New Method for Generalised PR Target Design for Perpendicular
Magnetic Recording
P. Shah1, M.Z. Ahmed1 and Y. Kurihara2
1 Centre for Research in Information Storage Technology, University of Plymouth, Plymouth PL4 8AA, UK.
2 Department of Electronic Control Engineering, Niihama National College of Technology, Niihama,792-8580, Japan.
Email:{purav.shah,m.ahmed}@plymouth.ac.uk, kurihara@ect.niihama-nct.ac.jp
I. INTRODUCTION
In recent years, perpendicular magnetic recording (PMR) has been the main topic of interest in the industry. Given
current estimates, that would suggest an areal density using PMR as great as one terabit per square inch – making possible
in two to three years a 3.5-inch disk drive capable of storing an entire terabyte of data [1]. As the areal density is increased,
however, the signal processing aspects of magnetic recording becomes more difficult.
The present technique for finding the optimised GPR targets is based on the minmimum mean squared error (MMSE)
between the equaliser output and the desired output, subject to the monic constraint [2]. In this paper, we present a new
method of designing GPR targets for PMR. This method is based on maximising the ratio of minimum squared eucledian
distance of the PR target to the noise penalty introduced by the PR filter. The description of the channel model and the
new method follows in the next section and the results and comparison follows after that.
II. SIMULATION MODEL
Figure(1(a)) shows the block diagram of the PMR system model used in this paper. The user data, denoted as ak, is
a sequence of input symbols taking values of 0, 1. To simulate the write current, the sequence ak is mapped to −1,+1.
The scaling factor of 0.5 is to ensure the transition takes values of −1, 0,+1. We approximate the single-transition step
repsonse, denoted as s(t), using the hyperbolic tangent function [3][4]:
s(t) = A · tanh
(
ln(3) tPW50
)
(1)
where A is the saturation level/amplitude from zero to peak(normalised to unity) and PW50 is the time taken for s(t) to
go from −A/2 to +A/2. It is assumed that t and PW50 are normalised to the symbol period, T . The dibit response p(t)
is defined as:
p(t) = s(t) − s(t − 1) (2)
The readback signal r(t) is the convolution of ak and p(t) plus some Additive White Gaussian Noise (AWGN):
r(t) =
∑
k
akp(t − kT )
︸ ︷︷ ︸
b(t)
+n(t) (3)
where n(t) is the AWGN with mean of 0 and variance of σ2. A Maximum Likelihood Sequence Detector (MLSD) is used
to provide the decoder solution which is used for performance evaluation.
III. GPR TARGET SEARCH METHOD
The present technique [2] for achieving optimised GPR target is optimal only if the receiver has noise prediction. If
there is no noise prediction, then the equaliser leads to additional noise. This is as shown in figure(1(b)). Considering a PR
equaliser with a monic constraint,where h(0) = 1, the new technique described in this paper is based on the calculation
of ratio of the minimum squared eucledian distance of the PR scheme under this monic constraint to the squared noise
penalty introduced by the filter. Consider the N tap coefficients h(N−12 ), · · · , · · · , h(N−12 ), where N is an odd integer.
The equalised signal y is:
y = r(t) ∗ h(t) (4)
= b(t) ∗ h(t) + n(t) ∗ h(t)
= b(t) ∗ h(t) + n(t) + nf (t)
1

Dibit
Responseak
p(t)
n(t)
r(t) y
0.5
PR
Equaliser MLSD
BER MEASUREMENT POINTS
aˆkb(t)
(a) Simulation Model
7-Tap
Monic FIR
Filter
y aˆk
n(t)
b(t) Trellis-basedEucledian
Distance
Measurement
7-Tap
Monic FIR
Filter Equivalent Simulation Model with
Minumum Eucledian Distance Measurement
(b)
y aˆk
n(t)
b(t) Trellis-basedEucledian
Distance
Measurement
nf(t)
7-Tap
Monic FIR
Filter
Equivalent Simulation Model with
Filter Noise Penalty
(c)
Figure 1: Simulation Block including GPR Target Search
PW50 Target
1.3 [1,4,7,3]
1.4 [1,5,8,4]
1.5 [1,5,8,4]
Figure 2: GPR Target Results
Here, nf (t) is the noise penalty from the filter. The analysis of the system is shown in Figure 1.
The rule of optimisation is to find the GPR target that maximises the ratio of minimum squared euclidean distance on
the trellis over the noise penalty. Thus, the effective design ratio is:
Design Ratio = Minimum Squared Eucledian Distance
Filter Noise Penalty
(5)
where, the filter noise penalty is computed as,
Filter Noise Penalty =
∑
∀j,j 6=0
h(j)2 (6)
The optimsed search looks for the PR target that maximises this Design Ratio. Results from this are in Figure 2.
RESULTS AND DISCUSSIONS
The GPR targets obtained using this new method for GPR search are the same with traditional method of GPR search
for most PW50. This new method provides consistently equal or better targets for PRML schemes that does not include
noise prediction. Future work will focus on investigating the effect of media noise.
REFERENCES
[1] R. Wood, Y. Hsu, and M. Schultz, “Perpendicular magnetic recording,” Internet Resource, July 2007. Hitachi GST
White Paper.
[2] P. Kovintavewat, I. Ozgunes, E. Kurtas, J. Barry, and S. McLaughlin, “Generalised partial response targets for per-
pendicular recording,” IEEE Transactions on Magnetics, vol. 38, pp. 2340–2342, September 2002.
[3] Y. Okamoto, H. Osawa, H. Saito, H. Muraoka, and Y. Nakamura, “Performance of prml systems in perpendicular
magnetic recording channel with jitter-like noise,” Journal of Magnetism and Magnetic Materials, vol. 235, no. 43,
pp. 251–264, 2001.
[4] H. Sawaguchi, Y. Nishida, H. Takano, and H. Aoi, “Performance analysis of modified prml channels for perpendicular
recording systems,” Journal of Magnetism and Magnetic Materials, vol. 235, pp. 265–272, 2001.
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