# Patent

## Title
Decoupling magneto-resistive asymmetry and offset loops

## Abstract

Removing magneto-resistive asymmetry (MRA) from a signal is disclosed. Removing MRA includes determining an estimated offset error associated with error due to offset in the signal, determining an estimated signal error associated with error due to offset and MRA in the signal, and removing at least a portion of MRA from the signal based at least in part on the estimated offset error and the estimated signal error.

## Background
CROSS REFERENCE TO OTHER APPLICATIONS
This application claims priority to U.S. Provisional Patent Application No. 60/901,921 entitled DECOUPLING MAGNETO-RESISTIVE ASYMMETRY AND OFFSET LOOPS filed Feb. 15, 2007 which is incorporated herein by reference for all purposes.


BACKGROUND OF THE INVENTION
Recordings on a magnetic disk can be performed either longitudinally or perpendicularly. In longitudinal recording, information is stored within or parallel to the plane of the magnetic disk. In perpendicular recording, information is stored perpendicular to the plane. Longitudinal recording products have been commercially available for some time; new perpendicular recording products are being developed because of the potential for much higher storage capacity compared to longitudinal recording.
A signal associated with a magnetic disk read channel may have a number of defects, such as offset (e.g., a constant voltage added to the signal), gain (e.g., a constant multiplied by the signal), or magneto-resistive asymmetry (MRA). MRA refers to distortion that results from a magneto-resistive read head operating in a nonlinear region of a magnetic field. Typically, feedback loops are used to handle offset, gain, and MRA. Existing offset loops and MRA loops are coupled, in that an offset error will cause the MRA loop to diverge. Perpendicular recording signals tend to have higher offset. Therefore, improved techniques for handling MRA would be desirable.



BRIEF DESCRIPTION OF THE DRAWINGS
Various embodiments of the invention are disclosed in the following detailed description and the accompanying drawings.
FIG. 1A is a diagram illustrating an example of an ideal signal and a signal with an offset.
FIG. 1B is a diagram illustrating an example of an ideal signal and a signal with MRA.
FIG. 1C is a diagram illustrating an example of an ideal signal and a signal with an offset and MRA.
FIG. 1D is a diagram illustrating an example of some thresholds that may be set.
FIG. 2 is a block diagram illustrating an embodiment of a system for removing errors due to MRA, gain, and offset from a signal.
FIG. 3 is a diagram illustrating an example of offset and MRA loop trajectories obtained in some embodiments.



DETAILED DESCRIPTION
The invention can be implemented in numerous ways, including as a process, an apparatus, a system, a composition of matter, a computer program product such as a computer readable storage medium comprising computer instructions, or a computer network wherein program instructions are sent over optical or communication links. In this specification, these implementations, or any other form that the invention may take, may be referred to as techniques. A component such as a processor or a memory described as being configured to perform a task includes both a general component that is temporarily configured to perform the task at a given time or a specific component that is manufactured to perform the task. In general, the order of the steps of disclosed processes may be altered within the scope of the invention.
A detailed description of one or more embodiments of the invention is provided below along with accompanying figures that illustrate the principles of the invention. The invention is described in connection with such embodiments, but the invention is not limited to any embodiment. The scope of the invention is limited only by the claims and the invention encompasses numerous alternatives, modifications and equivalents. Numerous specific details are set forth in the following description in order to provide a thorough understanding of the invention. These details are provided for the purpose of example and the invention may be practiced according to the claims without some or all of these specific details. For the purpose of clarity, technical material that is known in the technical fields related to the invention has not been described in detail so that the invention is not unnecessarily obscured.
FIG. 1A is a diagram illustrating an example of an ideal signal and a signal with an offset. In the example shown, the signals are read signals associated with magnetic disk storage. Signal 102 is an ideal signal. In some embodiments, values are stored magnetically as 0's or 1's on the recording media and are read back. Signal 104 corresponds to ideal signal 102 but includes an offset. As shown in this example, the offset shifts the entire ideal signal up (or down) by some constant (e.g., a DC voltage).
Signal 104 may be modeled using the following equation:

