PAM4 Signal Analysis Tutorial

Overview

This tutorial demonstrates:

PAM4 signal analysis techniques
Level separation measurements
EVM calculations
Eye diagram analysis
Type-safe data processing

Basic Setup

Required Imports

from typing import Dict, List, Optional, Union, Tuple
import numpy as np
import numpy.typing as npt
from serdes_validation_framework.data_analysis.pam4_analyzer import (
    PAM4Analyzer,
    PAM4Levels,
    EVMResults,
    EyeResults
)

# Type aliases
FloatArray = npt.NDArray[np.float64]
SignalData = Dict[str, FloatArray]

Data Validation

def validate_signal_data(
    data: SignalData,
    required_columns: List[str]
) -> None:
    """
    Validate signal data structure
    
    Args:
        data: Signal data dictionary
        required_columns: List of required column names
        
    Raises:
        AssertionError: If validation fails
    """
    # Type validation
    assert isinstance(data, dict), \
        f"Data must be dictionary, got {type(data)}"
    
    # Check required columns
    missing = set(required_columns) - set(data.keys())
    if missing:
        raise ValueError(f"Missing required columns: {missing}")
    
    # Validate arrays
    for column in required_columns:
        array = data[column]
        
        # Type check
        assert isinstance(array, np.ndarray), \
            f"Column {column} must be numpy array, got {type(array)}"
        
        # Data type check
        assert np.issubdtype(array.dtype, np.floating), \
            f"Column {column} must be floating-point, got {array.dtype}"
        
        # Value validation
        assert len(array) > 0, f"Column {column} cannot be empty"
        assert not np.any(np.isnan(array)), \
            f"Column {column} contains NaN values"
        assert not np.any(np.isinf(array)), \
            f"Column {column} contains infinite values"

Signal Generation

Test Signal Creation

def generate_test_signal(
    duration: float = 1e-6,
    sample_rate: float = 256e9,
    noise_amplitude: float = 0.05
) -> SignalData:
    """
    Generate synthetic PAM4 test signal
    
    Args:
        duration: Signal duration in seconds
        sample_rate: Sampling rate in Hz
        noise_amplitude: Noise amplitude (0-1)
        
    Returns:
        Dictionary with time and voltage arrays
        
    Raises:
        AssertionError: If parameters are invalid
    """
    # Validate inputs
    assert isinstance(duration, float), "Duration must be float"
    assert isinstance(sample_rate, float), "Sample rate must be float"
    assert isinstance(noise_amplitude, float), "Noise amplitude must be float"
    assert duration > 0, "Duration must be positive"
    assert sample_rate > 0, "Sample rate must be positive"
    assert 0 <= noise_amplitude <= 1, "Noise amplitude must be between 0 and 1"
    
    try:
        # Calculate points
        num_points = int(duration * sample_rate)
        
        # Generate time array
        time = np.arange(num_points, dtype=np.float64) / sample_rate
        
        # Generate PAM4 levels
        levels = np.array([-3.0, -1.0, 1.0, 3.0], dtype=np.float64)
        symbols = np.random.choice(levels, size=num_points)
        
        # Add noise
        noise = np.random.normal(0, noise_amplitude, num_points)
        voltage = (symbols + noise).astype(np.float64)
        
        return {
            'time': time,
            'voltage': voltage
        }
        
    except Exception as e:
        raise RuntimeError(f"Signal generation failed: {e}")

Level Analysis

Basic Level Analysis

def analyze_signal_levels(
    voltage_data: FloatArray,
    threshold: float = 0.1
) -> Tuple[PAM4Levels, Dict[str, float]]:
    """
    Analyze PAM4 voltage levels
    
    Args:
        voltage_data: Voltage measurements array
        threshold: Detection threshold
        
    Returns:
        Tuple of (PAM4Levels, statistics)
    """
    # Validate inputs
    assert isinstance(voltage_data, np.ndarray), \
        "Voltage data must be numpy array"
    assert isinstance(threshold, float), "Threshold must be float"
    assert np.issubdtype(voltage_data.dtype, np.floating), \
        "Voltage data must be floating-point"
    assert 0 < threshold < 1, "Threshold must be between 0 and 1"
    
    try:
        # Create analyzer
        analyzer = PAM4Analyzer({'voltage': voltage_data})
        
