Minimum-Latency Tracking of Rapid Variations in Two-Dimensional Storage Systems

Abstract

The trend of increasing storage densities results in growing sensitivity of system performance to variations of storage channel parameters. To counteract these variations, more adaptivity is needed in the data receiver. Accurate tracking of rapid variations is limited by latencies in the adaptation loops. These latencies are largely governed by delays of the bit detector. In two-dimensional storage systems, data are packaged in a group of adjacent tracks or rows, and for some of the rows the detection delays can increase dramatically with respect to one-dimensional systems. As a result, the effective latencies in the adaptation loops preclude the tracking of rapid variations and really limit the performance of the system. In this paper, a scheme is proposed that overcomes this problem and that can be used for timing recovery, automatic gain control, and other adaptive circuits. Rapid variations for all the rows are tracked using control information from rows for which detector latency is smallest. This works properly if rapid variations are common across the rows as is the case, for example, for the two-dimensional optical storage (TwoDOS) system. Experimental results for TwoDOS confirm that the scheme yields improved performance with respect to conventional adaptation schemes

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IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 1, JANUARY 200767
Minimum-Latency Tracking of Rapid Variations
in Two-Dimensional Storage Systems
S. Van Beneden?, J. Riani?, J. W. M. Bergmans?, and A. H. J. Immink?
Department of Electrical Engineering, Eindhoven University of Technology, 5600 MB Eindhoven, The Netherlands
Philips Research Laboratories, 5656 AA Eindhoven, The Netherlands
The trend of increasing storage densities results in growing sensitivity of system performance to variations of storage channel param-
eters. To counteract these variations, more adaptivity is needed in the data receiver. Accurate tracking of rapid variations is limited by
latencies in the adaptation loops. These latencies are largely governed by delays of the bit detector. In two-dimensional storage systems,
data are packaged in a group of adjacent tracks or rows, and for some of the rows the detection delays can increase dramatically with
respect to one-dimensional systems. As a result, the effective latencies in the adaptation loops preclude the tracking of rapid variations
and really limit the performance of the system. In this paper, a scheme is proposed that overcomes this problem and that can be used for
timing recovery, automatic gain control, and other adaptive circuits. Rapid variations for all the rows are tracked using control infor-
mation from rows for which detector latency is smallest. This works properly if rapid variations are common across the rows as is the
case, for example, for the two-dimensional optical storage (TwoDOS) system. Experimental results for TwoDOS confirm that the scheme
yields improved performance with respect to conventional adaptation schemes.
Index Terms—Adaptation, minimum latency, rapid variations, two-dimensional storage.
I. INTRODUCTION
S
respect to disc tilt, signal-to-noise ratio, SNR) and increased
sensitivity to piece-wise and temporal variations of physical
storage channel parameters are consequences of this trend and
necessitate an increasing amount and an increasing accuracy of
adaptivity (e.g., timing recovery, automatic gain control, and
other adaptive loops) in the data receiver [2][4]. This accuracy
is especially hard to accomplish for the tracking of rapid varia-
tions, and is limited by latencies in the adaptation loops.
Another consequence of the increasing densities is that SNRs
decrease. As a result, the bit-detector that forms part of the data
receiver needs to become more complex to maintain detection
reliability. This increased complexity inevitably increases the
detection delay. Because this delay contributes to the overall
latency intheadaptation loops,it will putan increasingly severe
limit on their capabilities to track rapid variations.
A widely adopted solution to improve these tracking capabil-
ities is to base adaptation on tentative decisions with a limited
detection delay instead of on final bit decisions [5]. This limited
delayenablestheadaptationloopstotrackrapidvariations.This
solution, however, becomes cumbersome as SNRs decrease, as
it becomes more difficultto producetentativedecisions with ac-
ceptable reliability and delay.
