Opposite Partial Response Filter for Shingled Magnetic Recording Systems

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IEEE MAGNETICS LETTERS, Volume 11 (2020) 6503604

Information Storage

Opposite Partial Response Filter for Shingled Magnetic Recording Systems

Chi Dinh Nguyen

^1,2

, Thu Phuong Nguyen

³

, and Sinh Cong Lam

⁴

1Faculty of Electrical and Electronic Engineering, Phenikaa University, Hanoi 12116, Vietnam

2Phenikaa Research and Technology Institute, A&A Green Phoenix Group JSC, Hanoi 11313, Vietnam

3Le Quy Don Technical University, Hanoi 100000, Vietnam

4Faculty of Electronics and Telecommunication, VNU University of Engineering and Technology, Hanoi 11310, Vietnam

Received 21 May 2020, revised 9 Jun 2020, accepted 17 Jun 2020, published 22 Jun 2020, current version 7 Jul 2020.

Abstract—Shingled magnetic recording (SMR) is regarded as the most influential technology for the next-generation magnetic recording systems. The SMR tracks are partly overlapped by each other, and the SMR systems can obtain higher area densities by increasing track per inch density. As a result, this brings more interference from the adjacent sidetracks, i.e., intertrack interference (ITI) while reading the home track. In this letter, we are interested in applying the filtering process to the squeezed tracks before recording to improve the quality of retrieved data. The preprocessing is to reduce the effect of unwanted signals from the sidetracks on the home track. The results show that the SMR system’s performance is vastly improved even under the extremely severe effects of the ITI.

Index Terms—Information storage, shingled magnetic recording, partial-response maximum likelihood, intertrack interference.

I. INTRODUCTION

There are three major technologies for the next-generation magnetic recording systems, namely, bit-patterned media recording (BPMR), energy-assisted magnetic recording (EAMR), and shingled magnetic recording (SMR) [Wood 2009, Gao 2018]. Two former technologies can push the area density (AD) beyond 1 Tb/in², but their complexity of manufacturing is very challenging. The BPMR systems require significant investment in the production of the patterned media and synchronization. The EAMR system, whereas, needs some extra components, such as heat or microwave parts, to aid the recording and retrieving information. Under the technical circumstances, the SMR is regarded as the most influential technology for the next-generation magnetic recording systems. The shingled recording technology might be termed as an intermediary step before the BPMR and EAMR’s technological challenges are resolved. The SMR not only poses fewer technical challenges but also requires lower investments [Greaves 2009, Amer 2011].

In the SMR systems, the tracks are partially overwritten on the previous existing tracks, thereby increasing the track per inch (TPI) of the system. A certain amount of successive overwritten tracks is packed as a zone. The last track of the zone is not overwritten by the others. There is an existing guard between two consecutive zones.

Fig. 1 illustrates the architecture of the SMR system compared to the traditional recording system. By squeezing tracks close together to obtain higher AD, the effect of intertrack interference (ITI) for the SMR system is immeasurably challenging to control and significantly degrades the bit-error-rate (BER) performance. It is important to note that there is existing writing ITI and retrieving (reading) ITI. The effect of ITI during the reading process is a significant cause of the degradation of the quality of the readback waveform. The main reason

Corresponding author: Chi Dinh Nguyen (e-mail: chi.nguyendinh@phenikaa- uni.edu.vn).

Digital Object Identifier 10.1109/LMAG.2020.3004298

Fig. 1. Shingled magnetic recording system versus traditional recording system.

for the ITI reading is that the read head senses unwanted signals from one or both adjacent tracks at the same time during the reading. The effect of ITI can be reduced by using narrower specified-designed readers, but they increase reader noise and media noise [Elidrissi 2014].

Several works have been suggested to overcome the challenges of the SMR system. The media noise analysis for the SMR systems was presented in Shi [2011], Galbraith [2014], and Wang [2015].