        # Analyze levels
        levels = analyzer.analyze_level_separation('voltage')
        
        # Calculate statistics
        stats = {
            'mean_separation': float(np.mean(levels.level_separations)),
            'min_separation': float(np.min(levels.level_separations)),
            'uniformity': float(levels.uniformity)
        }
        
        return levels, stats
        
    except Exception as e:
        raise RuntimeError(f"Level analysis failed: {e}")

Level Quality Checks

def check_level_quality(
    levels: PAM4Levels,
    min_separation: float = 0.5,
    max_uniformity: float = 0.2
) -> Dict[str, bool]:
    """
    Check PAM4 level quality metrics
    
    Args:
        levels: PAM4 level measurements
        min_separation: Minimum level separation
        max_uniformity: Maximum uniformity metric
        
    Returns:
        Dictionary of quality checks
    """
    # Validate inputs
    assert isinstance(min_separation, float), \
        "Minimum separation must be float"
    assert isinstance(max_uniformity, float), \
        "Maximum uniformity must be float"
    assert min_separation > 0, "Minimum separation must be positive"
    assert max_uniformity > 0, "Maximum uniformity must be positive"
    
    try:
        return {
            'level_separation': all(sep >= min_separation 
                                  for sep in levels.level_separations),
            'level_uniformity': levels.uniformity <= max_uniformity,
            'monotonic_levels': np.all(np.diff(levels.level_means) > 0)
        }
        
    except Exception as e:
        raise RuntimeError(f"Quality check failed: {e}")

EVM Analysis

EVM Calculation

def calculate_signal_evm(
    measured: FloatArray,
    reference: Optional[FloatArray] = None
) -> EVMResults:
    """
    Calculate Error Vector Magnitude
    
    Args:
        measured: Measured signal array
        reference: Optional reference signal array
        
    Returns:
        EVMResults object with calculations
    """
    # Validate measured signal
    assert isinstance(measured, np.ndarray), \
        "Measured signal must be numpy array"
    assert np.issubdtype(measured.dtype, np.floating), \
        "Measured signal must be floating-point"
    
    # Validate reference if provided
    if reference is not None:
        assert isinstance(reference, np.ndarray), \
            "Reference signal must be numpy array"
        assert np.issubdtype(reference.dtype, np.floating), \
            "Reference signal must be floating-point"
        assert len(reference) == len(measured), \
            "Signal lengths must match"
    
    try:
        # Create analyzer
        analyzer = PAM4Analyzer({'voltage': measured})
        
        # Calculate EVM
        if reference is not None:
            analyzer.data['reference'] = reference
            return analyzer.calculate_evm('voltage', 'reference')
        else:
            return analyzer.calculate_evm('voltage')
            
    except Exception as e:
        raise RuntimeError(f"EVM calculation failed: {e}")

EVM Quality Checks

def check_evm_quality(
    evm_results: EVMResults,
    max_rms_evm: float = 5.0,
    max_peak_evm: float = 10.0
) -> Dict[str, bool]:
    """
    Check EVM quality metrics
    
    Args:
        evm_results: EVM measurement results
        max_rms_evm: Maximum RMS EVM percentage
        max_peak_evm: Maximum peak EVM percentage
        
    Returns:
        Dictionary of quality checks
    """
    # Validate inputs
    assert isinstance(max_rms_evm, float), "Maximum RMS EVM must be float"
    assert isinstance(max_peak_evm, float), "Maximum peak EVM must be float"
    assert max_rms_evm > 0, "Maximum RMS EVM must be positive"
    assert max_peak_evm > 0, "Maximum peak EVM must be positive"
    assert max_peak_evm >= max_rms_evm, "Peak EVM limit must exceed RMS limit"
    
    return {
        'rms_evm': evm_results.rms_evm_percent <= max_rms_evm,
        'peak_evm': evm_results.peak_evm_percent <= max_peak_evm
    }

