High-Resolution Direction Finding on Uniform Linear Arrays: A Comparative Evaluation of MUSIC Algorithm Derivatives

Year 2025, Volume: 13 Issue: 3, 1122 - 1136, 30.09.2025

Emrah Onat

https://doi.org/10.29109/gujsc.1696029

Abstract

This paper investigates various Multiple Signal Classification (MUSIC) algorithms for Direction of Arrival (DoA) estimation, including 'Traditional MUSIC', 'Root MUSIC', 'Forward/Backward Spatial Smoothing (FBSS) MUSIC', and 'Improved/Modified MUSIC'. The study elaborates on the principles underlying each algorithm and explores the factors influencing the accuracy of DoA estimation, such as the number of array elements, antenna spacing, number of snapshots, Signal-to-Noise Ratio (SNR), and scanning angle resolution. Through extensive MATLAB simulations employing the Monte Carlo method, the performance of these algorithms is evaluated and compared in scenarios involving coherent, non-coherent, and single/dual-source incident signals. The Root Mean Square Error (RMSE) is calculated as a function of the aforementioned parameters to quantify estimation accuracy. Additionally, the computational efficiency of each algorithm is assessed by comparing their execution durations. The results provide valuable insights into the strengths and limitations of each MUSIC variant, offering guidance for their application in practical DoA estimation tasks.

Keywords

ASP (Array Signal Processing) , DoA (Direction of Arrival) , MUSIC (Multiple Signal Classification) , ULA (Uniform Linear Array) , Root MUSIC , Improved/Modified MUSIC , FBSS (Forward/Backward Spatial Smoothing).