Besides the increasing density, there is also a general trend of
increasing data rates [6]. The development of two-dimensional
(2-D) storage systems fits with this trend and permits exploita-
tion of parallelism. The parallelism is achieved by packaging
TEADILY increasing storage densities are a clear trend in
storage systems [1]. Reduced margins (e.g., margins with
Digital Object Identifier 10.1109/TMAG.2006.886844
Fig. 1. Examples of 2-D detectors which have varying detection delays for dif-
ferent rows.
data in a group of adjacent tracks or rows and by parallel pro-
cessing of these rows. The complexity of 2-D bit detectors in-
creases dramatically with respect to one-dimensional detectors,
andalsotheirdetectiondelayscanincreasedramatically[7],[8].
In many practical systems, the 2-D detector is split into sev-
eral smaller units to limit overall complexity [9]–[11]. A couple
of schematic models of such detectors reported in literature are
showninFig.1.Inthisfigure,sevenparallelbitrowsare shown:
two “outer” rows and five “inner” rows (rows positioned near
the center of the group of adjacent rows). The decisions of the
different units are indicated in thick black arrows. The different
units are numbered in order of execution. If the output of one
unit is used as input of a next unit (indicated by the grey ar-
rows), detection delayincreases. Differentconnections between
thedifferentunitsarepossible:a)ina“V-shape”[12](wherethe
two outer rows have the smallest detection delay); b) sequen-
tially starting from the top row [10], [13]; and c) different iter-
ations of the joint detection [7], [8], [14]. In the latter case (dif-
ferent iterations are performed), the decisions of the outer rows
will be more reliable than the ones of the inner rows during the
firstiterations becausefewerISI occursattheouter rows (dueto
0018-9464/$20.00 © 2006 IEEE
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68IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 1, JANUARY 2007
the 2-D structure, where inner row bits have more neighboring
bits than outer row bits) [15]. As a result, decisions of the outer
row during an early iteration can be used in the adaptation loops
limiting the detection delay of the outer row. For the inner row,
however, more iterations are required to achieve an acceptable
reliability, resulting in an increased detection delay for the inner
rows.
In all these detectors, the detection delay of inner data rows
adds substantial latency in the adaptation loops. In the experi-
mental two-dimensional optical storage (TwoDOS) system, for
example,thedelayfortheinnerrowsisaround100–200symbol
intervals,versusadelayofonly10–20intervalsforthesiderows
[16], [12]. As a result, the effective latencies in the adaptation
loops for these inner rows preclude the tracking of rapid varia-
tions and really limit the performance of the system.
Benefitingfromthefactthatina2-Dsystemthedelaystendto
differ per row, in this paper we propose a scheme that uses con-
trolinformationfromrowsforwhichdetectorlatencyissmallest
to track rapid variations for all the rows. The scheme works effi-
ciently if rapid variations are common across the rows, as is the
case, for example, in TwoDOS. In the proposed scheme these
rapid common variations are tracked using control information
of the rows with the minimum latency in the adaptation loop,
while the slow row-dependent variations are tracked using the
delayed control information of the specific row under consider-
ation. This scheme can be used for timing recovery, automatic
gain control (AGC), and other adaptation loops, and is analyzed
and validated experimentally. It shows improved performance
with respect to conventional adaptation loops in case substan-
tial loop-delays are present.
The scheme that is proposed in this paper is general and can
be applied to any 2-D storage system. In this paper a partic-
ular example of a 2-D storage system, namely the TwoDOS
system, is used to illustrate the design of the adaptation loops
and to provide experimental results. In Section II, a general re-
ceiver model for 2-D storage systems is discussed and a gen-
eral parameter-domain model of an adaptation loop is derived
from this receiver model. The effect of latencies on the perfor-
mance of adaptation loops is discussed in Section III. The gen-
eral scheme for minimum-latency tracking of rapid variations is
explained in Section IV. In Section V the design of first-order
loops according to the described scheme is explained, analyzed
and verified by means of simulations. These first-order loops
can be used, for example, for dc compensation and AGC. Min-
imum-latency tracking suited for timing recovery is the subject
of Section VI, where the design of second-order loops is dis-
cussed.Finally SectionVII presentsexperimentalresultsfor the
TwoDOS system. These results show that the new scheme im-
proves the performance of the system with respect to conven-
tional schemes.
