Implementation of the Oversampled Per-Survivor Processing Viterbi Algorithm (OPSP-VA) for timing recovery in magnetic recording channels, plus an Interpolated Timing Recovery (ITR 2012) reference system for comparison.
Two independent timing recovery architectures are implemented:
Integrates per-survivor PLLs into a Viterbi decoder for robust timing recovery in high-jitter environments. Each survivor path in the Viterbi trellis maintains its own timing phase
- N=2 configuration: T/2-spaced FSE + Early-Late TED
- N=1 configuration: T-spaced FSE + Mueller-Müller TED
- Configurable training mode: full-supervision (
"auto") or decision-directed ("decision_directed") - DDF (Decision Feedback) slicer for DD mode: cancels GPR target ISI before symbol slicing
An interpolated timing recovery architecture with 5% fractional oversampling (
- FSE at
$T_s$ spacing + cubic/quadratic Farrow interpolation - Single NCO/PLL with second-order loop filter
- Mueller-Müller TED
- Configurable interpolator: cubic or quadratic Farrow
- Configurable TED: ground-truth or decision-directed (DDF-based)
-
Channel Modeling: PMR/LMR dibit responses with media jitter (
$\sigma_j/T$ ), clock jitter ($\sigma_w/T$ ), and frequency offset - Frontend: Butterworth LPF + Fractionally Spaced Equalizer (Wiener or LMS-adaptive)
- OPSP-VA: Per-survivor PLLs, configurable TED (Early-Late / MM), GPR target trellis
- ITR 2012: Interpolated timing recovery with NCO, Farrow structure, MM TED
-
Analysis: BER computation,
$\tau$ convergence tracking, FSE MSE monitoring, eye diagrams
.
├── src/
│ ├── channel/ # Signal generation, pulse shapes, jitter models
│ │ ├── channel_model.py # Main synthesis: readback signal with impairments
│ │ ├── signal_gen.py # Binary sequence generation
│ │ ├── jitter.py # Media and clock jitter models
│ │ └── pulse_shape.py # Transition/dibit responses
│ ├── frontend/
│ │ ├── filters.py # Butterworth LPF design
│ │ └── fse.py # Fractionally Spaced Equalizer (NLMS)
│ ├── opsps_va/ # OPSP-VA core
│ │ ├── viterbi.py # Main decoder: per-survivor PLL + Viterbi
│ │ ├── survivor_pll.py # Per-survivor PLL state management
│ │ ├── ted.py # Early-Late and Mueller-Müller TED
│ │ ├── trellis.py # GPR trellis builder
│ │ └── pll_design.py # PLL gain design (convergence-based)
│ └── utils/
│ ├── gpr_target.py # GPR target + FIR joint optimization
│ └── metrics.py # BER, MSE computation
├── experiments/
│ └── itr_2012/ # ITR 2012 reference system
│ ├── simulation.py # Full ITR simulation + BER sweep
│ ├── farrow_interpolator.py
│ └── mmse_interpolator.py
├── scripts/ # Experiment scripts
│ ├── run_ber_curve_sweep.py # Dual-mode BER sweep (auto + DD)
│ ├── run_single_condition_param_search.py # Grid search for optimal params
│ ├── ber_sweep_n1_n2_c256.py # N=1 vs N=2 BER comparison
│ ├── calibrate_table1_kd.py # TED slope calibration
│ ├── scan_table1_gain_scale.py # PLL gain/delay scan
│ └── ...
├── tests/ # Pytest unit/integration tests
├── data/ # Output data, figures, CSV results
├── requirements.txt
└── main.py # Default system simulation entrypoint
- Python 3.10+
- Libraries:
numpy,scipy,matplotlib
git clone <repository-url>
cd PSP
pip install -r requirements.txt# Default OPSP-VA simulation (N=2, PMR channel)
python main.py
# ITR 2012 simulation
python experiments/itr_2012/simulation.py
# BER sweep comparing training modes for OPSP-VA
python scripts/run_ber_curve_sweep.py
# Single-condition parameter grid search
python scripts/run_single_condition_param_search.pypytest tests/The OPSP-VA decoder supports two training modes:
| Mode | Description | TED Source | FSE Source | Typical BER (N=2, 25dB) |
|---|---|---|---|---|
"auto" |
Full supervision | Ground-truth (all symbols) | Ground-truth | ~0.007 |
"decision_directed" |
Preamble-only supervision | Preamble: ground-truth / Data: slicer decisions | Slicer decisions | ~0.46 |
The ITR 2012 reference system was evaluated under the same channel conditions as OPSP-VA: PMR channel, ND=2.5, media jitter
| Parameter | Value |
|---|---|
| Oversampling |
|
| ADC sampling rate | 105 spT |
| FSE taps | 21 (Wiener, Ts-spaced) |
| Interpolator | Quadratic Farrow |
| TED | Mueller-Müller |
| PLL gains (acq) | |
| PLL gains (track) | |
| LMS step |
|
| GPR target | 5-tap (Wiener-designed) |
| SNR (dB) | Ground-Truth BER | Decision-Directed BER |
|---|---|---|
| 4 | ||
| 6 | ||
| 8 | ||
| 10 | ||
| 12 |
|
|
| 14+ |
|
Note: The ground-truth mode BER (
$3.3\times10^{-4}$ ) is an upper bound limited by Viterbi traceback edge effects — the true BER is zero (0 errors in the middle section of every sector at all SNRs). The DD mode floor at$2.27\times10^{-3}$ (186 errors/81900 bits) is also dominated by tail-edge artifacts rather than actual detection errors.
-
Ground-truth mode achieves error-free detection above SNR
$\approx$ 4 dB with the quadratic Farrow interpolator. The Wiener-designed FSE + GPR target combination fully equalizes the channel under ideal timing knowledge. -
Decision-directed (DDF-based) mode is SNR-dependent:
- Below 6 dB: unreliable ($\sim$0.3 BER), as the DDF slicer makes too many errors to sustain timing lock.
- 6–10 dB: transition zone where BER drops from
$10^{-1}$ to$10^{-3}$ . - Above 10 dB: BER floor at
$2.3\times10^{-3}$ , matching the ground-truth tail-artifact level — the DD loop recovers timing nearly as well as full supervision.
-
Comparison with OPSP-VA DD: Unlike OPSP-VA's per-survivor PLL architecture (where DD mode diverges within $\sim$1000 symbols due to decision-error accumulation), ITR 2012's single-NCO architecture averages TED errors over the entire sequence, making it far more robust in DD mode.
- Kovintavewat et al., "A new timing recovery architecture for fast convergence," IEEE Trans. Magnetics, 2003.
- Kovintavewat et al., "Performance of Interpolated Timing Recovery in Perpendicular Magnetic Recording Channel," I-SEEC 2012.
- Kovintavewat et al., "Generalized partial-response targets for perpendicular recording with jitter noise," IEEE Trans. Magnetics, 2002.
Note: This project is intended for research and educational purposes in digital communications and magnetic recording.