Eye Analysis

Eye Measurements

def analyze_eye_diagram(
    time_data: FloatArray,
    voltage_data: FloatArray,
    ui_period: float = 8.9e-12
) -> EyeResults:
    """
    Analyze eye diagram parameters
    
    Args:
        time_data: Time points array
        voltage_data: Voltage measurements array
        ui_period: Unit interval in seconds
        
    Returns:
        EyeResults object with measurements
    """
    # Validate inputs
    assert isinstance(ui_period, float), "UI period must be float"
    assert ui_period > 0, "UI period must be positive"
    
    # Validate arrays
    validate_signal_data(
        {'time': time_data, 'voltage': voltage_data},
        ['time', 'voltage']
    )
    
    try:
        # Create analyzer
        analyzer = PAM4Analyzer({
            'time': time_data,
            'voltage': voltage_data
        })
        
        # Analyze eye diagram
        return analyzer.analyze_eye_diagram(
            'voltage',
            'time',
            ui_period=ui_period
        )
        
    except Exception as e:
        raise RuntimeError(f"Eye analysis failed: {e}")

Eye Quality Checks

def check_eye_quality(
    eye_results: EyeResults,
    min_height: float = 0.2,
    min_width: float = 0.4
) -> Dict[str, bool]:
    """
    Check eye quality metrics
    
    Args:
        eye_results: Eye measurement results
        min_height: Minimum eye height
        min_width: Minimum eye width
        
    Returns:
        Dictionary of quality checks
    """
    # Validate inputs
    assert isinstance(min_height, float), "Minimum height must be float"
    assert isinstance(min_width, float), "Minimum width must be float"
    assert min_height > 0, "Minimum height must be positive"
    assert min_width > 0, "Minimum width must be positive"
    
    return {
        'eye_height': eye_results.worst_eye_height >= min_height,
        'eye_width': eye_results.worst_eye_width >= min_width,
        'uniform_eyes': len(set(eye_results.eye_heights)) == 3
    }

Complete Example

Full Analysis Pipeline

def analyze_pam4_signal() -> None:
    """Demonstrate complete PAM4 analysis pipeline"""
    try:
        # 1. Generate test signal
        signal = generate_test_signal(
            duration=1e-6,      # 1 µs
            sample_rate=256e9,  # 256 GSa/s
            noise_amplitude=0.05
        )
        
        # 2. Analyze levels
        levels, level_stats = analyze_signal_levels(
            signal['voltage']
        )
        level_quality = check_level_quality(levels)
        
        print("\nLevel Analysis:")
        print(f"Uniformity: {level_stats['uniformity']:.3f}")
        print(f"Min Separation: {level_stats['min_separation']:.3f}")
        print("Quality Checks:", level_quality)
        
        # 3. Calculate EVM
        evm = calculate_signal_evm(signal['voltage'])
        evm_quality = check_evm_quality(evm)
        
        print("\nEVM Analysis:")
        print(f"RMS EVM: {evm.rms_evm_percent:.2f}%")
        print(f"Peak EVM: {evm.peak_evm_percent:.2f}%")
        print("Quality Checks:", evm_quality)
        
        # 4. Analyze eye
        eye = analyze_eye_diagram(
            signal['time'],
            signal['voltage']
        )
        eye_quality = check_eye_quality(eye)
        
        print("\nEye Analysis:")
        print(f"Worst Height: {eye.worst_eye_height:.3f}")
        print(f"Worst Width: {eye.worst_eye_width:.3f}")
        print("Quality Checks:", eye_quality)
        
        # 5. Overall quality
        overall_quality = all([
            all(level_quality.values()),
            all(evm_quality.values()),
            all(eye_quality.values())
        ])
        
        print(f"\nOverall Quality: {'PASS' if overall_quality else 'FAIL'}")
        
    except Exception as e:
        print(f"Analysis failed: {e}")

Best Practices

1. Array Validation

def validate_array(
    array: FloatArray,
    name: str = "array"
) -> None:
    """Validate numeric array"""
    assert isinstance(array, np.ndarray), \
        f"{name} must be numpy array"
    assert np.issubdtype(array.dtype, np.floating), \
        f"{name} must be floating-point"
    assert len(array) > 0, \
        f"{name} cannot be empty"
    assert not np.any(np.isnan(array)), \
        f"{name} contains NaN values"