II. RECEIVER MODEL
A data receiver model for 2-D storage systems is shown in
Fig. 2. Inputs of the model are
where
is the number of adjacent data rows. In magnetic
recording, for example, these replay signals are generated by
read heads. The data receiver contains a bit detector that relies
uponawell-definedrelationshipbetweenthestoreddataandthe
digitized replay signals,
Fig. 2. Data receiver model for 2-D storage system.
desireddetectorinputsignals[5].Thisrelationshipisoftenchar-
acterized by a so-called target response, and is often linear. To
approach this relationship as closely as possible, the replay sig-
nals are preprocessed by digital signal processing blocks (e.g.,
timing adjustment, prefilter, dc compensation) before they enter
thedetector.Becausephysicalparametersofthestoragechannel
(e.g., bandwidth, amplitude, dc offset, etc.) may vary in time,
adaptivity is needed to counteract the parameter variations such
that the relationship between the stored data and the detector
input signal does not vary in time and is consistent with the
targetresponse.Tothisendthereceiverincludesapreprocessing
block with several adjustable parameters (e.g., an AGC gain,
equalizer taps, etc.) that are controlled by dedicated adaptation
loops.
For each adjustable parameter, a value
adaptation block and is subsequently used in the preprocessing
blockstocounteractsystemparametervariations.Wedenotethe
ideal value of the adjustable parameter by
on the channel parameters and can hence be time-varying). Ide-
ally
should be equal to to . A difference
results in an undesired mismatch between the actual and the
desired detector input signal. Accurate tracking of
alently, minimizing
) will minimize this mismatch and as re-
sultwill improvereceiver performance. Anexample of an adap-
tive parameter is the dc-offset for a specific row. The value
the estimated dc-offset while
(possibly time-varying) dc-offset that has to be added to the in-
coming signal to eliminate any residual dc-offset in the detector
input.
The preprocessing block, the bit detector and the adaptation
block form a closed loop which comprises the individual adap-
tation loops. These loops are of the data-aided (DA) type. A DA
adaptation loop uses the detected bits as side information to fa-
cilitate adaptation. As a result the bit detector forms part of the
loop and the detection delays introduce a latency in the loop.
This latency will limit the capability of the loop to track fast
variations of . The effect of latency on the tracking capabilities
of an adaptation loop is subject of the next section.
is produced by the
(clearly depends
between and
(or equiv-
is
is the ideal dc-offset, i.e., the
III. EFFECT OF LATENCY ON LOOP BEHAVIOR
In the left part of Fig. 3, a discrete-time parameter-domain
model of an adaptation loop with latency is given [17]. This
model is valid in the tracking mode of operation. An ideal pa-
rameter value
is the first input of the model and this value can
be time-varying (the time index
of this paper for notational simplicity). A noise component
(input-referred noise) is the second input of the loop. The pur-
pose of the loop is to minimize the mismatch
is omitted in the remainder
between the
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VAN BENEDEN et al.: MINIMUM-LATENCY TRACKING OF RAPID VARIATIONS IN TWO-DIMENSIONAL STORAGE SYSTEMS 69
Fig. 3. (a) General parameter-domain model of an adaptation loop with a loop
filter characterized by the transfer function ????. This loop is sampled at the
baud rate ???, i.e., ?
corresponds to a delay of ? seconds. b) Loop filters of
first-order adaptation loop and of second-order high-gain adaptation loop.
ideal parameter value
timate , a loop filter with transfer characteristic
by an ideal integrator is used. In the right part of Fig. 3 different
types of loop filters are shown. In most cases (e.g., for dc con-
trol, automatic gain control, adaptive equalization) a first-order
loop is sufficient. In this case, the loop filter is just a multiplier:
, whereis the total gain of the loop. Timing
recovery, however, requires a second-order adaptation loop in
order to be able to track frequency variations. To this end, the
loop filter needs to be extended with an ideal integrator and a
second gain
, which determines together with
havior of the loop.
