Open Access

ARTICLE

Joint Estimation of Elevation and Azimuth Angles with Triple-Parallel ULAs Using Metaheuristic and Direct Search Methods

Fawad Zaman^1,#, Adeel Iqbal^2,#, Bakhtiar Ali¹, Abdul Khader Jilani Saudagar^3,*

1 Department of Electrical Engineering, COMSATS University Islamabad, Islamabad, 45550, Pakistan
2 School of Computer Science & Engineering, Yeungnam University, Gyeongsan-si, 38541, Republic of Korea
3 Information Systems Department, College of Computer and Information Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, 11432, Saudi Arabia

* Corresponding Author: Abdul Khader Jilani Saudagar. Email:
# These authors contributed equally to this work

(This article belongs to the Special Issue: Computer Modeling for Future Communications and Networks)

Computer Modeling in Engineering & Sciences 2025, 145(2), 2535-2550. https://doi.org/10.32604/cmes.2025.072638

Received 31 August 2025; Accepted 21 October 2025; Issue published 26 November 2025

Abstract

Accurate estimation of the Direction-of-Arrival (DoA) of incident plane waves is essential for modern wireless communication, radar, sonar, and localization systems. Precise DoA information enables adaptive beamforming, spatial filtering, and interference mitigation by steering antenna array beams toward desired sources while suppressing unwanted signals. Traditional one-dimensional Uniform Linear Arrays (ULAs) are limited to elevation angle estimation due to geometric constraints, typically within the range [0, π]. To capture full spatial characteristics in environments with multipath and angular spread, joint estimation of both elevation and azimuth angles becomes necessary. However, existing 2D and 3D array geometries often entail increased hardware complexity and computational cost. This work proposes a novel and efficient framework for joint elevation and azimuth angle estimation using three spatially separated, parallel ULAs. The array configuration exploits spatial diversity and orthogonal projections to capture complete directional information with minimal structural overhead. A customized objective function based on the mean square error between measured and reconstructed array outputs is formulated to guide the estimation process. To solve the resulting non-convex optimization problem, three strategies are investigated: a global Genetic Algorithm (GA), a local Pattern Search (PS), and a hybrid GA-PS method that combines global exploration with local refinement. The proposed framework supports automatic pairing of elevation and azimuth angles, eliminating the need for manual post-processing. Extensive simulations validate the robustness, convergence, and accuracy of all three methods under varying signal-to-noise ratio conditions. Results confirm that the hybrid GA-PS approach achieves superior estimation performance and reduced computational complexity, making it well-suited for real-time and resource-constrained applications in next-generation sensing and communication systems.

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