y=x+o+n 

where x is ideal signal 102, o is the offset, n is the noise, and y is signal 104.
Offset is a particular problem in perpendicular recording because perpendicular recording signals tend to have low frequency noise due to effects such as baseline wander. Offset is also a problem when using a tunneling magnetoresistive (TMR) head, which exhibit noise whose power is inversely proportional with frequency, so at lower frequencies (e.g., closer to DC or an offset), the noise power is higher. Low frequency noise may be considered to be a time-varying offset.
FIG. 1B is a diagram illustrating an example of an ideal signal and a signal with MRA. In the example shown, the signals are read signals associated with magnetic disk storage. Signal 102 is an ideal signal. Signal 106 corresponds to ideal signal 102 but includes MRA. As shown in this example, MRA affects the signal y more at higher or larger magnitudes (i.e., |y|) than at lower magnitudes. In this example, signal 106 appears asymmetric (goes more positive than negative). In perpendicular recording, the signal |y| spends little or no time at or near 0, so MRA can cause nonlinearities in the signal in perpendicular recording.
Signal 106 may be modeled using the following equation:

y=x+ax2+n 

where x is ideal signal 102, a is the MRA coefficient (ax2 is an estimate of the MRA), n is the noise, and y is signal 106.
FIG. 1C is a diagram illustrating an example of an ideal signal and a signal with an offset and MRA. In the example shown, the signals are read signals associated with magnetic disk storage. Signal 102 is an ideal signal. Signal 108 corresponds to ideal signal 102 but includes both offset and MRA.
Signal 108 may be modeled using the following equation:

y=x+ax2+o+n 

where x is ideal signal 102, a is the MRA coefficient (ax2 is an estimate of the MRA), o is the offset, n is the noise, and y is signal 108.
When |y| is small, MRA is small and the offset dominates in the signal y. When |y| is larger, both MRA and offset are present in the signal y.
Feedback loops may be used to compensate for defects in the system. Feedback loops compute an estimated error due to the defect and then change an appropriate circuit to compensate for the estimated error.
An offset (feedback) loop is used to compensate for offset in the system. An MRA (feedback) loop is used to compensate for MRA in the system. An estimated offset error eo is used to update the offset loop, and an estimated MRA error em is used to update the MRA loop. An estimate of the signal error e can be made, but it is not clear how much of the estimated error e is due to offset and how much of it is due to MRA. However, some assumptions can be made based on the fact that the error due to MRA is dominant at higher signal levels (|y|>threshold1) and is smaller at lower signal levels (|y|<threshold2).
The estimated signal error may be modeled using the following equation:

e(i)=ax2+o+n 

where e is the error component of y.
In the offset loop, the following update equation is used:

o=o+Koeo 

where eo=0 when |y(i)|>threshold1 and eo=e(i) when |y(i)|<threshold2.
where o is the offset compensation signal, Ko is the loop gain, eo is the estimated offset error, y(i) is the signal at time i and e(i) is an estimate of the signal error at time i. eo is set to 0 when |y(i)| is above threshold1 because at higher values of |y(i)|, the error is due to both MRA and offset, and it is not clear how much is from offset. To avoid feeding back error due to MRA into the offset loop, eo is set to 0 at this time. eo is set to e(i) when |y(i)|<threshold2 because at lower values of |y(i)|, the error is dominated by the effect of offset and there is little or no contribution from MRA. Therefore, the offset loop update equation can be updated at this time. Thus, the offset loop is only updated when the signal y is less than a threshold (to decouple the offset loop from the MRA loop).
In a typical MRA loop, the following update equation is used:

mra=mra+Kmem 

where em is set to 0 when |y(i)|<threshold and
em=e(i) when |y(i)|>threshold.
where mra is the MRA compensation signal, Km is the loop gain, em is the estimated MRA error. y(i) is the signal at time i and e(i) is an estimate of the signal error at time i. em is set to 0 when |y(i)| is below threshold because for lower values of |y(i)|, the effect of MRA is minimal and the effect of offset is dominant. Therefore, the MRA equation is not updated at this time. When |y(i)| is above threshold, both offset and MRA contribute to error. However, typical MRA loops are updated at this time. As a result, typical MRA loops are still coupled to the offset loop. If the signal contains an offset, then the error will also contain a DC offset, causing the loop to saturate. In a typical MRA loop, care must be taken to tune the bandwidth of the MRA loop to be sufficiently slower (i.e., lower bandwidth) than the bandwidth of the offset loop so that the loops will settle rather than fight each other. As such, the loop gains Ko and Km, and the threshold(s), which affect the bandwidth, need to be carefully tuned to ensure that the loops settle. Increasing the loop gain increases the speed of the loop.
It would be desirable to better decouple the offset loop from the MRA loop, particularly if there is offset in the signal y and/or when y contains MRA effects, such as in perpendicular recording.
In order to better decouple the offset loop from the MRA loop, in some embodiments, the MRA loop uses the following update equation:

