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完整後設資料紀錄
DC 欄位 | 值 | 語言 |
---|---|---|
dc.contributor.advisor | 劉俊麟 | zh_TW |
dc.contributor.advisor | Chun-Lin Liu | en |
dc.contributor.author | 周怡宏 | zh_TW |
dc.contributor.author | Yi-Hung Chou | en |
dc.date.accessioned | 2023-08-16T16:49:08Z | - |
dc.date.available | 2023-11-09 | - |
dc.date.copyright | 2023-08-16 | - |
dc.date.issued | 2023 | - |
dc.date.submitted | 2023-08-10 | - |
dc.identifier.citation | [1] X. Yu, G. Li, and W. Lu, “Power Consumption Based on 5G Communication,”in 2021 IEEE 5th Information Technology,Networking,Electronic and Automation Control Conference (ITNEC), vol. 5, Oct. 2021, pp. 910–914.
[2] H. Zhang, H. Guo, and W. Xie, “Research on Performance of Power Saving Tech-nology for 5G Base Station,” in 2021 International Wireless Communications and Mobile Computing (IWCMC), Jun. 2021, pp. 194–198. [3] W. bin Abbas, F. Gomez-Cuba, and M. Zorzi, “Bit Allocation for Increased Power Efficiency in 5G Receivers with Variable-Resolution ADCs,” in 2017 Information Theory and Applications Workshop (ITA), Feb. 2017, pp. 1–7. [4] G. N. Katsaros, R. Tafazolli, and K. Nikitopoulos, “On the Power Consumption of Massive-MIMO, 5G New Radio with Software-Based PHY Processing,” in 2022 IEEE Globecom Workshops (GC Wkshps), Feb. 2022, pp. 765–770. [5] J. Zhang, L. Dai, X. Li, Y. Liu, and L. Hanzo, “On Low-Resolution ADCs in Practical 5G Millimeter-Wave Massive MIMO Systems,” IEEE Communications Magazine, vol. 56, no. 7, pp. 205–211, Jul. 2018. [6] O. Bar-Shalom and A. Weiss, “DOA estimation using one-bit quantized measure-ments,” IEEE Transactions on Aerospace and Electronic Systems, vol. 38, no. 3, pp. 868–884, 2002. [7] U. S. Kamilov, A. Bourquard, A. Amini, and M. Unser, “One-Bit Measurements With Adaptive Thresholds,” IEEE Signal Processing Letters, vol. 19, no. 10, pp. 607–610, 2012. [8] C. Gianelli, L. Xu, J. Li, and P. Stoica, “One-bit compressive sampling with time-varying thresholds for sparse parameter estimation,” in 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM), Jul. 2016, pp. 1–5. [9] R. W. Heath, N. González-Prelcic, S. Rangan, W. Roh, and A. M. Sayeed, “An Overview of Signal Processing Techniques for Millimeter Wave MIMO Systems,”IEEE Journal of Selected Topics in Signal Processing, vol. 10, no. 3, pp. 436–453, 2016. [10] A. De Angelis, G. De Angelis, and P. Carbone, “Low-Complexity 1-bit Detection of Parametric Signals for IoT Sensing Applications,” IEEE Transactions on Instru-mentation and Measurement, vol. 70, pp. 1–8, 2021. [11] S. Sedighi, K. V. Mishra, M. R. B. Shankar, and B. Ottersten, “Localization Perfor-mance of 1-Bit Passive Radars in NB-IOT Applications,” in 2019 IEEE 8th Interna-tional Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Dec. 2019, pp. 156–160. [12] J. S. Ubhi, A. Tomar, and M. Kumar, “Low Power 3-Bit Flash ADC Design with Leakage Power Reduction at 45 nm Technology,”in 2018 Eighth International Con-ference on Information Science and Technology (ICIST), Jun. 2018, pp. 280–287. [13] D. Zhang, C. Svensson, and A. Alvandpour, “Power consumption bounds for SAR ADCs,” in 2011 20th European Conference on Circuit Theory and Design (ECCTD), Aug. 2011, pp. 556–559. [14] C.