Symbol Timing Recovery for Low-SNR Partial Response Recording Channels

Transcription

1 Symbol Timing Recovery for Low-SNR Partial Response Recording Channels Jingfeng Liu, Hongwei Song and B. V. K. Vijaya Kumar Data Storage Systems Center Carnegie Mellon University 5 Forbes Ave Pittsburgh, PA 523, USA kumar@ece.cmu.edu

2 Outline Timing recovery for data storage channels Loss of lock Piecewise linear phase drift approximation Frequency estimation-based feedforward symbol timing recovery (FOSTR) Simulation results Conclusions 2

3 Timing Recovery for Recording Channels yt () aht [ kt ()] t nt () k k n(t) ht Du D 2 t/ Du 2 tt/ Du u 2 2 a k h[t-(t)] y(t) D PW5 / T u a k channel bit (i.e., the bits after the modulation code encoder) sequence h[t-(t)] time-varying channel pulse response showing explicitly the effect of the phase drift n(t) additive noise y(t) continuous-time readback signal T channel bit interval PW5 width of the pulse at half height Objective: estimate (t) so that synchronous samples can be extracted for further processing by channel detector. 3

4 Current Timing Recovery Approach To Advanced Detector Estimated bits Simple Data Detector Timing Error Detector (TED) Readback Samples inst Loop Filter y k VCO Continuous Signal out Format for Sectors Preamble Synch Mark User Data Acquisition Mode Tracking Mode 4

5 Loss of Lock Problem Loss of Lock Rate BER PW5/T = 2.5 EPR4, PRML SNR = log (E/N ) SNR (db) SNR (db) Future recording systems have to operate at lower SNRs and higher ISI Phase offset drawn randomly from a uniform random variable in [-.5T.5T] At low SNR, the data detector in the timing recovery loop makes too many errors leading to large jitter and loss of lock Loss of lock declared whenever more than 5% of the bytes in a sliding window of 5 bytes are in error At 7-8 db SNR, loss of lock rate (LOLR) worse than -2 BER curve dominated by loss of lock events 5

6 Loss of Lock - Acquisition Large Initial Frequency Error + Small Tracking Bandwidth 3 Phase (T) 2 - Type I Loss of Lock Channel bits Phase trajectory of the recovered clock Phase trajectory of the actual clock Phase trajectory of the actual clock shifted up by one bit interval 6

7 Loss of Lock -Tracking Large Residual Tracking Jitter Type II Loss of Lock Phase offset (T) - -2 Phase offset (T) Bit Index (T) Bit Index (T) Jitter is the difference between estimated and introduced phase drifts To track faster phase drift, larger bandwidth is needed Larger BW allows more noise and leads to increased jitter 7

8 Upper bound for Loss of Lock in Tracking - -2 Loss of Lock Rate RMS Value of Residual Timing Jitter (T) J. Liu, H. Song and B. V. K. Vijaya Kumar, Bound for loss of lock rate in partial response recording channels, Electronics Letters, Vol. 38, No. 6, pp , 22. 8

9 Example Phase Drifts (Magnetic Tape Data) PSI (Tb) PSI (Tb) PSI (Tb) Data (Tb) x Data (Tb) x 4 PSI (Tb) Data (Tb) x Data (Tb) 9

10 Phase Drift Models Generally, phase drift (t) in recording systems can be characterized by following three models: Linear phase drift model: This model represents a constant frequency offset between the actual bit rate and the bit rate used for sampling. It is a popular model used to model the phase drifts present in hard disk drives. Sinusoidal phase drift model: This is a good model for phase drift when the head arm is fluctuating because the servo control is not working properly, e.g., when the servo loop cannot damp out the excessive vibration in the head media in interface. To track this kind of phase drift, we need a PLL of a relatively large bandwidth, like tape drives. Autoregressive (AR) phase drift model: This model reflects the random nature of phase drift especially during the tracking mode when the frequency offset is small and there is no initial phase offset.

11 Piecewise Linear Approximation of Phase Drift Phase (T) Phase Error (T) Bits (T) Actual phase Approximated Bits (T) Period: 5T Segment size: 5T (BW=./T) Piece-wise constant approximation Phase (T) Phase Error (T) Actual phase Approximated Bits (T) Bits (T) Period: 5T Segment size: 5T Piece-wise linear approximation

12 Phase/Frequency Offset Estimation N, f, d y, f d ML initial i initial i i In each segment, only the phase drift slope is estimated Brute-force joint ML phase/frequency offset estimation is too complex A quadratic polynomial approximation is used 7x oversampling seems adequate; still too complex, but currently used for benchmarking 2

13 RMS Error of Phase Drift Estimation RMS Error of Phase Drift Estimation (T) Bit Index 4 4 k k k M M f 2 initial initial initial M: block (segment) size k: bit index f2 : variance of frequency offset 2 : variance of phase offset EPR4, SNR = 7.5 db, Normalized Density 2.5 Linear phase drift model, initial phase offset drawn randomly from a uniform random variable in [-.5T.5T], frequency offset drawn randomly from a Gaussian with zero mean and standard deviation 3-4 /T, truncated to.4 /T Block size is 5 bits. Initial 8 bits are used for the initial phase offset estimation RMS phase drift error by phase offset estimation-based scheme is.34 T when the segment size is 8 bits 3 2

14 Frequency Offset Estimation-Based Timing Recovery Buffered Block Segments Segment # Segment #2 Segment #4 Segment #5 Segment #3 Segment #6 Estimated Phase Drift P # P #2 P #3 P #4 P #5 P #6 4

15 Amount of Residual Timing Jitter.7 RMS Value of Residual Timing Jitter (T) FOSTR Conventional Decision-Directed SNR (db) Sinusoidal phase drift with period 5 channel bits. For conventional M&M TED PLL based timing recovery scheme, BW (.8/T) is optimized by exhaustive search. For FOSTR, blocks of 5 bits (with 5% overlap), and decision-directed ML objective function 5

16 Loss of lock is the more dominant timing recovery problem at low SNR Proposed a frequency-offset estimation based symbol timing recovery (FOSTR) Numerical simulations of FOSTR show improvement over conventional PLL-based timing recovery Signal Processing for Storage (SPS) Technical Committee Meeting Noon-.3 PM, Nov. 9 (TODAY) Peacock Room, 3 rd Floor, Hyatt 6