mra=mra+Kmem 

where em is set to 0 when |y(i)|<threshold2 and
em=e(i)−e(j) when |y(i)|>threshold1.
where mra is the MRA compensation signal, Km is the loop gain, em is the estimated MRA error, y(i) is the signal at time i, and e(i) is an estimate of the signal error at time i. In some embodiments, e(j) is an estimate of the offset error. In some embodiments, j is the time at which the offset loop was last updated. In this case, e(j) is the most recently determined estimated offset error prior to the determination of the estimated signal error. In some embodiments, j is any time at which the offset loop was previously updated. In this case, e(j) is any previously determined estimated offset error.
Because the offset loop is only updated when the signal y is less than a threshold (to decouple the offset loop from the MRA loop), e(j) is approximately equal to offset+noise (o+n), so when |y(i)|>threshold1, subtracting e(j) from e(i) removes the offset and noise, leaving an estimate of substantially the MRA error. In other words:

e(i)−e(j)=(ax2+o+n)−(o+n)=ax2 

Although the noise terms may not actually be the same, they may be averaged in a filter (as more fully described below) so that they are approximately the same and cancel each other out in the above equation.
In some embodiments, a threshold is not used for the MRA loop. In other words, mra=mra+Km(e(i)−e(j)). This may work because e(i)−e(j) when y is low is small or close to zero so it does not substantially affect the update.
Although two thresholds are shown in the examples herein, in other embodiments one threshold may be used (i.e., threshold1=threshold2). Having one threshold may speed up the loops and/or permit more samples to be used (e.g., instead of discarding information greater than threshold1 but less than threshold2). In other embodiments, any number of thresholds may be used. For example, there may be different thresholds used for the offset loop and for the MRA loop. In some embodiments, the thresholds overlap (i.e., threshold1>threshold2).
This technique is not as sensitive to the bandwidth of the loop, and therefore the threshold(s) and loop gains do not have to be as carefully tuned or tuned at all.
FIG. 1D is a diagram illustrating an example of some thresholds that may be set. In this example, an example of a received signal y is shown along with the regions formed by the threshold values. In some embodiments, thresholds Th1, Th2, |Th3|, and |Th4| are the same, i.e., Th1=Th2=|Th3|=|Th4|. In some embodiments, Th1=|Th4| and Th2=|Th3|. For each region, the values of eo and em are shown, as defined above.
FIG. 2 is a block diagram illustrating an embodiment of a system for removing errors due to MRA, gain, and offset from a signal. In this example, system 200 is shown to include adder 202, variable gain amplifier (VGA) 204, MRA corrector 206, continuous time filter (CTF) 208, A/D converter 210, finite impulse response (FIR) filter 212, detector 214, error generator 216, multipliers (scalers) 224, 230, and 236, loop filters (LF) 220, 228, and 234, and D/A converters (DAC) 218, 226, and 232. LFs 220, 228, and 234 perform averaging and may comprise an integrator. A signal y is received from a read channel, such as a perpendicular recording channel. An offset correction voltage vo (e.g., corresponding to o above) is added to signal y via adder 202. The output of adder 202 is input to VGA 204 whose gain is adjustable based on VGA input vg, which is a gain correction. The output of VGA 204 is input to MRA corrector 206, which removes MRA from the signal based on MRA corrector input vm (mra above). The output of MRA corrector 206 is input to CTF 208, whose output is input to A/D 210, whose output is input to FIR 212 and error generator 216. The output of FIR 212 is input to detector 214, which outputs â, an estimate of y. Both the output of A/D 210 and â are input to error generator 216. In various embodiments, detector 214 is a decision feedback equalizer (DFE), Viterbi decoder, or other detector.
Error generator 216 is used to determine and output em, eg, and eo. Error generator 216 performs the threshold comparisons to output the appropriate values of em and eo as defined above. Three feedback loops are shown: an MRA loop, a gain loop, and an offset loop.
The MRA loop includes multiplier 224, LF 220, DAC 218, and MRA 206. em is scaled by multiplier 224 by Km, and input to LF 220, which performs averaging. The output of LF 220 is input to DAC 218, whose output vm is fed back to MRA corrector 206. Km is the loop gain; adjusting Km adjusts the bandwidth of the MRA loop. The threshold(s) used in error generator 216 to determine the value of em also affects the bandwidth of the loop. MRA corrector 206 uses vm to remove MRA error from signal y. In some embodiments, MRA corrector 206 performs the function Y=X+KX2 where X is the input to MRA corrector 206, K is vm, and Y is the output of MRA corrector 206. In some embodiments, the KX2 term substantially cancels out the MRA in X.
The gain loop includes multiplier 230, LF 228, DAC 226, and VGA 204. eg is scaled by multiplier 230 by Kg, and input to LF 228, which performs averaging. The output of LF 228 is input to DAC 226, whose output vg is fed back to VGA 204. In some embodiments, eg=sign(y)·e(i). VGA 204 uses vg to remove the gain error from the signal y. Kg is the loop gain; adjusting Kg adjusts the bandwidth of the gain loop.
The offset loop includes multiplier 236, LF 234, DAC 232, and adder 202. eo is scaled by multiplier 236 by Ko, and input to LF 234, which performs averaging. The output of LF 234 is input to DAC 232, whose output vo is fed back to adder 202. Adder 202 uses vo to remove offset error from signal y. Ko is the loop gain; adjusting Ko adjusts the bandwidth of the offset loop. The threshold(s) used in error generator 216 to determine the value of eo also affects the bandwidth of the loop.
FIG. 3 is a diagram illustrating an example of offset and MRA loop trajectories obtained in some embodiments. In this example, both the offset and the MRA compensation signal are scaled to fit on the same plot. The x-axis is time and the y-axis is the offset o and MRA compensation signal m. The initial offset is located at the origin, and the correct offset and the initial and final MRA compensation signals are located at the same position on the y-axis.
The plots for the traditional offset loop and the traditional MRA loop result when the following MRA update equation is used:

