{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:43:35Z","timestamp":1760147015975,"version":"build-2065373602"},"reference-count":37,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2023,1,3]],"date-time":"2023-01-03T00:00:00Z","timestamp":1672704000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Parameter estimation is extremely important for a radar jammer. With binary phase shift keying (BPSK) signals widely applied in radar systems, estimating the parameters of BPSK signals has attracted increasing attention. However, the BPSK signal is difficult to be processed by traditional time frequency analysis methods due to its phase jumping and abrupt discontinuity features which makes it difficult to extract PN (PN) codes of the BPSK signal. To solve this problem, a two-step PN codes estimation method based on sparse recovery is introduced in this paper. The proposed method first pretreats the BPSK signal by estimating its center frequency and converting it to zero intermediate frequency (ZIF). The pretreatment transforms phase jumps of the BPSK signal into the level jumps of the ZIF signal. By nonconvex sparsity promoting regularization, the level jumps of the ZIF signal are extracted through an iterative algorithm. Its effectiveness is verified by numeric simulations and semiphysical tests. The corresponding results demonstrate that the proposed method is able to estimate PN codes from the BPSK signal in serious electromagnetic environments.<\/jats:p>","DOI":"10.3390\/s23010554","type":"journal-article","created":{"date-parts":[[2023,1,4]],"date-time":"2023-01-04T03:27:44Z","timestamp":1672802864000},"page":"554","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["PN Codes Estimation of Binary Phase Shift Keying Signal Based on Sparse Recovery for Radar Jammer"],"prefix":"10.3390","volume":"23","author":[{"given":"Bo","family":"Peng","sequence":"first","affiliation":[{"name":"School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100089, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Qile","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mechatronical Engineering, Beijing Institute of Technology, Beijing 100089, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cemil, A., and \u00dcnl\u00fc, M. (2022). Analysis of ADAS Radars with Electronic Warfare Perspective. Sensors, 22.","DOI":"10.3390\/s22166142"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"He, X., Liao, K., Peng, S., Tian, Z., and Huang, J. (2022). Interrupted-Sampling Repeater Jamming-Suppression Method Based on a Multi-Stages Multi-Domains Joint Anti-Jamming Depth Network. Remote Sens., 14.","DOI":"10.3390\/rs14143445"},{"key":"ref_3","first-page":"537","article-title":"An overview of waveform optimization methods for cognitive radar","volume":"8","author":"Cui","year":"2019","journal-title":"J. Radars"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1017\/S1759078717000708","article-title":"A review of self-protection deceptive jamming against chirp radars","volume":"9","author":"Hanbali","year":"2017","journal-title":"Int. J. Microw. Wirel. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"2906","DOI":"10.1109\/LAWP.2017.2751648","article-title":"Signal diverse array radar for electronic warfare","volume":"16","author":"Guo","year":"2017","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"979","DOI":"10.1109\/78.917802","article-title":"Fractional convolution and correlation via operator methods and an application to detection of linear FM signals","volume":"49","author":"Akay","year":"2001","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1109\/TAES.2002.1008986","article-title":"Hough transform for long chirp detection","volume":"38","author":"Sun","year":"2002","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.dsp.2020.102683","article-title":"Parameter estimate of multi-component LFM signals based on GAPCK-Science Direct","volume":"100","author":"Gu","year":"2020","journal-title":"Digit. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1901","DOI":"10.1109\/78.403349","article-title":"The discrete polynomial-phase transform","volume":"43","author":"Peleg","year":"1995","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Jin, Y., and Ji, H.B. (2006, January 16\u201320). Cyclic Statistic Based Blind Parameter Estimation of BPSK and QPSK Signals. Proceedings of the 2006 8th International Conference on Signal Processing, Guilin, China.","DOI":"10.1109\/ICOSP.2006.344452"},{"key":"ref_11","unstructured":"Yang, W., Yang, X., and Yin, K. (2014, January 16\u201323). Research on parameter estimation of MPSK signals based on the generalized second-order cyclic spectrum. Proceedings of the 2014 XXXIth URSI General Assembly and Scientific Symposium, Beijing, China."},{"key":"ref_12","unstructured":"Zhan, Y., and Duan, C. (2015, January 6\u20137). The application of stochastic resonance in parameter estimation for PSK signals. Proceedings of the 2015 IEEE International Conference on Communication Software and Networks, Chengdu, China."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2552","DOI":"10.1109\/TCSI.2005.858163","article-title":"A fully integrated low-power BPSK demodulator for implantable medical devices","volume":"52","author":"Hu","year":"2005","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1478","DOI":"10.1109\/TCSI.2008.918174","article-title":"A Novel BPSK Demodulator for Biological Implants","volume":"55","author":"Luo","year":"2008","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1587\/elex.7.1592","article-title":"Ultra-low power BPSK demodulator for bio-implantable chips","volume":"7","author":"Nabovati","year":"2010","journal-title":"IEICE Electron. Express"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Wang, K., Yan, X., Zhu, Z., Hao, X., Li, P., and Yang, Q. (2020). Blind Estimation Methods for BPSK Signal Based on Duffing Oscillator. Sensors, 20.","DOI":"10.3390\/s20226412"},{"key":"ref_17","first-page":"729","article-title":"Jamming Signal Design of Pseudo-code Phase Modulation Fuze Based on Duffing Oscillator","volume":"43","author":"Yan","year":"2022","journal-title":"Acta Armamentarii"},{"key":"ref_18","unstructured":"Frigo, M., and Johnson, S.G. (1998, January 15). FFTW: An adaptive software architecture for the FFT. Proceedings of the International Conference on Acoustic, Speech and Signal Processing, Seattle, WA, USA."