Data storage device comprising two-dimensional data dependent noise whitening filters for two-dimensional recording

• US 9,183,877 B1
• Filed: 03/20/2015
• Issued: 11/10/2015
• Est. Priority Date: 03/20/2015
• Status: Active Grant

• Current Assignee: JP Morgan Chase Bank, N.A. (JP Morgan Chase & Co)
• Original Assignee: Western Digital Technologies Incorporated (Western Digital Corporation)
• Inventors: Chen, Yiming, Zheng, Ning
• Primary Examiner(s): Dinh, Tan X
• Application Number:
  US14/664,570
• Time in Patent Office: 235 Days
• Field of Search: None
• US Class Current: 1/1
• CPC Class Codes: G11B 20/10009 Improvement or modification of read or write signals
• CPC Class Codes: G11B 20/10046 filtering or equalising, e.g. setting the tap weights of an FIR filter
• CPC Class Codes: G11B 20/10268 bit detection or demodulation methods
• CPC Class Codes: G11B 20/10481 optimisation methods
• CPC Class Codes: G11B 5/012 Recording on, or reproducing or erasing from, magnetic disks G11B17/00, G11B19/00 take precedence
• CPC Class Codes: G11B 5/4886 relative to rotating disc

Abstract

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.

Claims

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<sub>k−

1,t</sub>(b) based on;

e<sub>k−

1,t</sub>(b)=n<sub>k−

1,t</sub>(b)−

A₁^T(b)n(b)−

m₁(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)−

A₂^T(b)n(b)−

m₂(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<sub>k−

1,t</sub>(b) represents a noise sample in the first 2D equalized samples;

A₁(b) represents a first data dependent noise prediction filter;

m₁(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;

A₂(b) represents a second data dependent noise prediction filter; and

m₂(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:

m₁(b)=[E(n<sub>k−

1,t</sub>(b))−

E^T(n<sub>k−

1,t</sub>(b)n(b))R<sup>−

1</sup>(b)E(n(b))][1−

E^T(n(b))R<sup>−

1</sup>(b)E(n(b))]<sup>−

1</sup>

A₁(b)=R¹(b)[E(n<sub>k−

1,t</sub>(b)n(b))−

m₁(b)E(n(b))]

R(b)=E(n(b)n^T(b)).

4. The data storage device as recited in claim 3, where:

m₂(b)=[E(n_k,t(b))−

E^T(n_k,t(b)n(b))R<sup>−

1</sup>(b)E(n(b))][1−

E^T(n(b))R<sup>−

1</sup>(b)E(n(b))]<sup>−

1</sup>

A₂(b)=R¹(b)[E(n_k,t(b)n(b))−

m₂(b)E(n(b))]

R(b)=E(n(b)n^T(b)).

5. The data storage device as recited in claim 4, where:

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:

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=−

1n(|Σ

(b)|)−

e_t^TΣ

<sup>−

1</sup>(b)e_t

where e_t=[e<sub>k−

1,t</sub>(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<sub>k−

1,t</sub>(b) based on;

e<sub>k−

1,t</sub>(b)=n<sub>k−

1,t</sub>(b)−

Ā

₁^T(b)n(b)−

m₁(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)−

m₂(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<sub>k−

1,t</sub>(b) represents a noise sample in the first 2D equalized samples;

Ā

₁(b)=[A₁(b), m₁(b)];

A₁(b) represents a first data dependent noise prediction filter;

m₁(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)=[A₂(b), m₂(b)];

A₂(b) represents a second data dependent noise prediction filter; and

m₂(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<sup>−

1</sup>(b)E(n<sub>k−

1</sub>(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<sup>−

1</sup>(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

₁²(b)=E(n<sub>k−

1,t</sub>²(b))−

E^T(n<sub>k−

1,t</sub>(b)n(b))R<sup>−

1</sup>(b)E(n<sub>k−

1,t</sub>(b)n(b));

and

σ

₂²(b)=E(n_k,t²(b))−

E^T(n_k,t(b)n(b))R<sup>−

1</sup>(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:

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=−

1n(|Σ

(b)|)−

e_t^TΣ

<sup>−

1</sup>(b)e_t

where e_t=[e<sub>k−

1,t</sub>(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<sub>k−

1,t</sub>(b) based on;

e<sub>k−

1,t</sub>(b)=n<sub>k−

1,t</sub>(b)−

A₁^T(b)n(b)−

m₁(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)−

A₂^T(b)n(b)−

m₂(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<sub>k−

1,t</sub>(b) represents a noise sample in the first 2D equalized samples;

A₁(b) represents a first data dependent noise prediction filter;

m₁(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;

A₂(b) represents a second data dependent noise prediction filter; and

m₂(b) represents a DC component of predicted noise in the second 2D equalized samples.

16. The method as recited in claim 15, where:

m₁(b)=[E(n<sub>k−

1,t</sub>(b))−

E^T(n<sub>k−

1,t</sub>(b)n(b))R<sup>−

1</sup>(b)E(n(b))][1−

E^T(n(b))R<sup>−

1</sup>(b)E(n(b))]<sup>−

1</sup>

A₁(b)=R¹(b)[E(n<sub>k−

1,t</sub>(b)n(b))−

m₁(b)E(n(b))]

R(b)=E(n(b)n^T(b)).

17. The method as recited in claim 16, where:

m₂(b)=[E(n_k,t(b))−

E^T(n_k,t(b)n(b))R<sup>−

1</sup>(b)E(n(b))][1−

E^T(n(b))R<sup>−

1</sup>(b)E(n(b))]<sup>−

1</sup>

A₂(b)=R¹(b)[E(n_k,t(b)n(b))−

m₂(b)E(n(b))]

R(b)=E(n(b)n^T(b)).

18. The method as recited in claim 17, where:

19. The method as recited in claim 18, further comprising computing a covariance matrix of the form:

20. The method as recited in claim 18, further comprising generating a branch metric br of the 2D sequence detector according to:

br=−

1n(|Σ

(b)|)−

e_t^TΣ

<sup>−

1</sup>(b)e_t

where e_t=[e<sub>k−

1,t</sub>(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<sub>k−

1,t</sub>(b) based on;

e<sub>k−

1,t</sub>(b)=n<sub>k−

1,t</sub>(b)−

Ā

₁^T(b)n(b)−

m₁(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)−

m₂(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<sub>k−

1,t</sub>(b) represents a noise sample in the first 2D equalized samples;

Ā

₁(b)=[A₁(b), m₁(b)];

A₁(b) represents a first data dependent noise prediction filter;

m₁(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)=[A₂(b), m₂(b)];

A₂(b) represents a second data dependent noise prediction filter; and

m₂b 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<sup>−

1</sup>(b)E(n<sub>k−

1</sub>(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<sup>−

1</sup>(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

₁²(b)=E(n<sub>k−

1,t</sub>²(b))−

E^T(n<sub>k−

1,t</sub>(b)n(b))R<sup>−

1</sup>(b)E(n<sub>k−

1,t</sub>(b)n(b));

and

σ

₂²(b)=E(n_k,t²(b))−

E^T(n_k,t(b)n(b))R<sup>−

1</sup>(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:

26. The method as recited in claim 25, further comprising generating a branch metric br of the 2D sequence detector according to:

br=−

1n(|Σ

(b)|)−

e_t^TΣ

<sup>−

1</sup>(b)i e_t

where e_t=[e<sub>k−

1,t</sub>(b), e_k,t(b)]^T.