In the model, a delay of
symbol intervals is present which
mimics the overall latency in the loop. The model has a low-
pass frequency characteristic. If
the slow variations but not the fast ones. In this way also the
high-frequency noise components
and its estimate . To generate this es-
followed
the be-
changes, then will track
are rejected.
A. Loop Behavior
As the dynamic properties of the loop do not depend on the
input-referred noise , we neglect this noise for the time being.
The adaptation loop is linear and can be characterized by means
of the parameter transfer function
mismatch transfer function
inthe -domainofrespectively
Onlyfirst-orderadaptationloopsareconsideredhere.Extension
to second-order loops is straightforward. For first-order loops
the loop filter has transfer function
total gain of the loop. The mismatch transfer function
evaluated to be
and the
(the response
and totheloopexcitation ).
, whereis the
is
(1)
Let beaunitstepfunction.Then,for
be approximated as an exponentially decaying function
where
is the time constant of the loop expressed in sampling
intervals. For small
, the time constant can be expressed as
.
The mismatch magnitude responses for varying time con-
stants
and loop-delaysare shown in Fig. 4. In the left part
of the figure, the response is shown for varying time constants
,themismatchcan
,
Fig. 4. Mismatch transfer magnitudes of a first-order adaptation loop as func-
tion of the normalized frequency ? ? ???????. a) No loop-delay, ? ? ?
(left part). b) Time constant ? ? ??? (right part).
and zero delay
widthoftheloopdecreases.Theequivalentbandwidthisdefined
by the normalized loop cutoff frequency
normalized frequency where the amplitude of the transfer func-
tion is
3 dB. In the right part of Fig. 4, the magnitude response
of the mismatch transfer function is shown for a given time con-
stant
and for varying loop-delays
resonance peak appears near the cutoff frequency
creasing loop-delays. If the ideal parameter value
content in this frequency region, the total mismatch power will
increase due to this resonance peak (in other words, the loop en-
hances rather than suppresses variations around this frequency).
If the delay is increased too much, the loop can become un-
stable. The edge of the stability region demarcates a relation-
ship between the loop-delay and the time constant of the loop:
[18]. This relationship reveals the smallest
allowable time constant for a given loop-delay.
The responses shown in Fig. 4 indicate that in a practical
system the presence of a large loop-delay can influence the
choice of a proper time constant considerably. In general, to
limit resonance effects or even to avoid instability, a larger time
constant with respect to the zero loop-delay case is needed,
whichwillmakethelooplesscapableoftrackingfastparameter
variations.
. By increasing , the equivalent band-
, i.e., the
. An increasing
for in-
has spectral
B. Gradient Noise
Gradient noise is defined as the additional mismatch in the
adaptation loop due to the input-referred noise . This gradient
noise does not introduce a bias in the estimate
the variance of the mismatch
but influences
:
(2)
where
sumed to be white and Gaussian, then the mismatch variance
can be expressed as
is the normalized equivalent noise bandwidth (if the loop-delay
is omitted, otherwise the noise bandwidth
higher due to the resonance effect) and
the input-referred noise . In practice,
is the power spectral density of . If is as-
, where
will be slightly
is the variance of
is much smaller than
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70IEEE TRANSACTIONS ON MAGNETICS, VOL. 43, NO. 1, JANUARY 2007
Fig. 5. Spectral content of different inputs of a control loop. The input param-
eter value ? is assumed to consist of two components: ?
more the spectrum of the noise ? is also shown.
and ?