mra=mra+Kmem 

where em is set to 0 when |y(i)|<threshold2 and em=e(i) when |y(i)|>threshold1.
The plots for the offset loop with modified MRA loop and modified MRA loop result when the following MRA update equation is used:

mra=mra+Kmem 

where em is set to 0 when |y(i)|<threshold2 and em=e(i)−e(j) when |y(i)|>threshold1.
As shown, the trajectory for the offset loop with modified MRA loop takes about 4000 time units (e.g., clock cycles) to reach the correct offset, whereas the trajectory for the traditional offset loop takes about 8000 time units to reach the correct offset.
Similarly, the trajectory for the modified MRA loop takes about does not move from the correct MRA compensation value, whereas the trajectory for the traditional MRA loop jumps up and then settles back to the correct MRA compensation value after about 6000 time units.
Although the foregoing embodiments have been described in some detail for purposes of clarity of understanding, the invention is not limited to the details provided. There are many alternative ways of implementing the invention. The disclosed embodiments are illustrative and not restrictive.

## Claims

1. A method of removing magneto-resistive asymmetry (MRA) from a signal, including:
using a processor to determine an estimated offset error which is an estimate of the error due to offset in the signal, including by determining the estimated offset error using those portions of the signal where the magnitude of the signal is less than a first threshold and excluding at least some portion of the signal where the magnitude of the signal is greater than the first threshold from the determination of the estimated offset error;
using the processor to determine an estimated signal error which is an estimate of the combined error due to offset combined with MRA in the signal, including by determining the estimated signal error using those portions of the signal where the magnitude of the signal is greater than a second threshold and excluding at least some portion of the signal where the magnitude of the signal is less than the second threshold from the determination of the estimated signal error; and
removing at least a portion of MRA, using the processor, from the signal based at least in part on the estimated offset error and the estimated signal error, including by subtracting the estimated offset error from the estimated signal error to obtain an estimated MRA error.

2. A method as recited in claim 1, wherein the estimated offset error is a most recently determined estimated offset error prior to the determination of the estimated signal error.

3. A method as recited in claim 1, wherein the estimated offset error is an average of two or more estimated offset errors.

4. A method as recited in claim 1, wherein removing at least a portion of MRA includes updating a signal used in an MRA feedback loop.

5. A method as recited in claim 1, wherein the estimated offset error is used in an offset feedback loop.

6. A method as recited in claim 1, wherein the signal is associated with a perpendicular recording channel.

7. A method as recited in claim 1, wherein a detector is used to determine the estimated offset error and/or estimated signal error.

8. A method as recited in claim 1, wherein a detector is used to determine the estimated offset error and/or estimated signal error and the detector includes a DFE or Viterbi detector.

9. A method as recited in claim 1, wherein:
removing at least a portion of MRA further includes using the estimated MRA error to adjust, after processing by a variable gain amplifier, an amplified signal; and
the method further includes removing at least a portion of an offset, including by using the estimated offset error to adjust, prior to processing by the variable gain amplifier, an unamplified signal.

10. A method as recited in claim 1, wherein the first threshold and the second threshold are set to the different values.

11. A method as recited in claim 1, wherein removing at least a portion of MRA includes using an update equation MRA of mra=mra+Kmem, where:
mra is the MRA compensation signal;
Km is the loop gain;
when the magnitude of the signal at time i is less than the first threshold, em is set to 0; and
when the magnitude of the signal at time i is greater than the second threshold, em is set to the estimated signal error at time i minus the estimated offset error at time j.

