Perpendicular magnetic recording (PMR) in the hard disk drive is approaching its physical limits. In an earlier work, the dedicated servo (DS) recording system ...
IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 10, OCTOBER 2015
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Signal Processing for Dedicated Servo Recording System Yibin Ng, Kui Cai, Kheong Sann Chan, Moulay Rachid Elidrissi, Maria Yu-Lin, Zhi-Min Yuan, Chun Lian Ong, and Shiming Ang Data Storage Institute, A∗ STAR (Agency for Science, Technology and Research), Singapore 117608 Perpendicular magnetic recording (PMR) in the hard disk drive is approaching its physical limits. In an earlier work, the dedicated servo (DS) recording system has been proposed to provide continuous position error signal for servo, enable higher servo sampling rate, and improve the overall servo performance. A further benefit is that the DS layer results in surface area savings at the data layer. However, it was also reported that the embedded servo layer introduces baseline variation and non-linear transition shift (NLTS) to the readback signal of the data layer. In this paper, we propose novel signal processing techniques to improve the bit error rate (BER) in DS recording. The synchronous averaging technique is proposed to improve the BER in the presence of baseline variation distortions. Further, the servo and data-dependent noise prediction method is proposed to mitigate the effect of the NLTS. Through the use of these techniques the linear density loss from the conventional PMR media is reduced. Index Terms— Data-dependent noise prediction, dedicated servo (DS), DS media, non-linear transition shift (NLTS), perpendicular magnetic recording (PMR), servo and data-dependent noise prediction (SDDNP).
I. I NTRODUCTION ERPENDICULAR magnetic recording (PMR) is approaching its areal density (AD) limit at around 1 Tb/in2 [1]. Shingled writing [2] is able to maintain the write ability on PMR media and further extend the AD growth of the PMR. With almost constant grain size or cluster size in PMR, to prevent a large media signal-to-noise ratio penalty, this AD growth has to come from an increase in track density. It is shown in spinstand studies that shingled magnetic recording (SMR) can increase the AD by 30%, compared with conventional PMR [3]. However, this AD gain on the spinstand may not be possible in actual drive working environment with mechanical vibrations. When there is an offtrack-induced mechanical disturbance during the writing process, the writing track squeezes into the adjacent track. If the track width of the adjacent track is less than the squeeze to death width in the 747 curve, hard failure occurs. Therefore, the servo performance during the writing process is the key for SMR to realize the AD capability of the head and medium. To enable higher servo sampling rate and improve the servo performance, the dedicated servo (DS) recording system was proposed [3]. In DS recording, an additional magnetic recording layer is added between the data recording layer and soft magnetic underlayer of the PMR media. This additional recording layer is used to record the servo information only. DS provides a continuous position error signal (PES), which enables real time monitoring of position error, and results in improved track squeeze performance in the drive. With DS, the higher track density is achievable. Furthermore, nearly all the surface of the data recording layer can now be dedicated for data-recording, thus achieving higher AD. However, the servo layer in the DS recording system introduces distortions to the readback signals of the data layer [3]. The transitions of the servo patterns result in baseline variation
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Manuscript received March 16, 2015; revised May 17, 2015; accepted July 6, 2015. Date of publication July 15, 2015; date of current version September 16, 2015. Corresponding author: Y. Ng (e-mail: ng_yibin@ dsi.a-star.edu.sg). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TMAG.2015.2456851
in the readback signal of the data layer. Since this baseline variation is deterministic and repeats with a period equal to that of the servo pattern, it can be estimated from the readback signals. In this paper, we propose the synchronous averaging technique to mitigate this linear distortion. We also performed reader asymmetry correction to correct the observed asymmetry in the signal. Furthermore, the dc signal from the servo layer results in a non-linear transition shift (NLTS) on the readback signals of the data layer. In [4], the mean-adjusted data-dependent noise prediction (MA-DDNP) detector has been proposed to combat the channels affected by NLTS. In this paper, we first investigate the performance of DS recording with MA-DDNP. In conventional MA-DDNP, given the same data pattern, the noise characteristics are assumed to be the same within the readback signals of each data sector. However, in DS recording the noise characteristics can change depending on the polarity of the magnetization in the servo layer. In this paper, we propose an improvement to the MA-DDNP detector by modifying the noise component of MA-DDNP to consider the magnetization polarity of the servo layer. We call this servo and data-dependent noise prediction (SDDNP). The rest of this paper is as follows. In Section II, we introduce the staggered servo pattern used in DS recording and its effects on the readback signal on the data layer. Sections III–V propose various signal processing techniques to mitigate the effects of these distortions. Section VI shows the bit error rate (BER) results and Section VII concludes this paper. II. D EDICATED S ERVO R ECORDING S YSTEM In the servo layer of the DS medium, the staggered dc+/dc− servo pattern is used. This is shown in Fig. 1. The four different staggered servo segments are dc+/dc−, dc+, dc−/dc+, and dc−. This staggered servo pattern introduces distortion to the readback signal of the data recorded on the data layer. The two main sources of distortion [3] are: 1) transitions of servo signal causing a baseline jump in the readback signal of the data layer and 2) servo signal-induced transition shift at data layer. For the servo signal transitions causing baseline jump in the data readback signal, this is essentially a linear distortion which can be cancelled out from the readback signals.
