The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
Copyrights notice
The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
pandangan teks lengkap
113
Teorem anggaran parameter untuk isyarat LFM telah dibangunkan kerana kelebihan transformasi Fourier pecahan (FrFT). Kaedah anggaran tradisional dalam domain Fourier pecahan (FrFD) hampir berdasarkan carian dua dimensi yang mempunyai percanggahan antara prestasi anggaran dan kerumitan. Untuk menyelesaikan masalah ini, kami memperkenalkan pengejaran padanan ortogon (OMP) ke dalam FrFD, mencadangkan kaedah pengoptimuman yang diubah suai untuk menganggar frekuensi awal dan kekerapan akhir bagi isyarat LFM terhad jalur pecahan. Dalam algoritma ini, spektrum pecahan pembezaan yang digunakan untuk membentuk matriks cerapan dalam OMP diperoleh daripada formulasi analisis spektrum isyarat LFM, dan kemudian, berdasarkan isyarat LFM mempunyai spektrum segi empat tepat anggaran dalam FrFD dan korelasi antara Isyarat LFM dan matriks pemerhatian menghasilkan nilai maksimum pada pinggir spektrum (lihat Bahagian.3.3 untuk butiran), maklumat spektrum tepi boleh diekstrak oleh OMP. Akhir sekali, anggaran kekerapan awal dan kekerapan akhir diperoleh melalui pendaraban maklumat tepi dengan resolusi kekerapan pensampelan. Kaedah yang dicadangkan mengelakkan pembinaan semula dan prosedur pencarian puncak tradisional, dan lelaran diperlukan hanya dua kali. Oleh itu, kerumitan pengiraan adalah jauh lebih rendah daripada kaedah sedia ada. Sementara itu, Memandangkan vektor pada frekuensi awal dan titik frekuensi akhir kedua-duanya mempunyai modulus yang lebih besar, supaya anggaran lebih hampir kepada nilai sebenar, prestasi ralat min kuasa dua punca ternormal (NRMSE) yang lebih baik boleh dicapai. Kedua-dua analisis teori dan hasil simulasi menunjukkan bahawa algoritma yang dicadangkan mempunyai kerumitan yang agak rendah dan ketepatan anggarannya lebih tinggi daripada algoritma berasaskan carian dan pembinaan semula.
Xiaomin LI
Nanjing University of Science and Technology,Henan Institute of Science and Technology
Huali WANG
The Army Engineering University of PLA
Zhangkai LUO
Space Engineering University
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Salinan
Xiaomin LI, Huali WANG, Zhangkai LUO, "Parameter Estimation of Fractional Bandlimited LFM Signals Based on Orthogonal Matching Pursuit" in IEICE TRANSACTIONS on Fundamentals,
vol. E102-A, no. 11, pp. 1448-1456, November 2019, doi: 10.1587/transfun.E102.A.1448.
