Uyarlamalı Sinyal Kaynağı Tahmini: Özdeğer Analizi ve Optimize Edilmiş Dinamik Eşikleme Yaklaşımı

Öz

Bu çalışma, radar, kablosuz iletişim ve sensör ağlarında çok önemli olan uyarlanabilir eşiklemeyi kullanarak sinyal kaynaklarını tanımlama yöntemini sunmaktadır. Minimum Tanım Uzunluğu (MDL), Akaike Bilgi Kriteri (AIC) ve yeni bir özdeğer tabanlı uyarlanabilir eşikleme olmak üzere üç yaklaşım, gürültülü, düşük menzilli koşullar ve birbirine yakın kaynaklar için tasarlanmış ultra geniş bant (UWB) sensör dizileri üzerinde simülasyonlar yoluyla karşılaştırılmıştır. MDL ve AIC, model karmaşıklığı ve veri uyumunu dengelemek için kovaryans matrisi özdeğerlerini kullanırken, önerilen uyarlanabilir eşikleme, özdeğer dağılımını kullanarak gürültü tabanını dinamik olarak ayarlar ve yüksek gürültülü senaryolarda sağlamlığı artırır. Sonuçlar, tüm yöntemlerin düşük gürültülü koşullarda iyi performans gösterdiğini, ancak önerilen yöntemin gürültünün yüksek olduğu veya kaynakların birbirine yakın olduğu durumlarda daha üstün olduğunu göstermektedir. Ek olarak, eşik fonksiyonundaki duyarlılık parametreleri, hafif bir arama yoluyla optimize edilerek, değişen gürültü ve kaynak yapılandırmaları arasında istikrarlı bir performans sağlar.

Anahtar Kelimeler

• Uyarlamalı Eşikleme
• Kaynak Tahmini
• Özdeğer Analizi
• Optimizasyon

Adaptive Signal Source Estimation Using Eigenvalue Analysis and Optimized Dynamic Thresholding

Öz

This study presents a method for identifying signal sources using adaptive thresholding, crucial in radar, wireless communication, and sensor networks. Three approaches—Minimum Description Length (MDL), Akaike Information Criterion (AIC), and a novel eigenvalue-based adaptive thresholding—are compared through simulations on ultra-wideband (UWB) sensor arrays designed for noisy, low-range conditions with closely spaced sources. MDL and AIC employ covariance matrix eigenvalues to balance model complexity and data fit, while the proposed adaptive thresholding dynamically adjusts the noise floor using eigenvalue distribution, improving robustness in high-noise scenarios. Results show that all methods perform well under low-noise conditions, but the proposed method excels when noise is high or sources are closely located. Additionally, sensitivity parameters in the threshold function are optimized via a lightweight search, providing stable performance across varying noise and source configurations.

Anahtar Kelimeler

• Adaptive Thresholding
• Source Estimation
• Eigenvalue Analysis
• Optimization

Kaynakça

1. [1] D. G. . Manolakis, V. K. . Ingle, and S. M. . Kogon, “Statistical and adaptive signal processing : spectral estimation, signal modeling, adaptive filtering, and array processing,” p. 796, 2005.
2. [2] D. H. D. H. Johnson and D. E. Dudgeon, “Array signal processing: concepts and techniques,” Book, p. 533, 1993, Accessed: Mar. 16, 2025. [Online]. Available: https://search.worldcat.org/title/25546138.
3. [3] J. Bin, L. An’Nan, and X. Jie, “An improved signal number estimation method based on information theoretic criteria in array processing,” 2019 IEEE 11th International Conference on Communication Software and Networks, ICCSN 2019, pp. 193–197, Jun. 2019, doi: 10.1109/ICCSN.2019.8905347.
4. [4] Jacob. Benesty, Israel. Cohen, and J. . Chen, “Fundamentals of signal enhancement and array signal processing,” 2019.
5. [5] J. M. Kahn and J. R. Barry, “Wireless infrared communications,” Proceedings of the IEEE, vol. 85, no. 2, pp. 265–298, 1997, doi: 10.1109/5.554222.
6. [6] R. F. Cinar, A. Demirkol, and Z. Demir, “An ambiguity function aided target density function for radar imaging,” Optoelectronics and Advanced Materials, Rapid Communications, vol. 9, no. 5–6, pp. 850–854, 2015.
7. [7] R. F. Cinar and A. Demirkol, “An active sensor imaging for dense target environments,” Optoelectronics and Advanced Materials, Rapid Communications, vol. 14, no. 11–12, pp. 501–508, Nov. 2020.
8. [8] J. Rissanen, “Modeling by shortest data description,” Automatica, vol. 14, no. 5, pp. 465–471, Sep. 1978, doi: 10.1016/0005-1098(78)90005-5.