2. Parameter Validation

def validate_parameter(
    value: float,
    name: str,
    min_value: Optional[float] = None,
    max_value: Optional[float] = None
) -> None:
    """Validate numeric parameter"""
    assert isinstance(value, float), \
        f"{name} must be float"
    if min_value is not None:
        assert value >= min_value, \
            f"{name} must be >= {min_value}"
    if max_value is not None:
        assert value <= max_value, \
            f"{name} must be <= {max_value}"

3. Result Validation

def validate_measurements(
    results: Dict[str, float],
    limits: Dict[str, float]
) -> bool:
    """
    Validate measurement results against limits
    
    Args:
        results: Dictionary of measurements
        limits: Dictionary of measurement limits
        
    Returns:
        True if all measurements pass
        
    Raises:
        ValueError: If validation fails
    """
    try:
        for name, value in results.items():
            limit = limits.get(name)
            if limit is not None:
                if not isinstance(value, float):
                    raise ValueError(f"Measurement {name} must be float")
                if value > limit:
                    return False
        return True
        
    except Exception as e:
        raise ValueError(f"Measurement validation failed: {e}")

4. Error Handling

class AnalysisError(Exception):
    """Base class for analysis errors"""
    pass

class ValidationError(AnalysisError):
    """Error in data validation"""
    pass

class MeasurementError(AnalysisError):
    """Error in measurement calculation"""
    pass

def handle_analysis_errors(func):
    """Decorator for handling analysis errors"""
    def wrapper(*args, **kwargs):
        try:
            return func(*args, **kwargs)
        except ValidationError as e:
            print(f"Validation Error: {e}")
            raise
        except MeasurementError as e:
            print(f"Measurement Error: {e}")
            raise
        except Exception as e:
            print(f"Unexpected Error: {e}")
            raise
    return wrapper

Advanced Topics

Custom Analysis Pipeline

@handle_analysis_errors
def custom_analysis_pipeline(
    data: SignalData,
    config: Dict[str, float]
) -> Dict[str, Any]:
    """
    Create custom analysis pipeline
    
    Args:
        data: Signal data dictionary
        config: Analysis configuration
        
    Returns:
        Analysis results dictionary
    """
    # Validate inputs
    validate_signal_data(data, ['time', 'voltage'])
    required_config = {'min_eye_height', 'max_evm', 'min_snr'}
    missing = required_config - set(config.keys())
    if missing:
        raise ValidationError(f"Missing configuration: {missing}")
    
    try:
        # Create analyzer
        analyzer = PAM4Analyzer(data)
        
        # Step 1: Level analysis
        levels = analyzer.analyze_level_separation('voltage')
        level_quality = check_level_quality(
            levels,
            min_separation=config.get('min_separation', 0.5)
        )
        
        # Step 2: EVM calculation
        evm = analyzer.calculate_evm('voltage')
        evm_quality = check_evm_quality(
            evm,
            max_rms_evm=config['max_evm']
        )
        
        # Step 3: Eye analysis
        eye = analyzer.analyze_eye_diagram(
            'voltage',
            'time'
        )
        eye_quality = check_eye_quality(
            eye,
            min_height=config['min_eye_height']
        )
        
        # Compile results
        return {
            'levels': {
                'measurements': levels,
                'quality': level_quality
            },
            'evm': {
                'measurements': evm,
                'quality': evm_quality
            },
            'eye': {
                'measurements': eye,
                'quality': eye_quality
            },
            'overall_quality': all([
                all(level_quality.values()),
                all(evm_quality.values()),
                all(eye_quality.values())
            ])
        }
        
    except Exception as e:
        raise MeasurementError(f"Analysis pipeline failed: {e}")

Signal Processing Utilities

def process_signal(
    signal: FloatArray,
    sample_rate: float
) -> FloatArray:
    """
    Apply signal processing with validation
    
    Args:
        signal: Input signal array
        sample_rate: Sample rate in Hz
        
    Returns:
        Processed signal array
    """
    # Validate inputs
    validate_array(signal, "signal")
    assert isinstance(sample_rate, float), "Sample rate must be float"
    assert sample_rate > 0, "Sample rate must be positive"
    
    try:
        # 1. Remove DC offset
        signal = signal - np.mean(signal)
        