Abstract: Parameter estimation theorems for LFM signals have been developed due to the advantages of fractional Fourier transform (FrFT). The traditional estimation methods in the fractional Fourier domain (FrFD) are almost based on two-dimensional search which have the contradiction between estimation performance and complexity. In order to solve this problem, we introduce the orthogonal matching pursuit (OMP) into the FrFD, propose a modified optimization method to estimate initial frequency and final frequency of fractional bandlimited LFM signals. In this algorithm, the differentiation fractional spectrum which is used to form observation matrix in OMP is derived from the spectrum analytical formulations of the LFM signal, and then, based on that the LFM signal has approximate rectangular spectrum in the FrFD and the correlation between the LFM signal and observation matrix yields a maximal value at the edge of the spectrum (see Sect.3.3 for details), the edge spectrum information can be extracted by OMP. Finally, the estimations of initial frequency and final frequency are obtained through multiplying the edge information by the sampling frequency resolution. The proposed method avoids reconstruction and the traditional peak-searching procedure, and the iterations are needed only twice. Thus, the computational complexity is much lower than that of the existing methods. Meanwhile, Since the vectors at the initial frequency and final frequency points both have larger modulus, so that the estimations are closer to the actual values, better normalized root mean squared error (NRMSE) performance can be achieved. Both theoretical analysis and simulation results demonstrate that the proposed algorithm bears a relatively low complexity and its estimation precision is higher than search-based and reconstruction-based algorithms.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.E102.A.1448/_p
Salinan
@ARTICLE{e102-a_11_1448,
author={Xiaomin LI, Huali WANG, Zhangkai LUO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Parameter Estimation of Fractional Bandlimited LFM Signals Based on Orthogonal Matching Pursuit},
year={2019},
volume={E102-A},
number={11},
pages={1448-1456},
abstract={Parameter estimation theorems for LFM signals have been developed due to the advantages of fractional Fourier transform (FrFT). The traditional estimation methods in the fractional Fourier domain (FrFD) are almost based on two-dimensional search which have the contradiction between estimation performance and complexity. In order to solve this problem, we introduce the orthogonal matching pursuit (OMP) into the FrFD, propose a modified optimization method to estimate initial frequency and final frequency of fractional bandlimited LFM signals. In this algorithm, the differentiation fractional spectrum which is used to form observation matrix in OMP is derived from the spectrum analytical formulations of the LFM signal, and then, based on that the LFM signal has approximate rectangular spectrum in the FrFD and the correlation between the LFM signal and observation matrix yields a maximal value at the edge of the spectrum (see Sect.3.3 for details), the edge spectrum information can be extracted by OMP. Finally, the estimations of initial frequency and final frequency are obtained through multiplying the edge information by the sampling frequency resolution. The proposed method avoids reconstruction and the traditional peak-searching procedure, and the iterations are needed only twice. Thus, the computational complexity is much lower than that of the existing methods. Meanwhile, Since the vectors at the initial frequency and final frequency points both have larger modulus, so that the estimations are closer to the actual values, better normalized root mean squared error (NRMSE) performance can be achieved. Both theoretical analysis and simulation results demonstrate that the proposed algorithm bears a relatively low complexity and its estimation precision is higher than search-based and reconstruction-based algorithms.},
keywords={},
doi={10.1587/transfun.E102.A.1448},
ISSN={1745-1337},
month={November},}
Salinan
TY - JOUR
TI - Parameter Estimation of Fractional Bandlimited LFM Signals Based on Orthogonal Matching Pursuit
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1448
EP - 1456
AU - Xiaomin LI
AU - Huali WANG
AU - Zhangkai LUO
PY - 2019
DO - 10.1587/transfun.E102.A.1448
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E102-A
IS - 11
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - November 2019
AB - Parameter estimation theorems for LFM signals have been developed due to the advantages of fractional Fourier transform (FrFT). The traditional estimation methods in the fractional Fourier domain (FrFD) are almost based on two-dimensional search which have the contradiction between estimation performance and complexity. In order to solve this problem, we introduce the orthogonal matching pursuit (OMP) into the FrFD, propose a modified optimization method to estimate initial frequency and final frequency of fractional bandlimited LFM signals. In this algorithm, the differentiation fractional spectrum which is used to form observation matrix in OMP is derived from the spectrum analytical formulations of the LFM signal, and then, based on that the LFM signal has approximate rectangular spectrum in the FrFD and the correlation between the LFM signal and observation matrix yields a maximal value at the edge of the spectrum (see Sect.3.3 for details), the edge spectrum information can be extracted by OMP. Finally, the estimations of initial frequency and final frequency are obtained through multiplying the edge information by the sampling frequency resolution. The proposed method avoids reconstruction and the traditional peak-searching procedure, and the iterations are needed only twice. Thus, the computational complexity is much lower than that of the existing methods. Meanwhile, Since the vectors at the initial frequency and final frequency points both have larger modulus, so that the estimations are closer to the actual values, better normalized root mean squared error (NRMSE) performance can be achieved. Both theoretical analysis and simulation results demonstrate that the proposed algorithm bears a relatively low complexity and its estimation precision is higher than search-based and reconstruction-based algorithms.
ER -