9. [9] W. Cheng, Z. Zhang, H. Cao, Z. He, and G. Zhu, “A Comparative Study of Information-Based Source Number Estimation Methods and Experimental Validations on Mechanical Systems,” Sensors 2014, Vol. 14, Pages 7625-7646, vol. 14, no. 5, pp. 7625–7646, Apr. 2014, doi: 10.3390/S140507625.
10. [10] Y. Lee et al., “Source Enumeration Approaches Using Eigenvalue Gaps and Machine Learning Based Threshold for Direction-of-Arrival Estimation,” Applied Sciences 2021, Vol. 11, Page 1942, vol. 11, no. 4, p. 1942, Feb. 2021, doi: 10.3390/APP11041942.
11. [11] A. Hyvärinen and E. Oja, “Independent component analysis: algorithms and applications,” Neural Networks, vol. 13, no. 4–5, pp. 411–430, Jun. 2000, doi: 10.1016/S0893-6080(00)00026-5.
12. [12] L. Huang, T. Long, E. Mao, and H. C. So, “MMSE-based MDL method for robust estimation of number of sources without eigendecomposition,” IEEE Transactions on Signal Processing, vol. 57, no. 10, pp. 4135–4142, 2009, doi: 10.1109/TSP.2009.2024043.
13. [13] A. Wiesel and A. O. Hero, “Decomposable principal component analysis,” IEEE Transactions on Signal Processing, vol. 57, no. 11, pp. 4369–4377, 2009, doi: 10.1109/TSP.2009.2025806.
14. [14] W. S. B. Ouedraogo, A. Souloumiac, M. Jaïdane, and C. Jutten, “Non-negative blind source separation algorithm based on minimum aperture simplicial cone,” IEEE Transactions on Signal Processing, vol. 62, no. 2, pp. 376–389, Jan. 2014, doi: 10.1109/TSP.2013.2287683.
15. [15] K. Han and A. Nehorai, “Improved source number detection and direction estimation with nested arrays and ULAs using jackknifing,” IEEE Transactions on Signal Processing, vol. 61, no. 23, pp. 6118–6128, 2013, doi: 10.1109/TSP.2013.2283462.
16. [16] T. Salman, A. Badawy, T. M. Elfouly, A. Mohamed, and T. Khattab, “Estimating the number of sources: An efficient maximization approach,” in 2015 International Wireless Communications and Mobile Computing Conference (IWCMC), IEEE, Aug. 2015, pp. 199–204. doi: 10.1109/IWCMC.2015.7289082.
17. [17] H. Akaike, “Information Theory and an Extension of the Maximum Likelihood Principle,” in Biogeochemistry, vol. 1998, Springer Science and Business Media Deutschland GmbH, 1998, pp. 199–213. doi: 10.1007/978-1-4612-1694-0_15.
18. [18] H. Akaike, “A New Look at the Statistical Model Identification,” IEEE Trans. Automat. Contr., vol. 19, no. 6, pp. 716–723, 1974, doi: 10.1109/TAC.1974.1100705.
19. [19] M. Wax and T. Kailath, “Detection of signals by information theoretic criteria,” IEEE Trans. Acoust., vol. 33, no. 2, pp. 387–392, 1985, doi: 10.1109/TASSP.1985.1164557.
20. [20] S. Kritchman and B. Nadler, “Determining the number of components in a factor model from limited noisy data,” Chemometrics and Intelligent Laboratory Systems, vol. 94, no. 1, pp. 19–32, Nov. 2008, doi: 10.1016/J.CHEMOLAB.2008.06.002.
21. [21] K. P. . Burnham and D. Raymond. Anderson, “Model selection and multi-model inference : a practical information-theoretic approach,” 2011.
22. [22] Z. Lu, “Source Enumeration in Sensor Array Processing: A Model Order Selection Problem,” Nov. 2012.
23. [23] P. Liashchynskyi and P. Liashchynskyi, “Grid Search, Random Search, Genetic Algorithm: A Big Comparison for NAS,” Dec. 2019, Accessed: Sep. 09, 2025. [Online]. Available: https://arxiv.org/pdf/1912.06059.
24. [24] S. Singer, J. N.- Scholarpedia, and undefined 2009, “Nelder-mead algorithm,” var.scholarpedia.org, Accessed: Sep. 09, 2025. [Online]. Available: http://var.scholarpedia.org/article/Nelder-Mead_algorithm
25. [25] J. C. Chen, R. E. Hudson, and Kung Yao, “Maximum-likelihood source localization and unknown sensor location estimation for wideband signals in the near-field,” IEEE Transactions on Signal Processing, vol. 50, no. 8, pp. 1843–1854, Aug. 2002, doi: 10.1109/TSP.2002.800420.
26. [26] R. Schmidt, “Multiple emitter location and signal parameter estimation,” IEEE Trans. Antennas Propag., vol. 34, no. 3, pp. 276–280, Mar. 1986, doi: 10.1109/TAP.1986.1143830.
27. [27] M. Shakeri, K. R. Pattipati, and D. L. Kleinman, “Optimal measurement scheduling for state estimation,” IEEE Trans. Aerosp. Electron. Syst., vol. 31, no. 2, pp. 716–729, Apr. 1995, doi: 10.1109/7.381919.
28. [28] Q. Liang, W. Wang, X. Liu, Z. Na, M. Jia, and B. Zhang, Eds., Communications, Signal Processing, and Systems, vol. 571. Singapore: Springer Singapore, 2020. doi: 10.1007/978-981-13-9409-6.