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Fig. 1.
IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 10, OCTOBER 2015
Staggered dc+/dc− servo pattern aligned with the data tracks.
Fig. 3.
Estimated linear distortion signal before and after LPF.
sectors, each of length 33 289 bits. If we denote the readback (i) signal of each of these data sectors as rk , where i takes values 0 to 47 and k takes values 0 to 33 288, then the linear distortion signal lk is estimated as 1 (i) lˆk = rk . 48 47
Fig. 2.
Distorted readback signal from the data layer of the DS medium.
Fig. 2 shows the readback signal of DS media obtained from spinstand. This corresponds to one sector of data bits of length 32 768, with an additional 511 preamble bits and 10 postamble bits. As can be observed, the readback signal is distorted with baseline variations. Given the servo pattern, this linear distortion is deterministic and it repeats with a period equal to that of the staggered servo pattern. In Section III, we propose the synchronous averaging technique to deal with this linear distortion. The second issue is that in DS medium, the servo signal induces a transition shift at the data layer. More specifically, the dc+ in the servo layer expands the bit length of a positively magnetized bit in the data layer. Conversely, the dc− in the servo layer expands the bit length of a negatively magnetized bit in the data layer. The result is an NLTS effect on the readback signal of the data layer. From a signal processing perspective, this NLTS effect results in a non-zero mean on the overall noise affecting the readback signal of the data layer [4]. In Section V, we propose the SDDNP detector to deal with this non-linear distortion. III. S YNCHRONOUS AVERAGING To remove the linear distortion in the signal, synchronous averaging is performed on the readback signal. The idea behind synchronous averaging is to average together sections of the readback signal waveform with a period equal to that of the underlying servo layer. This captures the effect of the servo layer on the data layer waveform averaged out over many repetitions. Once we know the average signal level of the servo layer, it is subtracted from each readback signal waveform to remove the linear distortion introduced by the servo layer. In this paper, we perform synchronous averaging as follows. From the spinstand, we obtain the readback samples of 48 data
(1)
i=0
Next, we pass lˆk through a low-pass filter (LPF) to remove the high-frequency components. The filter is designed with passband cutoff frequency at 1 MHz, using 51 taps. The estimated linear distortion signal after LPF is shown in Fig. 3. To obtain the readback signal after synchronous averaging gk , we take gk = rk − lˆk
(2)
where lˆk denotes the estimated linear distortion after LPF. We propose to obtain lˆl during the factory self-test of the hard disk drive (HDD), store it in firmware memory, and subtract it from the readback signals of each data sector when the HDD is being used in the field. Fig. 4(a) and (b) shows the readback signals before and after synchronous averaging. It can be observed that the upper and lower envelopes of the readback signal after synchronous averaging are less distorted. IV. R EADER A SYMMETRY C ORRECTION It can be observed from Fig. 4(b) that the reader asymmetry is present. To perform reader asymmetry correction, we largely follow the work of [5] with some slight modifications. Asymmetry is first defined as asymmetry =
|peak P| − |peak N| |peak P|+|peak N| 2
.