Thereby, besides the ITI, the measured noise from the home track can be decomposed into three components, namely, electronic noise, transition noise, and nontransition noise. The research works on the effects of the skew angle in the SMR have been shown in Elidrissi [2014] and Yu [2014]. The designs of the SMR for the BPMR and two-dimensional magnetic recording media have been introduced in Todd [2012] and Wang [2013]. In Ozaki [2010] and Kumar [2013], ITI cancelation based on the cross-correlation has been intended to improve the system performance. The idea of estimating ITI and subtracting ITI from the readback signal has also used in Hatatsch [2011] and Todd [2012]. The shuffled multitrack detection for the SMR channels, where three detectors are deployed simultaneously,

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6503604 IEEE MAGNETICS LETTERS, Volume 11 (2020)

Fig. 2. Block diagram of the projected model with opposite PR filter.

was projected in Han [2014]. A concatenation of three codes has been designed to tackle the effect of ITI in the SMR systems [Tang 2016].

Moreover, the effective approaches to mitigating the ITI effect for the BPMR systems can also be applied to the SMR systems, such as Kovintavewat [2014], Nguyen [2015], and Koonkarnkhai [2019].

In this letter, we are interested in applying the filtering process to the squeezed tracks before the recording process. The preprocessing is to reduce the effect of unwanted signals from the sidetracks on the home track. Notably, the projected model requires, first, the readback signal to be equalized to a partial response (PR) target before doing the ITI cancelation at the receiver part; second, at the transmitter part, the signal on the squeezed track is passed through by a filter where its coefficients are predetermined as the opposite coefficients of the corresponding PR target vector at the receiver.

The rest of this letter is organized as follows. The projected system model is introduced in Section II, and an analysis of the projected solution is also presented in this part. We then present the simulation results in Section III. Finally, the concluding remarks are shown in Section IV.

II. PROJECTED MODEL WITH APPLYING THE OPPOSITE PR FILTER

A. Preliminaries

A block diagram of the projected model is shown in Fig. 2. Through the track interface, the user data are transferred in tracks. We assumed that each zone of the SMR system includes two tracks, N+1th track (squeezed track) and Nth track. We considered that the isolated re- producing step-response waveform at the reading point is given by g(t )=A·tanh((ln 3/T50)·t ), where A is the half of its maximum amplitude, and T50is the time required for g(t) increases from –A/2 to A/2 [Ozaki 2010]. The normalized recording density K is defined as K =T50/Tb,where Tb=1 is the recording bit interval. We used K=1.3 herein. The noise at the reading point includes additive white Gaussian noise (AWGN) and jitter noise. A ratio of 0.2:0.8 between AWGN power and jitter noise power was used in this study. The signal-to-noise ratio (SNR) is defined as follows:

SNR=10 log₁₀

A² σ_w²+σ_jn²· |g(t )|²

(1) whereσ_w²is the AWGN noise power,σjn²is the jitter noise power, g(t ) is differentiated step response, and|g(t )|²indicates the power of g(t ).

Moreover, it is essential to note that the correlation method has been deployed to detect and cancel the ITI herein. Therefore, for simplicity while without loss of generality, it is assumed that the information on the N+1th track is detectable and known in some previous read operation and stored in, for instance magnetic random-access memory [Kumar 2013]. The target of this study is to detect the Nth track’s signal under the ITI effect from the N+1th track.

B. Projected System Model

During the reading process, the channel output r^N[k] is equalized to the PR target of f_r(i)=[1221],i=[0,3], which corresponds to the PR polynomial F (D)=1+2D+2D²+D³ to match the SMR channel, where D indicates the delay operator. The equalizer coefficients are trained and updated based on the least mean square algorithm. The equalization is one of the two main processes of the partial-response maximum-likelihood technique, which is commonly used in data storage systems nowadays. The ITI effect on the output of the equalizer is eliminated before proceeding to the channel detector.