-L. Liu and P. P. Vaidyanathan, “One-bit sparse array DOA estimation,” in 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Mar. 2017, pp. 3126–3130. [15] J. Li, M. M. Naghsh, S. J. Zahabi, and M. Modarres-Hashemi, “Compressive radar sensing via one-bit sampling with time-varying thresholds,” in 2016 50th Asilomar Conference on Signals, Systems and Computers, Nov. 2016, pp. 1164–1168. [16] P. Carbone, J. Schoukens, A. De Angelis, A. Moschitta, and F. Santoni, “One-Bit Constrained Measurements of Parametric Signals,” IEEE Transactions on Instru-mentation and Measurement, vol. 71, pp. 1–13, 2022. [17] J. Han, G. Li, and X.-P. Zhang, “Design of Adaptive Thresholds For One-Bit Radar Imaging Based on Adversarial Samples,” in 2019 6th Asia-Pacific Conference on Synthetic Aperture Radar (APSAR), Nov. 2019, pp. 1–5. [18] ——, “One-Bit Radar Imaging Via Adaptive Binary Iterative Hard Thresholding,”IEEE Transactions on Computational Imaging, vol. 7, pp. 1005–1017, 2021. [19] C. Gianelli, L. Xu, J. Li, and P. Stoica, “One-Bit compressive sampling with time-varying thresholds for multiple sinusoids,” in 2017 IEEE 7th International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), Dec. 2017, pp. 1–5. [20] A. Eamaz, F. Yeganegi, and M. Soltanalian, “Covariance Recovery for One-Bit Sampled Non-Stationary Signals With Time-Varying Sampling Thresholds,” IEEE Trans-actions on Signal Processing, pp. 1–15, 2022, conference Name: IEEE Transactions on Signal Processing. [21] ——, “Covariance Recovery for One-Bit Sampled Data With Time-Varying Sampling Thresholds—Part I: Stationary Signals,” Mar. 2022. [Online]. Available: https://www.techrxiv.org/articles/preprint/Covariance_Recovery_for_One-Bit_ Sampled_Data_With_Time-Varying_Sampling_Thresholds_Part_I_Stationary_Signals/19224669/1 [22] ——, “Covariance Recovery for One-Bit Sampled Data With Time-Varying Sampling Thresholds—Part II: Non-Stationary Signals,” Mar. 2022. [Online]. Available: https://www.techrxiv.org/articles/preprint/Covariance_Recovery_for_One-Bit_Sampled_Data_With_Time-Varying_Sampling_Thresholds_Part_II_Non-Stationary_Signals/19224687/1 [23] C.-L. Liu and Z.-M. Lin, “One-Bit Autocorrelation Estimation With Non-Zero Thresholds,” in ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Jun. 2021, pp. 4520–4524. [24] J. Capon, “High-Resolution Frequency-Wavenumber Spectrum Analysis,” Proceed-ings of the IEEE, vol. 57, no. 8, pp. 1408–1418, Aug. 1969. [25] P. Stoica and R. L. Moses, Spectral Analysis of Signals. Upper Saddle River, N.J: Pearson/Prentice Hall, 2005. [26] R. Roy and T. Kailath, “ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques,” IEEE Transactions on Acoustics, Speech, and Signal Pro-cessing, vol. 37, no. 7, pp. 984–995, Jul. 1989. [27] R. Price, “A useful theorem for nonlinear devices having Gaussian inputs,” IRE Transactions on Information Theory, vol. 4, no. 2, pp. 69–72, 1958. [28] A. Eamaz, F. Yeganegi, and M. Soltanalian, “Modified Arcsine Law for One-Bit Sampled Stationary Signals with Time-Varying Threshold,” in ICASSP 2021-2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Jun. 2021, pp. 5459–5463. [29] Y.