12. A method as recited in claim 11, wherein the estimated offset error at time j is the most recently determined estimated offset error prior to the determination of the estimated signal error.

13. A system for removing magneto-resistive asymmetry (MRA) from a signal, including:
a processor configured to:
determine an estimated offset error which is an estimate of the error due to offset in the signal, including by determining the estimated offset error using those portions of the signal where the magnitude of the signal is less than a first threshold and excluding at least some portion of the signal where the magnitude of the signal is greater than the first threshold from the determination of the estimated offset error;
determine an estimated signal error which is an estimate of the combined error due to offset combined with MRA in the signal, including by determining the estimated signal error using those portions of the signal where the magnitude of the signal is greater than a second threshold and excluding at least some portion of the signal where the magnitude of the signal is less than the second threshold from the determination of the estimated signal error; and
remove at least a portion of MRA from the signal based at least in part on the estimated offset error and the estimated signal error, including by subtracting the estimated offset error from the estimated signal error to obtain an estimated MRA error; and

a memory coupled with the processor, wherein the memory provides the processor with instructions.

14. A system as recited in claim 13, wherein a detector is used to determine the estimated offset error and/or estimated signal error.

15. A system as recited in claim 13, wherein:
the processor is further configured to remove at least a portion of MRA by using the estimated MRA error to adjust, after processing by a variable gain amplifier, an amplified signal; and
the processor is further configured to remove at least a portion of an offset, including by using the estimated offset error to adjust, prior to processing by the variable gain amplifier, an unamplified signal.

16. A system as recited in claim 13, wherein the first threshold and the second threshold are set to the different values.

17. A system as recited in claim 13, wherein removing at least a portion of MRA includes using an update equation MRA of mra=mra+Kmem, where:
mra is the MRA compensation signal;
Km is the loop gain;
when the magnitude of the signal at time i is less than the first threshold, em is set to 0; and
when the magnitude of the signal at time i is greater than the second threshold, em is set to the estimated signal error at time i minus the estimated offset error at time j.

18. A system as recited in claim 17, wherein the estimated offset error at time j is the most recently determined estimated offset error prior to the determination of the estimated signal error.

19. A system as recited in claim 13, wherein the estimated offset error is an average of two or more estimated offset errors.

20. A computer program product for removing magneto-resistive asymmetry (MRA) from a signal, the computer program product being embodied in a non-transitory computer readable storage medium and comprising computer instructions for:
determining an estimated offset error which is an estimate of the error due to offset in the signal, including by determining the estimated offset error using those portions of the signal where the magnitude of the signal is less than a first threshold and excluding at least some portion of the signal where the magnitude of the signal is greater than the first threshold from the determination of the estimated offset error;
determining an estimated signal error which is an estimate of the combined error due to offset combined with MRA in the signal, including by determining the estimated signal error using those portions of the signal where the magnitude of the signal is greater than a second threshold and excluding at least some portion of the signal where the magnitude of the signal is less than the second threshold from the determination of the estimated signal error; and
removing at least a portion of MRA from the signal based at least in part on the estimated offset error and the estimated signal error, including by subtracting the estimated offset error from the estimated signal error to obtain an estimated MRA error.

21. A computer program product as recited in claim 20, wherein a detector is used to determine the estimated offset error and/or estimated signal error.

22. A computer program product as recited in claim 20, wherein:
the computer instructions for removing at least a portion of MRA further include computer instructions for using the estimated MRA error to adjust, after processing by a variable gain amplifier, an amplified signal; and
the computer program product further includes computer instructions for removing at least a portion of an offset, including by using the estimated offset error to adjust, prior to processing by the variable gain amplifier, an unamplified signal.

23. A computer program product as recited in claim 20, wherein the first threshold and the second threshold are set to the different values.

24. A computer program product as recited in claim 20, wherein removing at least a portion of MRA includes using an update equation MRA of mra=mra+Kmem, where:
mra is the MRA compensation signal;
Km is the loop gain;
when the magnitude of the signal at time i is less than the first threshold, em is set to 0; and
when the magnitude of the signal at time i is greater than the second threshold, em is set to the estimated signal error at time i minus the estimated offset error at time j.

25. A computer program product as recited in claim 24, wherein the estimated offset error at time j is the most recently determined estimated offset error prior to the determination of the estimated signal error.

26. A computer program product as recited in claim 20, wherein the estimated offset error is an average of two or more estimated offset errors.