(3)
Here, peak P is defined as the average value of a cluster of readback samples identified as having the largest values. Similarly, peak N is defined as the average value of a cluster of readback samples identified as having the smallest values. These clusters are identified using the k-means clustering algorithm [6], which is a method to partition data samples into k clusters. In k-means clustering, each data sample is assigned
NG et al.: SIGNAL PROCESSING FOR DS RECORDING SYSTEM
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model for the asymmetric readback signal will be gk = dk + casym dk2 where casym = asymmetry/2. Solving (4) for dk yields −1 + 1 + 4casym gk dk = . 2casym
Fig. 4. (a) Raw readback signal from spinstand. (b) Readback signal after synchronous averaging. (c) Readback signal after synchronous averaging, reader asymmetry, and scaling correction.
(4)
(5)
Note that gk , here, is a scaled down version of gk obtained in Section III. This is necessary because dk has a nominal peak amplitude of 1, and typical values of casym are within −0.3 to 0.3 [5] which means that gk will be within a certain small range of values. Scaling down gk to gk ensures that the solution in (5) will converge. Furthermore, we scale each portion of the readback signal such that the upper and lower envelopes have less distortion. This is achieved by multiplying each portion of the readback signal corresponding to each staggered servo segment with a normalization factor. The result of the readback signal after synchronous averaging, asymmetry correction, and scaling correction is shown in Fig. 4(c). Comparing with Fig. 4(b), the upper and lower envelopes of the readback signal are now less distorted. V. S ERVO AND DATA -D EPENDENT N OISE P REDICTION The dc signal from the servo layer results in an NLTS on the readback signals of the data layer. In [4], the MA-DDNP detector has been proposed to combat the channels affected by NLTS. We first investigate the performance of DS recording with MA-DDNP. To implement the MA-DDNP, we denote the equalized channel output as k k+ yk = sk ak−I + n k ak−M (6)
Fig. 5. Readback samples after k-means clustering. The number of clusters used here is 12. Bold lines: peak P and peak N values found through a linear regression algorithm.
where sk , n k , and ak are the desired signal, noise component, and recorded data bit, respectively. The data-dependence of sk k is made explicit in (6), where ak−I is a shorthand notation for the sequence {ak−I , . . . , ak } and I + 1 = N p is the length of the equalization target. The signal sk can be expressed as N p −1 k sk ak−I = pi ak−i
(7)
i=0
to the cluster whose centroid has the shortest Euclidean distance with the data sample. The partitioned clusters are shown in Fig. 5 for one segment of the readback signal. Each data sample in Fig. 5 corresponds to one readback sample. Next, peak P and peak N values are obtained by running a linear regression algorithm [6] through the samples of the topmost and bottommost clusters, respectively. In this example, peak P and peak N have values around 61 and −54, respectively, which gives asymmetry = 0.12. An alternative to using k-means clustering will be to simply assign the largest and smallest readback samples to the peak P and peak N values, respectively. We compared these two methods and found that using k-means clustering to obtain asymmetry gives slightly better BER results. If we denote the readback signal without asymmetry as dk whose nominal peak amplitude is 1, a simplified quadratic
where [ p0 p1 . . . p N p −1 ]T are the target coefficients. k+ Similarly, the data-dependence of the n k is denoted by ak−M , for some non-negative integers and M. Denoting the predicted noise sample as nˆ k and the predictor error variance as σ p2 , the branch metric in the trellis can be shown to be k+ 2 k k+ yk − nˆ k ak−M − sk (ak−I . (8) lnσ p ak−M + k+ 2σ p2 ak−M The predicted noise sample is computed using Gauss–Markov theorem [7] L k+ k+ k+ nˆ k ak−M = E n k ak−M + f i ak−M
×
i=1 k−i n k−i ak−i−I −
k−i+ E n k−i ak−i−M (9)
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and
IEEE TRANSACTIONS ON MAGNETICS, VOL. 51, NO. 10, OCTOBER 2015
k−i k−i n k−i ak−i−I = yk−i − sk−i ak−i−I
(10)