The equalizer output on Nth track z^N[k] can be expressed as follows:

z^N[k]= L i=−L

h^N[i]·a^N[k−i]+ L i=−L

h^N+1[i]·a^N+1[k−i]+w^N[k]

(2) where h^N[i] and h^N+1[i] are the equalized channel response of length 2L+1 for the Nth track and N+1th track, respectively. a^N[k] and a^N⁺¹[k] are user data sequence for the Nth track and N+1th track.

w^N[k] is total noise for the Nth track. The second term is the ITI effect from the N+1th track, and it needs canceling to improve the performance. The correlation metric for the N+1th track can be calculated as follows:

ξ^N⁺¹[m]=E

z^N·a^N⁺¹

= T k=1

z^N[k]·a^N⁺¹[k−m] (3)

where T is the number of samples taken for the correlation process; the value of m is chosen heuristically. Based on (2), (3) can be rewritten as follows:

ξ^N⁺¹[m]= T

k=1

⎛

⎜⎜

⎝ L i=−L

h^N[i]·a^N[k−i]

+ ^L

i=−L

h^N⁺¹[i]·a^N⁺¹[k−i]+w^N[k]

⎞

⎟⎟

⎠·a^N⁺¹[k−m]

= L i=−L

h^N[i]

T k=1

a^N[k−i]·a^N⁺¹[k−m]

+ L i=−L

h^N⁺¹[i]

T k=1

a^N⁺¹[k−i]·a^N⁺¹[k−m]+ T

k=1

w^N[k]

·a^N⁺¹[k−m]. (4)

The first and the third terms on the right-hand side side are approxi- mately equal to 0, since the user data sequences are not correlated with each other, and not correlated to the total noise sequencew^N[k] either.

Thereby, (4) can be represented as ξ^N⁺¹[m]=

L i=−L

h^N⁺¹[i]

T k=1

a^N⁺¹[k−i]·a^N⁺¹[k−m]=T·h^N⁺¹[m]

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IEEE MAGNETICS LETTERS, Volume 11 (2020) 6503604

where T

k=1

a^N⁺¹[k−i]·a^N⁺¹[k−m]=

T if i=m 0 if i=m. . Therefore, the estimation of h^N⁺¹can be found out as

h^N+1=

ξ^N⁺¹[m^N+1]ξ^N⁺¹[m^N+1+1]. . . ξ^N⁺¹[m^N+1+2L]

T (6)

where m^N⁺¹=arg max

m s^N⁺¹[m], and s^N⁺¹[m]=^2L

i=0|ξ^N⁺¹[i+m]|.

From (2) and (6), the output of the ITI canceler is computed as y^N[k]=z^N[k]−

L i=−L

h^N+1[i]·a^N+1[k−i]. (7)

The signal after removing the ITI is passed to a soft-output Viterbi algorithm detector, which does the maximum-likelihood detection, to reproduce the original user data. Therefore, the ITI cancelation is carried out through three steps: calculate the correlation metric for the N+1th track, construct the estimation of the equalized channel response for the N+1th track, and remove the ITI effect from the N+1th track.

As shown in the next section, by comparing the histograms of the channel output in cases of existing the effect of ITI and nonexisting the effect of ITI, we recognize that under the effect of ITI, the histogram of the channel output is significantly different compared to the case without the effect of the ITI. Therefore, we propose applying the filter to the squeezed track, aiming to reduce the ITI effect from the N+1th track and make the histogram of the channel output close to that of the case without the effect of the ITI.

As shown in Fig. 2, the squeezed track is passed through a PR channel where its coefficients are predetermined as the opposite coefficients of the corresponding PR target vector at the receiver. The signal at the output of the opposite PR filter can be expressed by

a^N⁺¹[k]=a^N⁺¹[k]⊗ f_t(i)

β (8)

where f_t(i)=[−1−2−2−1],i=[0,3];βis an attenuation term that ensures that the signal on the squeezed track does not ruin the signal on the Nth track after filtering, and the operator⊗indicates 1-D convolution.

