IEEE TRANSACTIONS ON MAGNETICS, VOL. 27, NO. 6, NOVEMBER 1991 4819

A Maximum Likelihood Peak Detecting Channel

K. Chopra and D. D. Woods Storage Technology Corparation

Louisville, Colurado 80028

A bstruct-Peak detection channel design has progressed beyond primitive bit-by-bit decision technology. This paper describes state-of-the- art peak detection using maximum likelihood methods on variable pulse response targets. A peak detecting channel using maximum likeli- hood detection is described and results are shown to be up to 3 dB better than simple peak detec- tion, consistent with the gain attributed to Viterbi detection.

The peak detection technique is suitable for disk recording channels using run-length-limited (RLL) codes for data storage. This paper demoa- strates the difference between modeled (1, 7) RLL coded channels with fixed idealized target responses and actual channel hardware. In particular, we note that while traditional modeling results suggest no benefit from using Viterbi-like algorithms in RLL coded channels, actual channel performance results do show measurable gains.

I. INTRODUCTION

The emergence of adaptive digital channels in high capacity disk drives has kindled a general upsurge of interest in practical, low cost implementations of maxi- mum likelihood detection schemes. The Viterbi algorithm has often been described as the method to achieve maxi- mum likelihood detection in partial response channels [l]. S e v d papers have shown modeling and simulation re- sults comparing the performance of these new digital channels with conventional peak detection [21,[31. Conventional bit-by-bit peak detecting channels using RLL codes are commonly employed to maximize linear recording density by limiting intersymbol interference (IS0 without tfie need for significant pulse slimming.

The prospect of achieving a significant signal-to-noise ratio ( S N R ) gain over conventional peak detection makes a compelling case for pushing ahead with the relatively complex adaptive digital channel structures. When com- paring channel capabilities, we f i i that the literature fails to reflect the sophistication of modem peak detecting channels. These more recently developed peak detecting channels are designed to function over a wide range of head and media variations, and with radial changes of up to 100% from the innermost cylinder to the outermost cylinder.

lhis paper discusses a technique used for analog peak detection which accommodates the dynamic nature of the channel response. We show how a current product successfully employs maximum likelihood detection concepts with RLL coded data to gain 1.5 to 3 dl3 of ef- fective SNR advantage over primitive bit-by-bit detection without the complexity of the Viterbi algorithm.

In Section II simple peak detection is described fol- lowed by a discussion of the maximum likelihood algo- rithm. The technique known as peak detection using maximum likelihood (PDML) is presented. The equiva- lence of PDML to Viterbi detection in terms of S N R is discussed. The robust technique is implemented with conventional analog and digital circuitry as discussed in Section III. Performance comparisons using simulation and measured results from a disk file environment are given in Section IV.

IL PEAK DE"I0N

Simple peak detection seeks to identify the existence of a peak within each predefined clock window. A peak exists within a clock window if the signal is both above a predefined threshold and its time derivative has a zero crossing. Errors resulting from noise during these processes are referred to as "missing (extra) bit" and "peak shift" respectively. Assuming Gaussian noise distribution with

and assuming the variance of the differentiator noise is a p s

Typically S N R m b is dominant for (0, k) codes, and SNRp dominates for (1,7) and (2,7) codes [21.

The noise variances have been shown to be related by

(3)

where Rk are the noise autocorrelation coefficients at the equalizer output [2],[4]. For practical operating points, where the headjelectronics noise is the dominant on-track error mechanism, especially at the inner diameter (ID), the noise autocorrelation is small and (3) duces to

(4)

i.e., SNRpf dominates S N R d by approximately 3 dl3. In typical disk products with a fixed data transfer rate

over a given data band, the channel response at the ID can

0018-9464/91$01.00 (Q 1991 IEEE

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be matched to the target pulse response (1-D)( 1+D)2d [5] where d=l for (1,7) Ru code. Head and media parametric variations in the production population will result in the product performance being dictated by head output responses that resemble higher order target functions, e.g., (l-D)(l+D)3. It has been demonstrated that SNRp,, the dominant error source, degrades severely with higher order targets [31. However, SNRps is relatively insensitive to slimmer target pulses, e.g., (1-D)(l+D). Practical considqations &=fore dictate the need for slimmer targets to achieve best overall error performance. Slimmer targets result in poorer S“b, thus the linal choice of target is a compromise.

Maximum likelihood techniques have been shown to be more effective in detecting missing bit type errors than simple threshold detection [4]. The PDML technique taka advantage of this effective SNR,b gain to extend the design target towards a lower order pulse response, such as ( I-D)( 1+D)d, allowing further improvements in overall channel performance. PDML offers similar benefits at the outer diameter (OD) where the natural response is slimmer and the dominant error mechanism changes to missing bit type m r s - d u e to Gaussian as well as deterministic noise sources such as overwrite and adjacent track crosstalk.

