Abstract
Last years, most sub-Nyquist sampling and parameters estimation methods for linear frequency modulated (LFM) signals are based on compressed sensing (CS) theory. However, nearly all CS reconstruction algorithms are with high computational complexity and difficult to be implemented in hardware. In this paper, a novel framework of sub-Nyquist sampling and low-complexity parameters estimation for LFM signals is proposed. The incoherent sampling in CS theory is introduced into the construction of sub-Nyquist sampling system, but no CS reconstruction algorithm is employed in the estimation of parameters. Based on the energy aggregation of LFM signals in the proper fractional Fourier transform (FRFT) domain, the chirp rate and center frequency can be estimated by linear operations. Accordingly, the proposed estimation method is easily realized compared with existing estimation methods based on CS. Simulation results verify its effectiveness and accuracy.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
D. L. Donoho, “Compressed sensing,” IEEE Trans. Inf. Theory 52, No. 4, 1289 (Apr. 2006). DOI: 10.1109/TIT. 2006.871582.
E. J. Candes, M. B. Wakin, “An introduction to compressive sampling,” IEEE Signal Processing Mag. 25, No. 2, 21 (Mar. 2008). DOI: 10.1109/MSP.2007.914731.
M. A. Davenport, P. T. Boufounos, M. B. Wakin, Richard G. Baraniuk, “Signal processing with compressive measurements,” IEEE J. Selected Topics Signal Processing 4, No. 2, 445 (Apr. 2010). DOI: 10.1109/JSTSP. 2009.2039178.
Zha Song, Liu Peiguo, Huang Jijun, “Parameter estimation of LFM signal via compressive sensing,” Proc. of IET Int. Radar Conf., 14–16 Apr. 2013, Xi’an, China (IEEE, 2013), pp. 1–5. 10.1049/cp.2013.0315.
M. Joneidi, A. Zaeemzadeh, S. Rezaeifar, Mahdi Abavisani, Nazanin Rahnavard, “LFM signal detection and estimation based on sparse representation,” Proc. of 49th Annual Conf. on Information Sciences and Systems, 18–20 Mar. 2015, Baltimore, MD, USA (IEEE, 2015), pp. 1–5. DOI: 10.1109/CISS.2015.7086856.
Z. Yang, W. Z. Cheng, “DOA estimation of LFM signals based on compressed sensing,” Application Research Computers 26, No. 12, 4642 (Dec. 2009). DOI: 0.3969/j.issn.1001-3695.2009.12.067.
Bing Liu, Ping Fu, Cong Xu, Jian-xin Gai, “Parameter estimation of LFM signal with compressive measurements,” J. Convergence Inf. Technol. 6, No. 3, 303 (Mar. 2011). DOI: 10.4156/jcit.vol6.issue3.35.
K. Wang, W. Ye, G. Lao, Y. Wang, “Fast algorithm on parameter estimation of wideband LFM signal based on down-chirp and CS,” Proc. of IEEE Int. Conf. on Signal Processing, Communications and Computing, 5–8 Aug. 2014, Guilin, China (IEEE, 2014), pp. 133–136. DOI: 10.1109/ICSPCC.2014.6986168.
H. Yan, C. Dong, G. Zhao, “Parameter estimation of LFM signal based on compressed sensing,” Chinese J. Radio Science 30, No. 3, 449 (June 2015). DOI: 10.13443/j.cjors.2014070103.
J. A. Tropp, J. N. Laska, M. F. Duarte, Justin K. Romberg, Richard G. Baraniuk, “Beyond Nyquist: Efficient sampling of sparse bandlimited signals,” IEEE Trans. Inf. Theory 56, No. 1, 520 (Jan. 2010). DOI: 10.1109/TIT. 2009.2034811.
L. B. Almeida, “The fractional Fourier transform and time-frequency representations,” IEEE Trans. Signal Processing 42, No. 11, 3084 (Nov. 1994). DOI: 10.1109/78.330368.
S.-C. Pei, J.-J. Ding, “Closed-form discrete fractional and affine Fourier transforms,” IEEE Trans. Signal Processing 48, No. 5, 1338 (May 2000). DOI: 10.1109/78.839981.
B. Fang, G. Huang, J. Gao, “Sub-Nyquist sampling and reconstruction model of LFM signals based on blind compressed sensing in FRFT domain,” Circuits, Systems, and Signal Processing 34, No. 2, 419 (Feb. 2015). DOI: 10.1007/s00034-014-9859-5.
H. Wang, L. Qi, F. Zhang, N. Zheng, “Parameters estimation of the LFM signal based on the optimum seeking method and fractional Fourier transform,” Proc. of Int. Conf. on Transportation, Mechanical, and Electrical Engineering, 16–18 Dec. 2011, Changchun, China (IEEE, 2011), pp. 2331–2334. DOI: 10.1109/TMEE.2011. 6199687.
S.-C. Pei, M.-H. Yeh, C.-C. Tseng, “Discrete fractional Fourier transform based on orthogonal projections,” IEEE Trans. Signal Processing 47, No. 5, 1335 (May 1999). DOI: 10.1109/78.757221.
H. Rabah, A. Amira, B. K. Mohanty, S. Almaadeed, P. K. Meher, “FPGA implementation of orthogonal matching pursuit for compressive sensing reconstruction,” IEEE Trans. Very Large Scale Integration (VLSI) Systems 23, No. 10, 2209 (Oct. 2015). DOI: 10.1109/TVLSI.2014.2358716.
Z. Chen, X. Hou, C. Gong, X. Qian, “Compressive sensing reconstruction for compressible signal based on projection replacement,” Multimedia Tools and Applications 75, No. 5, 2565 (Mar. 2016). DOI: 10.1007/s11042-015-2578-5.
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © N. Dong, J. Wang, 2018, published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radioelektronika, 2018, Vol. 61, No. 8, pp. 431–441.
About this article
Cite this article
Dong, N., Wang, J. Sub-Nyquist Sampling and Parameters Estimation of Wideband LFM Signals Based on FRFT. Radioelectron.Commun.Syst. 61, 333–341 (2018). https://doi.org/10.3103/S0735272718080010
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0735272718080010