        # 2. Apply filtering
        nyq = sample_rate / 2
        b, a = scipy.signal.butter(4, 0.1)
        filtered = scipy.signal.filtfilt(b, a, signal)
        
        # 3. Normalize amplitude
        normalized = filtered / np.max(np.abs(filtered))
        
        return normalized.astype(np.float64)
        
    except Exception as e:
        raise ValueError(f"Signal processing failed: {e}")

Advanced Visualization

def plot_analysis_results(
    data: SignalData,
    results: Dict[str, Any]
) -> None:
    """
    Create comprehensive visualization
    
    Args:
        data: Signal data dictionary
        results: Analysis results dictionary
    """
    try:
        # Set up plotting
        fig, ((ax1, ax2), (ax3, ax4)) = plt.subplots(2, 2, figsize=(12, 8))
        
        # 1. Signal trace
        ax1.plot(data['time'][:1000], data['voltage'][:1000], 'b-', alpha=0.7)
        ax1.set_title('Signal Trace')
        ax1.set_xlabel('Time (s)')
        ax1.set_ylabel('Voltage (V)')
        ax1.grid(True)
        
        # 2. Level histogram
        hist, bins = np.histogram(data['voltage'], bins=100)
        ax2.hist(data['voltage'], bins=100, density=True, alpha=0.7)
        for level in results['levels']['measurements'].level_means:
            ax2.axvline(level, color='r', linestyle='--', alpha=0.5)
        ax2.set_title('Level Distribution')
        ax2.set_xlabel('Voltage (V)')
        ax2.set_ylabel('Density')
        
        # 3. Eye diagram
        t_norm = (data['time'] % 8.9e-12) / 8.9e-12
        ax3.plot(t_norm, data['voltage'], 'b.', alpha=0.1, markersize=1)
        ax3.set_title('Eye Diagram')
        ax3.set_xlabel('UI')
        ax3.set_ylabel('Voltage (V)')
        
        # 4. Quality metrics
        metrics = [
            f"RMS EVM: {results['evm']['measurements'].rms_evm_percent:.2f}%",
            f"Eye Height: {results['eye']['measurements'].worst_eye_height:.3f}",
            f"Level Uniformity: {results['levels']['measurements'].uniformity:.3f}",
            f"Overall: {'PASS' if results['overall_quality'] else 'FAIL'}"
        ]
        ax4.text(0.1, 0.5, '\n'.join(metrics), transform=ax4.transAxes)
        ax4.set_title('Quality Metrics')
        ax4.axis('off')
        
        plt.tight_layout()
        plt.show()
        
    except Exception as e:
        print(f"Plotting failed: {e}")

References

PAM4 Modulation Theory
Signal Processing Handbook
IEEE 802.3 Specifications

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PAM4 Signal Analysis Tutorial

Overview

Basic Setup

Required Imports

Data Validation

Signal Generation

Test Signal Creation

Level Analysis

Basic Level Analysis

Level Quality Checks

EVM Analysis

EVM Calculation

EVM Quality Checks

Eye Analysis

Eye Measurements

Eye Quality Checks

Complete Example

Full Analysis Pipeline

Best Practices

1. Array Validation

2. Parameter Validation

3. Result Validation

4. Error Handling

Advanced Topics

Custom Analysis Pipeline

Signal Processing Utilities

Advanced Visualization

See Also

References

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PAM4 Signal Analysis Tutorial

Overview

Basic Setup

Required Imports

Data Validation

Signal Generation

Test Signal Creation

Level Analysis

Basic Level Analysis

Level Quality Checks

EVM Analysis

EVM Calculation

EVM Quality Checks

Eye Analysis

Eye Measurements

Eye Quality Checks

Complete Example

Full Analysis Pipeline

Best Practices

1. Array Validation

2. Parameter Validation

3. Result Validation

4. Error Handling

Advanced Topics

Custom Analysis Pipeline

Signal Processing Utilities

Advanced Visualization

See Also

References