where fi denotes the noise predictor coefficients and L is the length of the predictor. The trellis state is given by k+−1 ak−max(M,I +L) . From (9), one may observe that to perform k−L+ } noise prediction, noise mean values up to E{n k−L |ak−L−M are required. To compute this value, we need the data bits at ak−L+ to ak−L−M . However, as indicated earlier, our trellis state is given by ak+−1 to ak−max(M,I +L) . This means that, if max(M, I + L) < L + M, any additional data bits required can be obtained using the tentative bit decisions stored in the survivor paths. The number of states in the trellis is given by 2+max(M,I +L) . Further, the predictor error variance σ p2 is given by k+ k+ 2 k+
a σ p2 ak−M = E n k − nˆ k ak−M (11) k−M . From (9), we observe that in MA-DDNP, the noise characteristics depend only on the data pattern. However, in DS recording, the noise characteristics can change depending on the polarity of the magnetization in the servo layer. Therefore, we propose an improvement to the MA-DDNP detector by modifying the noise component of MA-DDNP to consider the magnetization polarity of the servo layer. We call this SDDNP. To facilitate the implementation of SDDNP, we define ck as ⎧ 1, if ak is within servo pattern dc−/dc+ ⎪ ⎪ ⎪ ⎨2, if ak is within servo pattern dc− ck = (12) ⎪ 3, if ak is within servo pattern dc+/dc− ⎪ ⎪ ⎩ 4, if ak is within servo pattern dc+. Subsequently, we modify (6) to be k k+ + n k ak−M , ck . yk = sk ak−I
(13)
Clearly in (13), the noise component n k is now dependent on ck , in addition to the data pattern. Furthermore, the branch metric in the trellis is now given by k+ k 2 k+ yk − nˆ k ak−M , ck − sk ak−I . (14) lnσ p ak−M , ck + k+ 2σ p2 ak−M , ck The predicted noise sample Gauss–Markov theorem [7]
nˆ k
is
computed
using
L k+ k+
k+ nˆ k ak−M , ck = E n k ak−M , ck + f i ak−M , ck i=1
k−i+ k−i
× n k−i ak−i−I − E n k−i ak−i−M , ck (15) where f i denotes the noise predictor coefficients and L is the length of the predictor as before. There are no changes to k+−1 the trellis state, given by ak−max(M,I +L) . There are also no changes to the number of states in the trellis. However, now a different set of predictor coefficients f i have to be used to compute the branch metric whenever ck changes. Furthermore, the predictor error variance σ p2 is given by k+ k+ 2 k+
, ck = E n k − nˆ k ak−M , ck ak−M , ck . (16) σ p2 ak−M
Fig. 6.
Readback signal with the corresponding ck identified.
The drawback of the SDDNP scheme can be observed from (15) and (16), whereas in the conventional MA-DDNP we need to store 2+M+1 values of σ p in memory, with the SDDNP we now need to store 4 × 2+M+1 values of σ p . Similarly, for the predictor coefficients fi , previously we need to store L × 2+M+1 values in memory using MA-DDNP. Using SDDNP, this number is increased to 4 × L × 2+M+1 . To identify the ck corresponding to each data bit, we can use the PES demodulated from the staggered dc+/dc− servo pattern [3, Fig. 11]. The square PES waveform can be utilized as a clock reference signal to keep track of which of the servo segments the reader is positioned at. Alternatively, we can identify ck using the linear distortion signal found in the synchronous averaging process. We can cross-correlate the estimated linear distortion after LPF signal in Fig. 3 with the readback signal and identify the time lag of maximum correlation. Thereafter, we can align the linear distortion signal with the readback signal and identify ck accordingly. Fig. 6 shows an example of the readback signal with the corresponding ck identified. VI. BER R ESULTS The amount of linear density loss between the DS medium and the PMR medium is head dependent. For the same set of comparing media, some heads have very small linear density loss but other heads may have larger linear density loss. In [3], for the same BER performance, one head showed no linear density loss between the DS medium and the PMR medium. Tested by a few heads, the majority of the heads showed a linear density gap between 4% and 6% between the two media. In this paper, we chose the head with the largest linear density loss and try to minimize the loss using the various signal processing techniques described above. To obtain the BER performance of the DS media, we first write 64 data sectors each of length 33 289 bits, using the spinstand. The data are written at three different linear densities, namely, 1497, 1697, and 1894 kilo flux change per inch (KFCI). Next, the corresponding readback signals are collected, timing recovery is performed, and the signals are downsampled to be processed at baud rate. We then use the first 48 data sectors as the training set to train the MA-DDNP
NG et al.: SIGNAL PROCESSING FOR DS RECORDING SYSTEM
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TABLE I L INEAR D ENSITIES A CHIEVABLE
Fig. 7. BER performance of the DS medium versus conventional PMR medium.
