DOA Methods: A Comprehensive Tutorial Repository

Educational Python implementation of classical Direction of Arrival (DOA) estimation methods for narrowband signals and Uniform Linear Arrays (ULA). Designed for beginner researchers and students in array signal processing.

🎯 Scope and Objectives

This repository provides:

Clean, well-commented implementations matching academic notation
Modular design with consistent APIs across all methods
Comprehensive tutorials with step-by-step explanations
Performance comparison tools and statistical analysis
Synthetic data generators for controlled testing
Visualization utilities for understanding algorithm behavior

📚 Implemented Methods

Classical Methods

Conventional Beamforming (Delay-and-Sum)
Capon Beamforming (MVDR - Minimum Variance Distortionless Response)

Subspace Methods

MUSIC (Multiple Signal Classification)
Root-MUSIC (Polynomial rooting version)
ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques)
Unitary ESPRIT (Real-valued computations)

Maximum Likelihood Methods

Stochastic ML
Deterministic ML
WSF (Weighted Subspace Fitting)

Sparse Methods

L1-SVD
SBL (Sparse Bayesian Learning)
SPICE (Sparse Iterative Covariance-based Estimation)

📁 Repository Structure

DOA Survey/
├── src/doa_methods/              # Core implementation
│   ├── array_processing/         # ULA geometry, signal models
│   ├── classical/               # Conventional & Capon beamforming
│   ├── subspace/                # MUSIC, ESPRIT variants
│   ├── maximum_likelihood/      # ML-based methods
│   ├── sparse/                  # Sparse reconstruction methods
│   ├── simulation/              # Data generators, scenarios
│   ├── evaluation/              # Performance metrics, comparison
│   └── utils/                   # Common utilities
├── tutorials/                   # Jupyter notebooks
├── examples/                    # Standalone demo scripts
├── tests/                       # Unit tests
└── docs/                        # API documentation

🚀 Quick Start

Installation

# Clone the repository
git clone https://github.com/username/doa-methods.git
cd doa-methods

# Install dependencies
pip install -r requirements.txt

# Install in development mode
pip install -e .

Basic Usage

import numpy as np
from doa_methods.array_processing import UniformLinearArray, SignalModel
from doa_methods.classical import ConventionalBeamforming
from doa_methods.subspace import MUSIC

# Create 16-element ULA
array = UniformLinearArray(M=16, d=0.5)

# Generate synthetic data
signal_model = SignalModel(array)
doas_true = np.deg2rad([-20, 10])  # Two sources at -20° and 10°
X, S, N = signal_model.generate_signals(
    doas=doas_true, 
    N_snapshots=100, 
    snr_db=10
)

# Conventional beamforming
cbf = ConventionalBeamforming(array)
doas_cbf = cbf.estimate(X, K=2)

# MUSIC algorithm
music = MUSIC(array)  
doas_music = music.estimate(X, K=2)

print(f"True DOAs: {np.rad2deg(doas_true):.1f}°")
print(f"CBF estimates: {np.rad2deg(doas_cbf):.1f}°")
print(f"MUSIC estimates: {np.rad2deg(doas_music):.1f}°")

🔬 Test Scenarios

The repository includes predefined scenarios for systematic evaluation:

Two closely spaced sources (resolution testing)
Multiple uncorrelated sources
Correlated sources (challenging scenario)
Low SNR conditions
Varying source powers
Limited snapshots (small sample size)

Performance is evaluated across:

Number of sources: 1-4
SNR range: -10 to 30 dB
Array sizes: 8, 16, 32, 64 elements
Snapshot counts: 10-1000

📊 Performance Metrics

RMSE (Root Mean Square Error)
Resolution capability analysis
Computational complexity comparisons
Success rate in challenging conditions
Bias and variance characterization

📖 Tutorials

Interactive Jupyter notebooks cover:

Array Processing Fundamentals - ULA geometry, steering vectors
Classical Methods - Beamforming principles and trade-offs
Subspace Methods - High-resolution techniques
Maximum Likelihood - Optimal estimation theory
Sparse Methods - Modern compressed sensing approaches
Performance Comparison - Systematic benchmarking
Real-World Considerations - Practical implementation issues

🔧 Development

# Install development dependencies
pip install -r requirements-dev.txt

# Run tests
pytest tests/

# Format code
black src/ tests/ examples/

# Type checking
mypy src/

# Build documentation
cd docs/
make html

📝 Contributing

Contributions are welcome! Please see CONTRIBUTING.md for guidelines.

📄 License

This project is licensed under the MIT License - see LICENSE file for details.

📚 References

Key references for implemented methods:

Schmidt, R. O. (1986). Multiple emitter location and signal parameter estimation. IEEE Transactions on Antennas and Propagation.
Roy, R., & Kailath, T. (1989). ESPRIT-estimation of signal parameters via rotational invariance techniques. IEEE Transactions on Acoustics, Speech, and Signal Processing.
Stoica, P., & Nehorai, A. (1989). MUSIC, maximum likelihood, and Cramer-Rao bound. IEEE Transactions on Acoustics, Speech, and Signal Processing.

🤝 Acknowledgments

This educational repository is designed to help researchers and students understand DOA estimation methods through clean implementations and comprehensive tutorials.

DOA

Install / Use

README