. Further-
unity, hence
pressed as
. The variance of can then be ex-
(3)
From this equation, it is clear that
which means that the mismatch variance will increase for de-
creasing time constants.
is proportional to,
IV. MINIMUM-LATENCY ADAPTATION
In a 2-D storage system, the detection delay can be especially
large for the inner rows. This large delay results in a large la-
tency in the adaptation loops for these rows. As described in
Section III, this latency makes the loops incapable of tracking
rapid parameter variations. In a 2-D system like the TwoDOS
system, it is possible to use control information from bit rows
with smaller latencies to counteract these rapid variations. The
principle of using control information with the smallest latency
is referred to as the minimum-latency adaptation strategy. As a
consequence, the aim is to design adaptation loops that make
use of the minimum-latency control information to counteract
rapid variations in all rows.
The minimum-latency adaptation strategy is only applicable
if rapid variations of system parameters are common for all the
rows. Subject to this basic premise, the overall model of the
ideal parameter value
should be:
is a slowly varying, row-dependent component (with highest
frequency
) and is a rapidly varying component
which is common for all the rows (highest frequency
and ). The parameters of all rows must show
this behavior: possibly different low-frequency content but
the same high-frequency content. The spectral content of the
ideal parameter value
together with the input referred noise
(assumed to be Gaussian and white) is sketched in Fig. 5.
The basic premise that rapid variations are common across
the rows can be validated experimentally for the TwoDOS
system. By way of illustration we consider the dc control loops
[19], which serve to counteract time-varying dc-offsets in the
rows. Here, dc-offset estimates
by separate adaptation loops where the gain values
chosen such that
is able to track fast variations of the ideal
dc-offset values
(in the experimental estimates
, where
for every row are generated
are
Fig. 6. Experimentally estimated spectral content of dc-offsets in TwoDOS
system:the dc-offsetestimate ?
of the innerrowand itsdifferent components:
?
and ?
. Also, the spectrum ? of the input noise ? is shown.
was found to be a proper value). Because
tude up to the normalized loop cutoff frequency
the spectral content of
up to (if noise is neglected). The spectral content of
the inner-row dc-offset estimate
estimate
is composed of different components which are
also shown in the figure. The common dc-offset component
is calculated by averaging the dc-offsets over all rows.
The row-dependent dc-offset component
subtracting
from. Finally,thepowerspectraldensity
of the input-referred noiseis obtained by taking the Fourier
transform of the difference between the ideal and the actual
detector input. For low frequencies, the row-dependent com-
ponent
is the most important component of
frequencies
determines. For even higher frequencies the offset estimate
is determined by the input-referred noise
offset component
can be explained by the fact that certain
channel parameters (e.g., the amount of defocus and the cover
layer thickness) are common across the adjacent rows. For the
TwoDOS system, the cover layer thickness exhibits variations
that extend over a limited amount of bits (100–1000 bits). As a
result these variations result in high-frequency common offset
variations. Other reasons for fast common channel parameter
variationsare:dust,fingerprints,scratchesonthedisc,dropouts,
etc. [20], [22]. These observations lend support to the assumed
parameter model, not just for TwoDOS but also for other 2-D
storage systems.
A basic assumption of the minimum-latency adaptation
strategy is that the common parameter value
using the minimum-latency control information. In reality,
also small and relatively slow variations occur between the
rows. In the minimum-latency adaptation strategy these slow
row-dependent components
information from the inner rows.
has unit ampli-
,
resembles the spectral content of
is shown in Fig. 6. This
is obtained by
. At higher
, the common component
. The common
is tracked
are handled by using delayed
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VAN BENEDEN et al.: MINIMUM-LATENCY TRACKING OF RAPID VARIATIONS IN TWO-DIMENSIONAL STORAGE SYSTEMS71
Fig.7. Parameter-domainmodelofthefirst-orderminimum-latencyadaptation
loops.