-H. Xiao, L. Huang, D. Ramírez, C. Qian, and H. C. So, “One-Bit Covariance Reconstruction with Non-zero Thresholds: Algorithm and Performance Analysis,”Mar. 2023. [30] R. Schreier and G. C. Temes, “Understanding Delta-Sigma Data Converters | IEEE eBooks | IEEE Xplore,” Hoboken, New Jersey, United States, 2005. [Online]. Available: https://ieeexplore.ieee.org/book/5264508 [31] C. C. Aggarwal, Neural Networks and Deep Learning: A Textbook. Cham: Springer International Publishing, 2018. [32] B. Hu and L. Lessard, “Control Interpretations for First-Order Optimization Methods,” Mar. 2017, arXiv:1703.01670 [cs, math]. [Online]. Available: http://arxiv.org/abs/1703.01670 [33] J. H. Wilkinson, The Perfidious Polynomial, ser. Studies in Mathematics, G. H. Golub, Ed. Washington, D.C.: Mathematical Association of America, 1984, vol. 24. [34] E. L. Lehmann and G. Casella, Theory of Point Estimation, 2nd ed., ser. Springer Texts in Statistics. New York: Springer, 1998. [35] A. Merberg and S. J. Miller. (2008, 5) The Cramer-Rao Inequality. [Online]. Avail-able: https://web.williams.edu/Mathematics/sjmiller/public_html/BrownClasses/162/Handouts/CramerRaoHandout08.pdf [36] F. M. Dekking, C. Kraaikamp, H. P. Lopuhaä, and L. E. Meester, “Efficiency and Mean Squared Error,” in A Modern Introduction to Probability and Statistics: Understanding Why and How, ser. Springer Texts in Statistics, F. M. Dekking, C. Kraaikamp, H. P. Lopuhaä, and L. E. Meester, Eds. London: Springer, 2005, pp. 299–311. [37] S. P. Boyd and L. Vandenberghe, Convex optimization. Cambridge University Press, 2004. [38] O. I. Elhasadi, “Newton’s and Halley’s methods for real polynomials,” Ph.D. disser-tation, Dortmund University, 2007. [39] J. Fang and H. Li, “Adaptive distributed estimation of signal power from one-bit quantized data,” IEEE Transactions on Aerospace and Electronic Systems, vol. 46, no. 4, pp. 1893–1905, 2010. [40] J. J. H. Laning and R. H. Battin., Random Processes in Automatic Control. NewYork, N. Y.: McGraw-Hill Book Co, 1956, eq. (B-4). [41] M. L. Boas, MATHEMATICAL METHODS IN THE PHYSICAL SCIENCES, 3rd ed. Hoboken, NJ, USA: John Wiley and Sons, Inc., 2006. | - |
dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/89025 | - |
dc.description.abstract | 在到達方向 (DOA)、頻譜分析和雷達應用中,單元類比數位轉換器的自相關估計越來越受歡迎。因為單元類比數位轉換器的成本效益高、功耗低和硬體設計簡單。傳統上,我們利用埃爾米特定律 (Hermite Law) 進行自相關估計,但其準確性和效率並不理想。以,我們的研究改進和優化埃爾米特定律演算法,以提高自相關估計的準確性以及加快演算法的速度。
為了提高埃爾米特定律演算法在自相關估計中的準確性,我們使用克拉馬-羅限(Cramér-Rao Bound)分析估計功率和相關係數的最佳臨界值 (threshold)。結果顯示,功率和相關係數的最佳臨界值並不一致。因此,選擇一個臨界值讓功率估計和相關係數估計同時達到最佳是困難的。然而,結合兩者克拉馬-羅限的結果,在相同臨界值下,我們發現 0.7085 會有最低的克拉馬-羅限。因此,我們認為0.7085 作為臨界值的選擇是最好的。 此外,我們使用迭代方法和近似埃爾米特定理來加速埃爾米特定理。對於前者,我們使用迭代方法避免計算多個根。對於後者,我們將埃爾米特定理簡化為閉合形式的近似埃爾米特定理。兩種方法都可以減少計算時間。 最後,我們進行了一個模擬實驗來分析迭代方法。其結果表明,迭代方法比原先的埃爾米特定律演算法快 3 倍多。 | zh_TW |
dc.description.abstract | One-bit autocorrelation estimation has gained attention in the direction of arrival, spectral analysis, and radar applications, attributed to its cost efficiency, lower power consumption, and simpler hardware design. Traditionally, researchers have employed the Hermite Law for autocorrelation estimation, but its accuracy and efficiency are suboptimal. Our study primarily focuses on improving and optimizing the Hermite Law algorithm to enhance the accuracy of autocorrelation estimation, reduce hardware costs, and speed up the algorithm.