References

• [1] S. Bicakcı, and S. A. Sis, "Rf Uygulamalarda Genel Amaçlı Tınlama Frekansı Takip Edici Sistem Tasarımı, " Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım Ve Teknoloji, vol. 5, no. 2, pp. 211-221, 2017.
• [2] H. Dilmen, and M. F. Talu, "Yapisal Özellikleri Kullanan Parcacik Filtresi ile Uzun Sureli Nesne Takibi," Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım Ve Teknoloji, vol. 5, no. 1, pp. 107-118, 2017.
• [3] H. Krim and M. Viberg, "Two decades of array signal processing research: the parametric approach," in IEEE Signal Processing Magazine, vol. 13, no. 4, pp. 67-94, July 1996, doi: 10.1109/79.526899.
• [4] E. Nurbaş, E. Onat, and T. E. Tuncer, "Collaborative Direction of Arrival estimation by using Alternating Direction Method of Multipliers in distributed sensor array networks employing Sparse Bayesian Learning framework", Digital Signal Processing, vol. 130, p. 103739, 2022.
• [5] B. Porat and B. Friedlander, "Direction finding algorithms based on high-order statistics," in IEEE Transactions on Signal Processing, vol. 39, no. 9, pp. 2016-2024, Sept. 1991, doi: 10.1109/78.134434.
• [6] P. Chevalier, A. Ferreol and L. Albera, "High-Resolution Direction Finding From Higher Order Statistics: The2rmq-MUSIC Algorithm," in IEEE Transactions on Signal Processing, vol. 54, no. 8, pp. 2986-2997, Aug. 2006, doi: 10.1109/TSP.2006.877661.
• [7] F. A. Uçkun, H. Özer, E. Nurbaş and E. Onat, "Direction Finding Using Convolutional Neural Networks and Convolutional Recurrent Neural Networks," 2020 28th Signal Processing and Communications Applications Conference (SIU), Gaziantep, Turkey, 2020, pp. 1-4, doi: 10.1109/SIU49456.2020.9302448.
• [8] W. Zhu and M. Zhang, "A Deep Learning Architecture for Broadband DOA Estimation," 2019 IEEE 19th International Conference on Communication Technology (ICCT), Xi'an, China, 2019, pp. 244-247, doi: 10.1109/ICCT46805.2019.8947053.
• [9] A. M. Elbir, "DeepMUSIC: Multiple Signal Classification via Deep Learning," in IEEE Sensors Letters, vol. 4, no. 4, pp. 1-4, April 2020, Art no. 7001004, doi: 10.1109/LSENS.2020.2980384.
• [10] E. Nurbaş and E. Onat, "Direction of Arrival Estimation by Using Deep Autoencoder Network," 2020 28th Signal Processing and Communications Applications Conference (SIU), Gaziantep, Turkey, 2020, pp. 1-4, doi: 10.1109/SIU49456.2020.9302422.
• [11] R. Schmidt, "Multiple emitter location and signal parameter estimation," in IEEE Transactions on Antennas and Propagation, vol. 34, no. 3, pp. 276-280, March 1986, doi: 10.1109/TAP.1986.1143830.
• [12] A. Barabell, "Improving the resolution performance of eigenstructure-based direction-finding algorithms," ICASSP '83. IEEE International Conference on Acoustics, Speech, and Signal Processing, Boston, MA, USA, 1983, pp. 336-339, doi: 10.1109/ICASSP.1983.1172124.
• [13] A. Paulraj, et al., "Performance analysis of the music algorithm with spatial smoothing in the presence of coherent sources," in: MILCOM 1986 -IEEE Military Communications Conference: Communications-Computers: Teamed for the 90's, vol.3, 1986, pp.41.5.1–41.5.5.
• [14] Pillai, S. U., Kwon, B., H., "Forward/Backward Spatial Smoothing Techniques for Coherent Signal Identification," IEEE Trans. On Acoustics, Speech and Signal Processing, DOI: 10.1109/29.17496, Vol. 37, No. 1, 1989.
• [15] D. Kundu, ‘Modified MUSIC algorithm for estimating DOA of signals’, Signal Processing, vol. 48, no. 1, pp. 85–90, 1996. doi:10.1016/0165-1684(95)00126-3.
• [16] Xinying Li, Guiqin Yang and Yaoke Gu, "Simulation analysis of MUSIC algorithm of array signal proccessing DOA," International Conference on Automatic Control and Artificial Intelligence (ACAI 2012), Xiamen, 2012, pp. 1838-1841, doi: 10.1049/cp.2012.1349.
• [17] M. Mahamed, N. Sheikh and D. Dikarov, "Direction of Arrival (DOA) Estimation for Radars in Near-Field Regions," 2024 IEEE International Conference on Microwaves, Communications, Antennas, Biomedical Engineering and Electronic Systems (COMCAS), Tel Aviv, Israel, 2024, pp. 1-5, doi:10.1109/COMCAS58210.2024.10666232.
