{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:32:39Z","timestamp":1760243559625,"version":"build-2065373602"},"reference-count":28,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2013,9,13]],"date-time":"2013-09-13T00:00:00Z","timestamp":1379030400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Applying the particle filter (PF) technique, this paper proposes a PF-based algorithm to blindly demodulate the chaotic direct sequence spread spectrum (CDS-SS) signals under the colored or non-Gaussian noises condition. To implement this algorithm, the PFs are modified by (i) the colored or non-Gaussian noises are formulated by autoregressive moving average (ARMA) models, and then the parameters that model the noises are included in the state vector; (ii) the range-differentiating factor is imported into the intruder\u2019s chaotic system equation. Since the range-differentiating factor is able to make the inevitable chaos fitting error advantageous based on the chaos fitting method, thus the CDS-SS signals can be demodulated according to the range of the estimated message. Simulations show that the proposed PF-based algorithm can obtain a good  bit-error rate performance when extracting the original binary message from the CDS-SS signals without any knowledge of the transmitter\u2019s chaotic map, or initial value, even when colored or non-Gaussian noises exist.<\/jats:p>","DOI":"10.3390\/e15093877","type":"journal-article","created":{"date-parts":[[2013,9,16]],"date-time":"2013-09-16T11:14:40Z","timestamp":1379330080000},"page":"3877-3891","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Blind Demodulation of Chaotic Direct Sequence Spread Spectrum Signals Based on Particle Filters"],"prefix":"10.3390","volume":"15","author":[{"given":"Ting","family":"Li","sequence":"first","affiliation":[{"name":"College of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dexin","family":"Zhao","sequence":"additional","affiliation":[{"name":"College of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiping","family":"Huang","sequence":"additional","affiliation":[{"name":"College of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Chunwu","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shaojing","family":"Su","sequence":"additional","affiliation":[{"name":"College of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yimeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"College of Mechatronics Engineering and Automation, National University of Defense Technology, Deya Road, Changsha 410073, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,9,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/TCSII.2004.836047","article-title":"Breaking two secure communication systems based on chaotic masking","volume":"51","author":"Alvarez","year":"2004","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1062","DOI":"10.1109\/81.728860","article-title":"Breaking chaotic switching using generalized synchronization: Examples","volume":"45","author":"Yang","year":"1998","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1016\/j.chaos.2003.12.041","article-title":"Breaking parameter modulated chaotic secure communication system","volume":"21","author":"Alvarez","year":"2004","journal-title":"Chaos Soliton. Fract."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/0375-9601(84)90009-4","article-title":"Robust communication based on chaotic spreading sequences","volume":"188","author":"Parlitz","year":"1994","journal-title":"Phys. Lett. A"},{"key":"ref_5","unstructured":"Azou, S., Pistre, C., Duff, L.L., and Burel, G. (, January September). Sea Trial Results of a Chaotic Direct-Sequence Spread Spectrum Underwater Communication System. Proceedings of IEEE-OCEANS\u201903, San Diego, CA, USA."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2637","DOI":"10.1109\/TSP.2004.832029","article-title":"Physical-layer secrecy in AWGN via a class of chaotic DS\/SS systems: Analysis and design","volume":"52","author":"Hwang","year":"2004","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1109\/TWC.2004.842948","article-title":"Detection performance of chaotic spreading LPI waveforms","volume":"4","author":"Yu","year":"2005","journal-title":"IEEE Trans. Wireless Commun."},{"key":"ref_8","unstructured":"Sameh, M., Ali, S.T., and Naceur, B.B. (, January August). Particle Filter for State and Unknown Input Estimation of Chaotic Systems. Proceedings of International Conference on Control, Engineering and Information Technology, Nanning, China."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1016\/j.physleta.2007.10.012","article-title":"Unknown input observer based chaotic secure communication","volume":"372","author":"Chen","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"800","DOI":"10.1109\/TCSI.2010.2089547","article-title":"Adaptive unknown-input observers-based synchronization of chaotic systems for telecommunication","volume":"58","author":"Dimassi","year":"2011","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"11442","DOI":"10.1016\/j.eswa.2011.03.017","article-title":"A new state estimation method for chaotic signals: Map-particle filter method","volume":"38","author":"Park","year":"2011","journal-title":"Expert Syst. Appl."