)
σ
2
2
(
b
)
]
.
26. The method as recited in claim 25 , further comprising generating a branch metric br of the 2D sequence detector according to:
br=− 1 n (|Σ( b )|)− e t T Σ −1 ( b )i e t
where e t =[e k−1,t (b), e k,t (b)] T .