To improve the accuracy of the Hermite Law algorithm in autocorrelation estimation, we use the Cramér-Rao Bound (CRB) to analyze the optimal threshold for estimating power and correlation coefficient. The results show that the optimal power and correlation coefficient thresholds are different. Therefore, choosing a threshold that simultaneously allows for the best power and correlation coefficient estimation is challenging. However, by combining CRB results, we find that 0.7085 is the optimal point in the CRB results, indicating the minimum values among the worst values of CRB. Thus, 0.7085 is the best choice for the optimal threshold. Additionally, we use iterative methods and the Approximate Hermite Law to speed up the Hermite Law. For the former, we used iterative methods to avoid calculating multiple roots. For the latter, we simplified the Hermite Law into the Approximate Hermite Law as a closed form. Both approaches reduce computational time. Finally, we conducted a simulation experiment to analyze the iterative methods. The results indicated that the iterative methods are over 3 times faster than the Hermite Law algorithm. | en |
dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2023-08-16T16:49:08Z No. of bitstreams: 0 | en |
dc.description.provenance | Made available in DSpace on 2023-08-16T16:49:08Z (GMT). No. of bitstreams: 0 | en |
dc.description.tableofcontents | 口試委員審定書 i
致謝 iii 摘要 v Absctract vii Contents ix List of Figures xv List of Tables xvii Chapter 1 Introduction 1 1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Structure of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 Chapter 2 Preliminaries 5 2.1 System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 One-Bit ADCs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 One-Bit Quantization . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 One-Bit Quantization Statistical Properties . . . . . . . . . . . . . . 12 2.2.1 Inverse Q-function Law . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.2 The Statistical Properties of the Gaussian Distribution . . . . . . . . 14 2.2.3 Price’s Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.3 Restoring Autocorrelation in One-Bit Quantization . . . . . . . . . . 16 2.3.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.2 The Power Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.3 The Arcsine Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3.4 The Modified Arcsine Law . . . . . . . . . . . . . . . . . . . . . . 19 2.3.5 The Hermite Law . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.6 Comparison of Hermite Law, Arcsine Law, and Modified Arcsine Law 26 2.4 Cramér-Rao Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2.4.1 Review of Statistical Properties for the Cramér-Rao Bound . . . . . 27 2.4.2 Cramér-Rao Bound . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.4.3 The Regularity Condition . . . . . . . . . . . . . . . . . . . . . . . 29 2.4.4 The Physical Meaning of Cramér-Rao Bound . . . . . . . . . . . . 29 2.5 Iterative Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5.2 Steepest Descent . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5.3 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.5.4 Halley’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Chapter 3 The Cramér-Rao Bound of Hermite Law 37 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.1.2 The Log-Likelihood Function for the Cramér-Rao Bound . . . . . . 38 3.2 The Cramér-Rao Bound for Standard Deviation . . . . . . . . . . . . 40 3.2.1 The Regularity Condition . . . . . . . . . . . . . . . . . . . . . . . 40 3.2.2 A Derivation of the Cramér-Rao Bound for Standard Deviation . . . 