detector, for a given combination of L, , M, and target length. The last 16 data sectors are then used to compute the BER, based on the predictor coefficients computed in the first 48 data sectors. This process is repeated for all possible combinations of L, , M, and target length, with the constraint that the number of trellis states equals 64. The best BER found through this process is shown in our plots below. Fig. 7 shows the BER results. The “1. DS, MA-DDNP” curve represents the BER results of DS medium with the staggered servo pattern, using the MA-DDNP detector. It can be observed that the SDDNP achieves a reasonable performance improvement over MA-DDNP, even without using synchronous averaging, reader asymmetry, or scaling correction (compare curves 1 and 2). By mitigating the linear distortion, a significant performance improvement is achieved using synchronous averaging (curves 3 and 4). Further, we observe that the reader asymmetry and scaling correction provide only a marginal performance improvement (curve 5). Also plotted for comparison is the BER performance of the conventional PMR medium. Depending on the readback signal and linear density, there are different combinations of L, , M, and target length that give the best/lowest BER. For example, for curve “1. DS, MA-DDNP,” at all three linear densities plotted, the optimum (i.e., give lowest BER) values of L, , M, and N p are, respectively, 3, 2, 4, and 2. As another example, for curve “6. PMR, MA-DDNP,” at linear density 1497 KFCI, the optimum values of L, , M, and N p are, respectively, 5, 0, 5, and 2. One can verify that both the combinations above give 64 trellis states. For comparison purposes, we also plotted the linear densities (KFCI) achievable in Table I. Shown in brackets are the linear density loss from the PMR medium. At raw BER of 10−2 , our various signal processing techniques have reduced the linear density loss with respect to PMR medium
from 8.1% to 5.4%. Similarly, at raw BER of 10−3 , the linear density loss is reduced from 13.1% to 8%. Despite this linear density loss, with better servo performance the DS recording system is able to increase the track density. Furthermore, there is surface area saving at data layer due to relocation of the servo wedges to the servo layer. This saved data area can be used to record more data for capacity increment. For example, using the linear densities in Table I at BER 10−2 , and assuming 3% surface area savings, a quick calculation will show as long as there is a 2% increase in track density we can break even in terms of AD. Any further increase in track density will result in AD gain. VII. C ONCLUSION The DS recording system is proposed to provide continuous PES for servo, and to improve the servo sampling rate and overall servo performance. Unlike the conventional servo that has limited servo sampling frequency due to the consideration of surface area occupation, the DS does not have such a limitation. The higher servo sampling rate is able to increase the servo bandwidth and have better rejection of mechanical disturbance, where the servo performance is improved. Furthermore, the DS layer enables surface area saving at the data layer. However, the staggered servo pattern written on the servo layer introduces various linear and non-linear distortions to the readback signal of the data layer. In this paper, we proposed the synchronous averaging, reader asymmetry correction, scaling correction, and SDDNP techniques to mitigate these distortions. Through the use of these methods we reduced the linear density loss from PMR media from 8.1% to 5.4% at BER 10−2 , and from 13.1% to 8% at BER 10−3 . R EFERENCES [1] H. Katada et al., “Head/media integration challenge towards 1 Tb/in2 perpendicular recording,” IEEE Trans. Magn., vol. 46, no. 3, pp. 798–803, Mar. 2010. [2] R. Wood, M. Williams, A. Kavcic, and J. Miles, “The feasibility of magnetic recording at 10 Tb/in2 on conventional media,” IEEE Trans. Magn., vol. 45, no. 2, pp. 917–923, Feb. 2009. [3] Z.-M. Yuan et al., “Dedicated servo recording system and performance evaluation,” IEEE Trans. Magn., vol. 51, no. 4, Apr. 2015, Art. ID 3100507. [4] Z. Wu, P. H. Siegel, J. K. Wolf, and H. N. Bertram, “Mean-adjusted pattern-dependent noise prediction for perpendicular recording channels with nonlinear transition shift,” IEEE Trans. Magn., vol. 44, no. 11, pp. 3761–3764, Nov. 2008. [5] F. Rezzi and G. Patti, “Asymmetry correction for a read head,” U.S. Patent 6 043 943, Mar. 28, 2000. [6] T. M. Mitchell, Machine Learning. New York, NY, USA: McGraw-Hill, 1997, chs. 6–8. [7] L. L. Scharf, Statistical Signal Processing. Reading, MA, USA: Addison-Wesley, 1991, p. 300.
