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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
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Des théorèmes d'estimation de paramètres pour les signaux LFM ont été développés en raison des avantages de la transformée de Fourier fractionnaire (FrFT). Les méthodes d'estimation traditionnelles dans le domaine de Fourier fractionnaire (FrFD) sont presque basées sur une recherche bidimensionnelle qui présente une contradiction entre performances d'estimation et complexité. Afin de résoudre ce problème, nous introduisons la recherche d'appariement orthogonal (OMP) dans le FrFD et proposons une méthode d'optimisation modifiée pour estimer la fréquence initiale et la fréquence finale des signaux LFM à bande limitée fractionnaire. Dans cet algorithme, le spectre fractionnaire de différenciation utilisé pour former la matrice d'observation dans OMP est dérivé des formulations analytiques du spectre du signal LFM, puis, sur cette base, le signal LFM a un spectre rectangulaire approximatif dans le FrFD et la corrélation entre le Le signal LFM et la matrice d'observation donnent une valeur maximale au bord du spectre (voir Sect.3.3 pour plus de détails), les informations sur le spectre de bord peuvent être extraites par OMP. Enfin, les estimations de la fréquence initiale et de la fréquence finale sont obtenues en multipliant les informations de bord par la résolution de la fréquence d'échantillonnage. La méthode proposée évite la reconstruction et la procédure traditionnelle de recherche de pic, et les itérations ne sont nécessaires que deux fois. Ainsi, la complexité de calcul est bien inférieure à celle des méthodes existantes. Parallèlement, étant donné que les vecteurs aux points de fréquence initiale et finale ont tous deux un module plus grand, de sorte que les estimations sont plus proches des valeurs réelles, de meilleures performances d'erreur quadratique moyenne normalisée (NRMSE) peuvent être obtenues. Les résultats de l'analyse théorique et de la simulation démontrent que l'algorithme proposé est d'une complexité relativement faible et que sa précision d'estimation est supérieure à celle des algorithmes basés sur la recherche et la reconstruction.
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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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
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@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},}
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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 -