43 3.3 The Cramér-Rao Bound for Correlation . . . . . . . . . . . . . . . . 46 3.3.1 A Derivation of the Cramér-Rao Bound for Correlation . . . . . . . 46 3.4 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.4.1 An Analysis of the Cramér-Rao Bound for Standard Deviation . . . 51 3.4.1.1 Correctness of the Cramér-Rao Bound for Standard Deviation 51 3.4.1.2 Cramér-Rao Bound for Standard Deviation under Different Correlations . . . . . . . . . . . . . . . . . . . . . . . . . 53 3.4.2 An Analysis of The Cramér-Rao Bound for Correlation . . . . . . . 56 3.4.2.1 Cramér-Rao Bound for Correlation under Different Correlations . . . . . . . . . 56 3.4.2.2 The Relationship Between Discrete Correlation and Digital Correlation . . . . . 58 3.4.3 Combining the Analysis of Cramér-Rao Bound for Standard Deviation and Correlation . . . . 59 3.4.3.1 Cramér-Rao Bound for Optimal Threshold . . . . . . . . . 60 3.4.3.2 Cramér-Rao Bound for Standard Deviation and Correlation under Various Correlations . . . . . 62 3.4.4 Conclusion Remark . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 4 Adaptive Hermite Law 67 4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 4.1.2 The Objective Function for the Iterative Method . . . . . . . . . . . 67 4.2 Iterative Methods for Correlation . . . . . . . . . . . . . . . . . . . 69 4.2.1 Steepest Descent . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 4.2.2 Newton’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.2.3 Halley’s Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 4.3 Accelerating the Iterative Methods: Strategies and Techniques . . . . 76 4.3.1 Select Initial Values for Iterative Methods . . . . . . . . . . . . . . 76 4.3.2 An Empirical Study of Truncated Hermite Law . . . . . . . . . . . 77 4.3.3 Approximated Hermite Law . . . . . . . . . . . . . . . . . . . . . 80 4.4 Algorithm Design with Iterative Methods . . . . . . . . . . . . . . . 83 4.5 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.5.1 Comparison Each Iterative Method: Steepest Descent, Newton’s Method, Halley’s Method . . 93 4.5.1.1 Evaluating Accuracy and Time Consumption of Iterative Methods at a Fixed Correlation and Fixed Threshold . . . . 94 4.5.1.2 Evaluating Accuracy and Time Consumption of Iterative Methods at Different Correlations and Fixed Threshold . . 97 4.5.1.3 Explaining Why the Estimation of Correlation is Less Accurate When Correlation is Negative .. 100 4.5.2 Performance Comparison Between Time-Varying Threshold and Constant Threshold Approaches . . . . 103 Chapter 5 Conclusion and Future Work 111 5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 5.2 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 References 115 Appendix A — Leibniz Integral Rule 121 Appendix B — Removing the Square Root Operation from the Recurrence Relation in Hermite Law 123 | - |
dc.language.iso | en | - |
dc.title | 單元量化功率和自我相關函數估計: Cramér-Rao界和自適應方法 | zh_TW |
dc.title | One-Bit Power and Autocorrelation Estimation: Cramér-Rao Bounds and Adaptive Methods | en |
dc.type | Thesis | - |
dc.date.schoolyear | 111-2 | - |
dc.description.degree | 碩士 | - |
dc.contributor.oralexamcommittee | 馮世邁;林源倍 | zh_TW |
dc.contributor.oralexamcommittee | See-May Phoong;Yuan-Pei Lin | en |
dc.subject.keyword | 單位元量化,Cramér-Rao界,Hermite定律,最陡下降法,牛頓法,哈雷法, | zh_TW |
dc.subject.keyword | One-Bit Quantization,Cramér–Rao Bound,Hermite Law,Steepest Descent,Newton's Method,Halley's Method, | en |
dc.relation.page | 125 | - |
dc.identifier.doi | 10.6342/NTU202303074 | - |
dc.rights.note | 同意授權(限校園內公開) | - |
dc.date.accepted | 2023-08-10 | - |
dc.contributor.author-college | 電機資訊學院 | - |
dc.contributor.author-dept | 電信工程學研究所 | - |
顯示於系所單位: | 電信工程學研究所 |
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