• [18] X. Zhou, F. Zhu, Y. Jiang, X. Zhou, W. Tan and M. Huang, "The Simulation Analysis of DOA Estimation Based on MUSIC Algorithm," 2020 5th International Conference on Mechanical, Control and Computer Engineering (ICMCCE), Harbin, China, 2020, pp. 1483-1486, doi: 10.1109/ICMCCE51767.2020.00325.
• [19] A. Dell’Aversano, A. Natale, A. Cuccaro and R. Solimene, "Linear Array Antenna Diagnostics Through a MUSIC Algorithm," in IEEE Access, vol. 7, pp. 176952-176959, 2019, doi: 10.1109/ACCESS.2019.2956680.
• [20] Hwang, H. K., Zekeriya Aliyazicioglu, Marshall Grice and Anatoly Yakovlev. “Direction of Arrival Estimation using a Root-MUSIC Algorithm.” Proceedings of the International MultiConference of Engineers and Computer Scientists 2008 Vol IIIMECS 2008, 19-21 March, 2008, Hong Kong
• [21] Xinying Li, Guiqin Yang and Yaoke Gu, "Simulation analysis of MUSIC algorithm of array signal proccessing DOA," International Conference on Automatic Control and Artificial Intelligence (ACAI 2012), Xiamen, 2012, pp. 1838-1841, doi: 10.1049/cp.2012.1349.
• [22] P. Wang, G. -j. Zhang, J. -j. Xiong, C. -y. Xue and W. -d. Zhang, "Root-MUSIC Algorithm with Real-Valued Eigendecomposition for Acoustic Vector Sensor Array," 2010 First International Conference on Pervasive Computing, Signal Processing and Applications, Harbin, China, 2010, pp. 652-656, doi: 10.1109/PCSPA.2010.163.
• [23] A. Liu, X. Zhang, J. Zhang and Q. Yang, "Enhanced root-MUSIC for coherent signals with multi-resolution composite arrays," 2019 IEEE Radar Conference (RadarConf), Boston, MA, USA, 2019, pp. 1-5, doi: 10.1109/RADAR.2019.8835637.
• [24] H. Paaso and M. Hirvonen, "Angular Resolution Improvement by Using Multi-Radar and FBSS MUSIC DoA Estimation Algorithm," 2019 IEEE Intelligent Vehicles Symposium (IV), Paris, France, 2019, pp. 730-735, doi: 10.1109/IVS.2019.8813780.
• [25] C. Liu, W. Feng, H. Li and H. Zhu, "Single Snapshot DOA Estimation Based on Spatial Smoothing MUSIC and CNN," 2021 IEEE International Conference on Signal Processing, Communications and Computing (ICSPCC), Xi'an, China, 2021, pp. 1-5, doi: 10.1109/ICSPCC52875.2021.9564893.
• [26] R. Zhagypar, K. Zhagyparova and M. T. Akhtar, "Spatially Smoothed TF-Root-MUSIC for DOA Estimation of Coherent and Non-Stationary Sources Under Noisy Conditions," in IEEE Access, vol. 9, pp. 95754-95766, 2021, doi: 10.1109/ACCESS.2021.3095345
• [27] Y. Wu, Y. Sun, W. Ge and W. Hong, "An improved forward-backward spatial smoothing MUSIC algorithm for coherent signal direction finding," IET International Radar Conference (IRC 2023), Chongqing, China, 2023, pp. 2009-2012, doi: 10.1049/icp.2024.1394.
• [28] Pooja Gupta, Vijay Verma, "Optimization of MUSIC and Improved MUSIC Algorithm to Estimate Direction of Arrival", International Journal of Image, Graphics and Signal Processing (IJIGSP), Vol.8, No.12, pp.30-37, 2016. DOI: 10.5815/ijigsp.2016.12.04
• [29] Z. Xiaofei, L. Wen, S. Ying, Z. Ruina and X. Dazhuan, "A Novel DOA estimation Algorithm Based on Eigen Space," 2007 International Symposium on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications, Hangzhou, China, 2007, pp. 551-554, doi: 10.1109/MAPE.2007.4393677.
• [30] P. Gupta and S. P. Kar, "MUSIC and improved MUSIC algorithm to estimate direction of arrival," 2015 International Conference on Communications and Signal Processing (ICCSP), Melmaruvathur, India, 2015, pp. 0757-0761, doi: 10.1109/ICCSP.2015.7322593.
• [31] Z. Wang, Z. Yang, S. Wu, H. Li, S. Tian and X. Chen, "An Improved Multiple Signal Classification for Nonuniform Sampling in Blade Tip Timing," in IEEE Transactions on Instrumentation and Measurement, vol. 69, no. 10, pp. 7941-7952, Oct. 2020, doi: 10.1109/TIM.2020.2980912.
• [32] Tuncer, T. E., Friedlander, B., "Classical and Modern Direction-of-Arrival Estimation," San Diego, CA, USA: Academic, 2009.
• [33] Stoica, P., Moses, R., "Spectral Analysis of Signals," Prentice Hall, 2005.