Comparative analysis of classical direction finding methods DOA

DOI: 10.31673/2412-9070.2026.017402

Abstract

Evaluation of DOA (Direction of Arrival) remains a fundamental problem in signal processing with applications in radar, sonar, wireless communications, and autonomous navigation. Its importance has grown even more with the widespread use of unmanned aerial vehicles (UAVs) in both civilian and military fields. At the same time, their growing accessibility introduces new risks, from espionage to airspace violation, making the task of reliable localization of UAV signal sources critically important. Although DOA algorithms were developed decades ago, they continue to evolve with new approaches and modern modifications.
This work presents a review of classical methods for estimating the direction of arrival (DOA). We examined six key approaches, which can be classified into four main groups: energy methods: Bartlett (DAS) and GCC-PHAT/SRP-PHAT; adaptive methods: MVDR/Capon; subspace methods: MUSIC and ESPRIT; and optimization methods: LASSO. For each method, an analysis was conducted regarding computational complexity, resolution (the ability to distinguish spatially close sources), and robustness to noise (effectiveness in low signal-to-noise ratio conditions). Experimental results, visualized in the form of polar directivity plots, demonstrate the key advantages and limitations of each approach in scenarios with different signal-to-noise ratios and the presence of spatially close sources. We also presented relevant modifications for each method found in the scientific literature. A unique feature of this article is the attention paid to the detailed derivation of formulas for classical DOA methods to ensure a better understanding of their principles at both the mathematical and intoitive levels. Article goal is describe the work of classical DOA methods, present their detailed mathematical derivation and analysis of key characteristics, and highlight the directions for their improvement.

Keywords: direction of signal arrival; sound; energy, adaptive, subspace methods; comparison criteria; application scenarios.