III. SIMULATION RESULTS

In this letter, we considered that the N+1th is overlapped by v, and the TPI is increased by 1/(1−v). The values of L and m are chosen heuristically. We used L=2 and−20≤m≤20 in this letter. The attenuation factorβis equal to 100.

We first considered the histograms of the received intensities at the output of the SMR channel. Fig. 3 shows the histograms of the signal without the effect of ITI, the signal with the effect of ITI but not using the opposite PR filter, and the signal with the effect of ITI and using the opposite PR filter. It is straightforward to recognize that the histogram of the signal with the effect of ITI is notably different from that of the signal without the effect of ITI. The difference indicates a severe effect of the ITI from the sidetracks. After applying the opposite PR filtering, the histogram of the signal is quite similar to that of the signal without the effect of ITI. As a result, the projected scheme is

Fig. 3. Histograms of received intensities at channel output, wherew:

with andwo: without.

Fig. 4. Eye patterns at the equalizer output,v=0.15. (a) Signal without filter. (b) Signal with filter.

efficient in removing the ITI effect for improving the performance.

The histograms are picked up at the overlap v of 0.1.

Fig. 4 shows the eye patterns at the equalizer output, where Fig. 4(a) and (b) show the eye patterns without and with the filter, respectively.

As shown in Fig. 4(a), the eye pattern opening (EPO) of the signal without the filter is almost 0. This indicates that the signal on the Nth track is severely distorted by the SMR channel. The EPO of the

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6503604 IEEE MAGNETICS LETTERS, Volume 11 (2020)

Fig. 5. BER comparison.

signal with the filter is, whereas, significantly improved in Fig. 4(b).

Therefore, the effect of ITI can be well eliminated by using the filter.

The eye patterns are taken at v=0.15.

Fig. 5 shows the BER performance comparison in three cases; the received signal without using the ITI canceller, the received one with using the ITI canceller but no using the filter [Kumar 2013], and the one with using ITI canceller and the opposite PR filter (projected scheme).

The ITI canceller is designed based on cross-correlation, as mentioned earlier. The projected model provides the most effective performance, followed by the model of using only the ITI canceller and the model of not using the ITI canceller, respectively. The quality of the projected model is very outstanding for all cases. For instance, at 10⁻⁵BER, the proposal provides gains of about 2 and 5 dB higher than those of the model of using only the ITI canceller and the model of not using the ITI canceller. Especially, as the effect of ITI increases (v=0.15), the performance of the model of using only the ITI canceller becomes very poor. For example, at SNR of 45 dB, it can only reach about 10⁻³BER, whereas the projected model can be obtained 10⁻⁶BER. Moreover, as shown in Fig. 5, there is an error floor for the projected model. This can be explained because of the increase in the overlap level. As the overlap level increases, the PR polynomial is not fit well. This causes the system performance to encounter the error floor in the range of 30 to 47 dB. We term that a dynamic PR target (e.g., generalized partial response) or an adapted PR target may be a better candidate as the overlap level changes. Finally, it is essential to note that the work in this letter addresses the effect of single-side ITI only; the quality of the projected scheme in the case of double-side ITI will be considered in the future works.

IV. CONCLUSION

This letter presents a novel scheme to improve the performance of the retrieved data for SMR systems. As the TPI density is increased, the ITI effect is much more severe due to the critical impact of unwanted signals from the adjacent tracks. We have demonstrated that applying a PR filter, where its coefficients are predetermined as the opposite

coefficients of the corresponding PR target vector at the receiver, to the squeezed tracks before recording improves the system performance significantly. The simulation results show that the projected scheme outperforms the earlier models for both cases of the values of overlap v

=0.1 and v=0.15. For instance, at 10⁻⁵BER, the projected model is about 5 and 2 dB better than the model without using the ITI canceller and the one with using the ITI canceller only, respectively.

ACKNOWLEDGMENT

This work was supported by the Vietnam National Foundation for Science and Tech- nology Development (NAFOSTED) under Grant 102.04-2019.307.

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