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1007\/s11071-010-9911-3","article-title":"Adaptive bidirectionally coupled synchronization of chaotic systems with unknown parameters","volume":"66","author":"Xu","year":"2011","journal-title":"Nonlinear Dyn."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/s11071-010-9802-7","article-title":"Complete (anti-)synchronization of chaotic systems with fully uncertain parameters by adaptive control","volume":"63","author":"Li","year":"2011","journal-title":"Nonlinear Dyn."},{"key":"ref_14","first-page":"5757","article-title":"A chattering-free robust adaptive sliding mode controller for synchronization of two different chaotic systems with unknown uncertainties and external disturbances","volume":"218","author":"Aghababa","year":"2012","journal-title":"Appl. Math. Comput."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1477","DOI":"10.7498\/aps.57.1477","article-title":"Breaking a chaotic direct sequence spreading spectrum secure communication system","volume":"57","author":"Hu","year":"2008","journal-title":"Acta Phys. Sin."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1824","DOI":"10.3724\/SP.J.1146.2006.02054","article-title":"Blind estimation of chaotic spread spectrum sequences","volume":"30","author":"Hu","year":"2008","journal-title":"J. Electr. Inform. Technol."},{"key":"ref_17","first-page":"e020510","article-title":"A novel unified equalization and demodulation of chaotic direct sequence spreading spectrum signal based on state estimation","volume":"60","author":"Xu","year":"2011","journal-title":"Acta Phys. Sin."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"274","DOI":"10.1063\/1.1688092","article-title":"Breaking a secure communication scheme based on the phase synchronization of chaotic systems","volume":"14","author":"Alvarez","year":"2004","journal-title":"Chaos"},{"key":"ref_19","unstructured":"Luca, M.B., Azou, S., Hodina, E., Serbanescu, A., and Burel, G. (, January June). Pseudoblind Demodulation of Chaotic DS-SS Signals through Exact Kalman Filtering. Proceedings of IEEE Communications Conference, Bucharest, Romania."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1016\/S0375-9601(98)00560-X","article-title":"Breaking chaotic secure communication using a spectrogram","volume":"247","author":"Yang","year":"1998","journal-title":"Phys. Lett. A"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1109\/TCSI.2002.808207","article-title":"Chosen ciphertext attack on chaos communication based on chaotic synchronization","volume":"50","author":"Hu","year":"2003","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"key":"ref_22","first-page":"107","article-title":"Novel approach to nonlinear\/non-Gaussian Bayesian state estimation","volume":"140","author":"Gordon","year":"1993","journal-title":"Proc. Ins. Electr. Eng."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"833","DOI":"10.1007\/s00034-008-9062-7","article-title":"Particle filter-based synchronization of chaotic colpitts circuits combating AWGN channel distortion","volume":"27","author":"Shi","year":"2008","journal-title":"Circuits Syst. Signal Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1088\/0957-0233\/18\/1\/004","article-title":"A particle filter approach for tomographic imaging based on different state-space representations","volume":"18","author":"Watzenig","year":"2007","journal-title":"Meas. Sci. Technol."},{"key":"ref_25","first-page":"4417","article-title":"Parameter modulated chaotic communication based on particle fitler","volume":"7","author":"Li","year":"2008","journal-title":"J. Comput. Inform. Syst."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1491","DOI":"10.1016\/j.chaos.2005.11.098","article-title":"Particle-filter-based estimation and prediction of chaotic states","volume":"32","author":"Zhang","year":"2007","journal-title":"Chaos Solition. Fract."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Grewal, M.S., and Andrews, A.P. (2001). Kalman Filtering: Theory and Practice Using Matlab, Wiley. [2nd ed.].","DOI":"10.1002\/0471266388"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Afraimovich, V., Cordonet, A., and Rulkov, N.F. (2002). Generalized synchronization of chaos in noninvertible maps. Phys. Rev. E, 66.","DOI":"10.1103\/PhysRevE.66.016208"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/9\/3877\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:49:17Z","timestamp":1760219357000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/15\/9\/3877"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9,13]]},"references-count":28,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2013,9]]}},"alternative-id":["e15093877"],"URL":"https:\/\/doi.org\/10.3390\/e15093877","relation":{},"ISSN":["1099-4300"],"issn-type":[{"type":"electronic","value":"1099-4300"}],"subject":[],"published":{"date-parts":[[2013,9,13]]}}}