In Section V, the minimum-latency adaptation strategy for
first-order loops is proposed and analyzed (applicable to the
AGC loop and the dc control loop). The minimum-latency
strategy is applied to second-order loops (as used for timing
recovery) in Section VI. In Section VII, the experimental vali-
dation of the minimum-latency adaptation strategy is presented
for the TwoDOS system.
V. FIRST-ORDER MINIMUM-LATENCY ADAPTATION LOOPS
To illustrate the application of the minimum-latency strategy
tofirst-orderloops,onlytworows(insteadof
sidered for simplicity: an “outer” row with small latency and an
“inner” row with large latency. Furthermore, every row has a
separate adaptation loop. In Fig. 7, a parameter-domain model
oftheminimum-latencyfirst-orderadaptationloopsisshownto-
gether with the assumed parameter model.1The input-referred
noises
andare inputs of the model and are uncorrelated.
Furthermore, a delay of
bits is present in the inner loop to
mimic the large detection delay of the inner row. In reality, also
a small detection delay
but this delay is omitted in the model to simplify the analysis.
Thisrelativelysmalldelaywillnothaveamajorinfluenceonthe
overall loop behavior. Following the minimum-latency adapta-
tion strategy, theouter loop is dimensioned tobe fast (largeloop
gain
) and the inner loop is dimensioned to be slow (small
loop gain
).
The key innovative feature of the minimum-latency adapta-
tion strategy is the connection between the fast outer loop and
the slow inner loop. This connection (thick line in Fig. 7) pro-
videstheinnerloopwithcontrolinformationconcerningthefast
commonparameter
thatisnotyetavailableintheinnerloop
due to the delay
. As a result,
ations of
(using control information of the outer row) and
slow variations of
(using delayed control information of the
innerrow).However,duetotheconnectionaportionof
inevitablybepresentintheestimate
loop behavior is analyzed which will prove that this portion is
sufficiently small.
rows)arecon-
is present in the outer loop,
is able to track fast vari-
will
.InSectionV-A,thebasic
1In the TwoDOS system, there are two outer rows that can be used to derive
the common rapid variations from. The outputs of these outer loops are aver-
aged and the result is used in the inner rows. This procedure fully exploits all
minimum-latency information.
Fig. 8. Mismatch transfer magnitudes of the inner minimum-latency adapta-
tion loop as a function of the normalized frequency ? ? ???????. The outer
loop has a time constant ?? ??? bits. The inner loop has the following time
constants: (a) ? ? ?? (left figure). (b) ? ? ??? (right figure).
A. Basic Behavior
Because the inner loop is dimensioned to be slow, the delay
of the inner loop will not have strong impact on the loop be-
havior(seeSectionIII-A).Forthisreasonweinitiallyomitdelay
in our analysis of the basic behavior, i.e., we set
the dynamic properties of the loops do not depend on the input
noises
and, these input noises are neglected. By transfor-
mation into the -domain, the basic loop behavior can be an-
alyzed. The inner loop will not show first-order behavior any-
more but becomes essentially a second-order adaptation loop,
whose behavior is determined by the total gains
The -transform of the inner-row estimate
rived to be
. As
and.
can easily be de-
(4)
where
form of respectively
From (4), it is clear that the estimate
value
is determined by all three ideal parameter components:
and. In Fig. 8, the mismatch magnitudes due to
these components are plotted for two different inner-row time
constants
while fixing the outer-loop time constant
bits. In the left part of the figure, the magnitudes are shown for
the case the inner-row adaptation loop is 5 times slower than
the outer-row adaptation loop, i.e.,
of the figure
. The mismatch magnitudes
due to each component are discussed.
•
: all spectral content of
up to the inner-loop cutoff frequency
presentintheestimate
andisnotpresentinthemismatch
. As a consequence the inner loop should be designed
such that
.
and
and
are the-trans-
.
of theideal parameter
at 100
. In the right part
(and as a result also of)
is
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