Direction of Arrival Estimation: A Tutorial Survey of Classical and Modern Methods

Direction of arrival (DOA) estimation is a fundamental problem in array signal processing with applications spanning radar, sonar, wireless communications, and acoustic signal processing. This tutorial survey provides a comprehensive introduction to classical and modern DOA estimation methods, specifically designed for students and researchers new to the field. We focus on narrowband signal processing using uniform linear arrays, presenting step-by-step mathematical derivations with geometric intuition. The survey covers classical beamforming methods, subspace-based techniques (MUSIC, ESPRIT), maximum likelihood approaches, and sparse signal processing methods. Each method is accompanied by Python implementations available in an open-source repository, enabling reproducible research and hands-on learning. Through systematic performance comparisons across various scenarios, we provide practical guidelines for method selection and parameter tuning. This work aims to bridge the gap between theoretical foundations and practical implementation, making DOA estimation accessible to beginners while serving as a comprehensive reference for the field. See https://github.com/AmgadSalama/DOA for detail implementation of the methods.