},{"key":"ref_19","unstructured":"(2022, March 09). Invertibility of Overlap-Add Processing. Available online: gauss256.github.io."},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Allen, R.L., and Mills, D.W. (2004). Signal Analysis: Times, Frequency, Scale and Structure, Wiley-Interscience.","DOI":"10.1002\/047166037X"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Yang, Z., Sun, I., Guo, P., and Zhang, Y. (2017). A Method of Symbol Rate Estimation Based on Wavelet Transform for Digital Modulation Signals. DEStech Transaction on Computer Science and Engineering, DEStech Publications, Inc.","DOI":"10.12783\/dtcse\/cii2017\/17280"},{"key":"ref_22","unstructured":"Wang, Q., and Ge, Q. (2012, January 17\u201319). Blind estimation algorithm of parameters in PN sequence for DSSS-BPSK signals. Proceedings of the 2012 International Conference on Wavelet Active Media Technology and Information Processing (ICWAMTIP), Chengdu, China."},{"key":"ref_23","unstructured":"Guolin, L., Min, H., and Ying, Z. (2007, January 16\u201318). PN Code Recognition and Parameter Estimation of PN-BPSK Signal Based on Synchronous Demodulation. Proceedings of the 2007 8th International Conference on Electronic Measurement and Instruments, Xi\u2019an, China."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Duong, V.M., Vesely, J., Hubacek, P., Janu, P., and Phan, N.G. (2022). Detection and Parameter Estimation Analysis of Binary Shift Keying Signals in High Noise Environments. Sensors, 22.","DOI":"10.3390\/s22093203"},{"key":"ref_25","unstructured":"Morelande, M., Senadji, B., Boashash, B., and Brisbane, Q.L.D. (1997, January 4). Complex-lag polynomial Wigner-Ville distribution. Proceedings of the IEEE TENCON \u201997. IEEE Region 10 Annual Conference. Speech and Image Technologies for Computing and Telecommunications, Brisbane, Australia."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1016\/j.acha.2010.08.002","article-title":"Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool","volume":"30","author":"Daubechies","year":"2011","journal-title":"Appl. Comput. Harmon. Anal."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"15161","DOI":"10.1038\/s41598-020-72193-2","article-title":"New insights and best practices for the successful use of Empirical Mode Decomposition, Iterative Filtering and derived algorithms","volume":"10","author":"Stallone","year":"2020","journal-title":"Sci. Rep."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"531","DOI":"10.1109\/TSP.2013.2288675","article-title":"Variational Mode Decomposition","volume":"62","author":"Dragomiretskiy","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1749","DOI":"10.1137\/20M1355987","article-title":"A variational approach to additive image decomposition into structure, harmonic, and oscillatory components","volume":"14","author":"Huska","year":"2021","journal-title":"SIAM J. Imaging Sci."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1109\/83.902288","article-title":"The digital TV filter and nonlinear denoising","volume":"10","author":"Chan","year":"2001","journal-title":"IEEE Trans. Image Process."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1786","DOI":"10.1109\/LSP.2015.2432095","article-title":"Convex Denoising using Non-Convex Tight Frame Regularization","volume":"22","author":"Parekh","year":"2015","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4422","DOI":"10.1109\/ACCESS.2018.2888944","article-title":"Total Variation Denoising With Non-Convex Regularizers","volume":"7","author":"Zou","year":"2018","journal-title":"IEEE Access"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"4481","DOI":"10.1109\/TSP.2017.2711501","article-title":"Sparse Regularization via Convex Analysis","volume":"65","author":"Selesnick","year":"2017","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"772","DOI":"10.1109\/TSP.2022.3145665","article-title":"JOT: A Variational Signal Decomposition Into Jump, Oscillation and Trend","volume":"70","author":"Cicone","year":"2022","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"825","DOI":"10.1007\/s10851-019-00937-5","article-title":"Non-convex Total Variation Regularization for Convex Denoising of Signals","volume":"62","author":"Selesnick","year":"2020","journal-title":"J. Math. Imaging Vis."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"202","DOI":"10.1016\/j.ymssp.2019.02.053","article-title":"Synthesis versus analysis priors via generalized minimax-concave penalty for sparsity-assisted machinery fault diagnosis","volume":"127","author":"Wang","year":"2019","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"1237","DOI":"10.1109\/TSP.2005.843719","article-title":"Iterative frequency estimation by interpolation on Fourier coefficients","volume":"53","author":"Aboutanios","year":"2005","journal-title":"IEEE Trans. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/554\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T17:57:59Z","timestamp":1760119079000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/23\/1\/554"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,3]]},"references-count":37,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["s23010554"],"URL":"https:\/\/doi.org\/10.3390\/s23010554","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2023,1,3]]}}}