Maximum likelihood sequence estimation in the presence of IS1 is commonly implemented with the Viterbi algorithm [1],[6],[7], and when used with peak detection provides up to a 3 dB gain in the absence of coding 181. A full Viterbi implementation for a two-state trellis recursively computes 2 - 2l-I branch metrics, stores and updates 2l-I survivor paths on each cycle, and stores 2I-l accumulated metrics, where P is the length of the channel impulse response [l]. PDML avoids this need for computation and extensive memory by using a continuous time analog approach.

Referring to the sample waveform in Figure 1, PDML qualifies peaks using a dynamically set threshold of amplitude “Th“ as similarly described by [6],[9],[10], and also makes use of the alternating polarity nature of the RLL code. PDML replicates the function of the two-state Viterbi detector by holding the highest peak voltage and qualifying that peak after a sufficient number of bit inter- vals have been observed [91,[111,[12].

+I 0 1 Bit dcciaiom

Figure 1. Example Waveform: Signal Plus Noise

Assuming a - 1 was previously qualified before, T = 0, PDML assigns point “ A +l. The code constraint requires point “B” to be assigned a 0, and point “C” is assigned a -1 only after the signal crosses the threshold. Both the d and k.code constraints are used in making the decisions.

m. IMPLEMENTATION

Hardware implementations of the highest peak sensing function required to carry out the two-state maxi- mum likelihood algorithm have been described previously [12],[13]. Figure 2 shows the key elements of the PDML channel. The raw analog input waveform is equalized and low pass filtered achieving optimal balance of residual IS1 and noise enhancement in order to minimize timing emrs in the RLL code window. These signals are combined to generate peak detection pulses and additional pointers for the highest peak discriminator. The discriminator hardware is built up of a series of cascaded timers together with decision logic to qualify peaks at the detector output. No external clock is required with the discriminator logic since movement of information through the cascade is driven entirely by peak detection events. The decision logic prevents spurious “ones” from reaching the output stage of the timers.

Figure 2. PDML Channel Components

For RLL (d, k) recording codes, the total delay r e q u i d in the cascade is given by

nTd 2 ( k + l ) T (6)

where T is the bit interval, Td is the delay of each thing element, and n is the number of timers.

The inherent robustness of this type of detector de- rives from the absence of sampling and data tracking errors which can severely restrict the performance of symbol rate sampling detectors. The total electronics for the PDML detector can be incorporated along with preceding signal equalization circuits in a single bipolar LSI circuit pack- age.

IV. PERFORMANCE COMpARlSON

A. Modeling PDML was evaluated against the conventional peak

detector both through simulation and in an actual high speed disk file environment. We first simulate with a target pulse response of (I-D)(I+D)~ as discussed in Section 11. Additive white Gaussian noise, (1, 7) code constraints and an intermediate operating density of 1.5 (pulsewidth 50 / bit interval), similar to an existing product were assumed. Figure 3 shows the simulation results for a Lorentzian channel. No appreciable difference appears between the detection schemes due to the

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dominance of the peak shift type of mor process. We next simulate with the target pulse response of (l-D)(l+D), showing maximum likelihood peak detection to provide an advantage of about 1.8 dB at 10" bit error me. Similarly, a set of simulation runs were made for the higher operating density of 2.5 and PDML provides an advantage of about 1 dB at bit MM rate. cg a:: Q -3 2 4 2 -5

*

- 2 3 4 5 6 7 8 9 1 0 1 1 1 2 1 3 1 4 1 5 SNR (dB)

El ' . 13 i4 is i 6 17 i8 i g io 21

S N R (dB1 + + - e - +

PD PDML PD PDML

Figme 3. Simulation R&&

(1 -DMI+D) (1 -DXl+D) (l-D)(l+D? (1-D)(1+DI2

B. Experimentation White Gaussian noise was injected into the actual

reading channel at the equalizer input in order to genexate a wide range of SNR. _ _ iif"==-=,-j 2 -8 g -9

21 22 23 24 25 26 27 28 29 m

21 22 23 24 25 26 27 28 29 SNR(dB1

A

-94 16 17 18 19 20 21 21 23

S N R (dB1

+ + PD PDML

Figure 4. Masued Channel Res&

Figure 4 shows how PDML behaves in a real channel. The channel response is not irlpnlized to a spec& target- instead the channel is optimizedat ID and OD to "ize MM rates. The results show the dB gain aariited to the

approach at both the ID and OD. maximumlkhhmi . . V. CONCLUSION

This paper has described an analog peak detection method employing maximum likelihood concepts. We have demonshated that the two-state m a x i " likelihood algorithm provides sisnifi.cant performance gains in IUL coded channel environments. Not only is the per fc"e of this new detection method better than simple peak detection, this robust method is easy to implement with analog circuitry. The perfmance gains are comparable to more complex structures using the Viterbi algorithm.

A m

The authors thank D. Gemindm and M. Ehmke for their contributions.

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