{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,14]],"date-time":"2026-01-14T18:31:56Z","timestamp":1768415516529,"version":"3.49.0"},"reference-count":33,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,11,27]],"date-time":"2021-11-27T00:00:00Z","timestamp":1637971200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,11,27]],"date-time":"2021-11-27T00:00:00Z","timestamp":1637971200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Wireless Com Network"],"published-print":{"date-parts":[[2021,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper, a new scheme based on permutation index\u2013differential chaos shift keying is proposed, modeled, and evaluated in AWGN channel environment. Data is sent by frames, and each frame is headed by a single reference signal and followed by some information-bearing signals. Modulation is performed through permutations of a reference signal according to the mapped data. At the receiver, each incoming information-bearing signal undergoes all inverse permutation possibilities to perform a correlation with the delayed and stored version of the received reference signal. To decode the information bits, the detector selects the highest correlator outputs. The proposed scheme named single reference\u2013permutation index\u2013differential chaos shift keying is an enhanced version of PI-DCSK, and uses a single reference signal for multiple information-bearing ones. Hence, the energy requirement is saved by almost a half. The bit error performance is studied using the baseband system model and analytically tested using Gaussian approximation method. Results show the BER performance outperforms other standard and recently developed differentially coherent chaos systems, including Permutation Index\u2013DCSK by an average of 2.25\u00a0dB. Moreover, the analytical form which is developed to predict the bit error rate (BER) is validated by simulation. Results demonstrate the performance in AWGN is closely matching with the simulation results, particularly at high SNR.<\/jats:p>","DOI":"10.1186\/s13638-021-02060-9","type":"journal-article","created":{"date-parts":[[2021,11,27]],"date-time":"2021-11-27T08:02:53Z","timestamp":1638000173000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["A new scheme to enhance the performance of permutation index\u2013differential chaos shift keying communications system"],"prefix":"10.1186","volume":"2021","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6642-9174","authenticated-orcid":false,"given":"Nizar","family":"Al Bassam","sequence":"first","affiliation":[]},{"given":"Oday","family":"Al-Jerew","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2021,11,27]]},"reference":[{"issue":"04","key":"2060_CR1","doi-asserted-by":"publisher","first-page":"973","DOI":"10.1142\/S0218127492000562","volume":"2","author":"U Parlitz","year":"1992","unstructured":"U. Parlitz, L.O. Chua, L. Kocarev, K. Halle, A. Shang, Transmission of digital signals by chaotic synchronization. Int. J. Bifurc. Chaos 2(04), 973\u2013977 (1992)","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"11","key":"2060_CR2","doi-asserted-by":"publisher","first-page":"1129","DOI":"10.1109\/81.735435","volume":"45","author":"G Kolumb\u00e1n","year":"1998","unstructured":"G. Kolumb\u00e1n, M.P. Kennedy, L.O. Chua, The role of synchronization in digital communications using chaos. II. Chaotic modulation and chaotic synchronization. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 45(11), 1129\u20131140 (1998)","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"issue":"12","key":"2060_CR3","doi-asserted-by":"publisher","first-page":"1684","DOI":"10.1109\/81.899920","volume":"47","author":"M Sushchik","year":"2000","unstructured":"M. Sushchik, L.S. Tsimring, A.R. Volkovskii, Performance analysis of correlation-based communication schemes utilizing chaos. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47(12), 1684\u20131691 (2000)","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"issue":"6","key":"2060_CR4","doi-asserted-by":"publisher","first-page":"847","DOI":"10.1007\/s00034-008-9063-6","volume":"27","author":"AJ Lawrance","year":"2008","unstructured":"A.J. Lawrance, J. Yao, Likelihood-based demodulation in multi-user chaos shift keying communication. Circuits Syst. Signal Process. 27(6), 847\u2013864 (2008)","journal-title":"Circuits Syst. Signal Process."},{"issue":"16","key":"2060_CR5","doi-asserted-by":"publisher","first-page":"2639","DOI":"10.1049\/iet-com.2012.0103","volume":"6","author":"M Long","year":"2012","unstructured":"M. Long, Y. Chen, F. Peng, Bit error rate improvement for chaos shift keying chaotic communication systems. IET Commun. 6(16), 2639\u20132644 (2012)","journal-title":"IET Commun."},{"key":"2060_CR6","doi-asserted-by":"crossref","unstructured":"G. Kis, Z. Jako, M. Kennedy, G. Kolumb\u00e1n, Chaotic communications without synchronization (1998)","DOI":"10.1049\/cp:19980010"},{"issue":"03","key":"2060_CR7","doi-asserted-by":"publisher","first-page":"685","DOI":"10.1142\/S0218127403006790","volume":"13","author":"CK Tse","year":"2003","unstructured":"C.K. Tse, F.C. Lau, A return map regression approach for noncoherent detection in chaotic digital communications. Int. J. Bifurc. Chaos 13(03), 685\u2013690 (2003)","journal-title":"Int. J. Bifurc. Chaos"},{"key":"2060_CR8","unstructured":"G. Kolumb\u00e1n, Z. J\u00e1k\u00f3, M.P. Kennedy, Enhanced versions of DCSK and FM-DCSK data transmission systems. In: ISCAS\u201999. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No. 99CH36349), vol. 4, pp. 475\u2013478 (1999). IEEE"},{"issue":"9","key":"2060_CR9","doi-asserted-by":"publisher","first-page":"1868","DOI":"10.1109\/TCSI.2004.834497","volume":"51","author":"WM Tam","year":"2004","unstructured":"W.M. Tam, F.C.-M. Lau, C. Tse, A multiple access scheme for chaos-based digital communication systems utilizing transmitted reference. IEEE Trans. Circuits Syst. I Regul. Pap. 51(9), 1868\u20131878 (2004)","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"issue":"5","key":"2060_CR10","doi-asserted-by":"publisher","first-page":"312","DOI":"10.1109\/TCSII.2012.2190859","volume":"59","author":"H Yang","year":"2012","unstructured":"H. Yang, G.-P. Jiang, High-efficiency differential-chaos-shift-keying scheme for chaos-based noncoherent communication. IEEE Trans. Circuits Syst. II Express Briefs 59(5), 312\u2013316 (2012)","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"issue":"4","key":"2060_CR11","doi-asserted-by":"publisher","first-page":"232","DOI":"10.1109\/TCSII.2013.2251949","volume":"60","author":"H Yang","year":"2013","unstructured":"H. Yang, G.-P. Jiang, Reference-modulated DCSK: a novel chaotic communication scheme. IEEE Trans. Circuits Syst. II Express Briefs 60(4), 232\u2013236 (2013)","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"issue":"03","key":"2060_CR12","doi-asserted-by":"publisher","first-page":"799","DOI":"10.1142\/S0218127411028829","volume":"21","author":"W Xu","year":"2011","unstructured":"W. Xu, L. Wang, G. Kolumb\u00e1n, A novel differential chaos shift keying modulation scheme. Int. J. Bifurc. Chaos 21(03), 799\u2013814 (2011)","journal-title":"Int. J. Bifurc. Chaos"},{"issue":"7","key":"2060_CR13","doi-asserted-by":"publisher","first-page":"448","DOI":"10.1109\/TCSII.2012.2198982","volume":"59","author":"G Kaddoum","year":"2012","unstructured":"G. Kaddoum, F. Gagnon, Design of a high-data-rate differential chaos-shift keying system. IEEE Trans. Circuits Syst. II Express Briefs 59(7), 448\u2013452 (2012)","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"issue":"10","key":"2060_CR14","doi-asserted-by":"publisher","first-page":"2855","DOI":"10.1109\/TCOMM.2010.10.080336","volume":"58","author":"M Xu","year":"2010","unstructured":"M. Xu, H. Leung, A novel high data rate modulation scheme based on chaotic signal separation. IEEE Trans. Commun. 58(10), 2855\u20132860 (2010)","journal-title":"IEEE Trans. Commun."},{"issue":"8","key":"2060_CR15","doi-asserted-by":"publisher","first-page":"3281","DOI":"10.1109\/TCOMM.2013.071013.130225","volume":"61","author":"G Kaddoum","year":"2013","unstructured":"G. Kaddoum, F.-D. Richardson, F. Gagnon, Design and analysis of a multi-carrier differential chaos shift keying communication system. IEEE Trans. Commun. 61(8), 3281\u20133291 (2013)","journal-title":"IEEE Trans. Commun."},{"issue":"4","key":"2060_CR16","doi-asserted-by":"publisher","first-page":"1027","DOI":"10.1109\/TCSI.2012.2209304","volume":"60","author":"P Chen","year":"2013","unstructured":"P. Chen, L. Wang, F.C. Lau, One analog STBC-DCSK transmission scheme not requiring channel state information. IEEE Trans. Circuits Syst. I Regul. Pap. 60(4), 1027\u20131037 (2013)","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"issue":"6","key":"2060_CR17","doi-asserted-by":"publisher","first-page":"733","DOI":"10.1109\/TCSI.2003.812616","volume":"50","author":"FC Lau","year":"2003","unstructured":"F.C. Lau, K.Y. Cheong, C. Tse, Permutation-based DCSK and multiple-access DCSK systems. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 50(6), 733\u2013742 (2003)","journal-title":"IEEE Trans. Circuits Syst. I Fundam. Theory Appl."},{"issue":"6","key":"2060_CR18","doi-asserted-by":"publisher","first-page":"567","DOI":"10.1007\/s00034-003-1018-3","volume":"22","author":"KY Cheong","year":"2003","unstructured":"K.Y. Cheong, F.C. Lau, K.T. Chi, Permutation-based M-ary chaotic-sequence spread-spectrum communication systems. Circuits Syst. Signal Process. 22(6), 567\u2013577 (2003)","journal-title":"Circuits Syst. Signal Process."},{"issue":"4","key":"2060_CR19","doi-asserted-by":"publisher","first-page":"2997","DOI":"10.1109\/TVT.2017.2774108","volume":"67","author":"M Herceg","year":"2017","unstructured":"M. Herceg, G. Kaddoum, D. Vranje\u0161, E. Soujeri, Permutation index DCSK modulation technique for secure multiuser high-data-rate communication systems. IEEE Trans. Veh. Technol. 67(4), 2997\u20133011 (2017)","journal-title":"IEEE Trans. Veh. Technol."},{"issue":"12","key":"2060_CR20","doi-asserted-by":"publisher","first-page":"1954","DOI":"10.1109\/TCSII.2018.2817930","volume":"65","author":"M Herceg","year":"2018","unstructured":"M. Herceg, D. Vranje\u0161, G. Kaddoum, E. Soujeri, Commutation code index DCSK modulation technique for high-data-rate communication systems. IEEE Trans. Circuits Syst. II Express Br. 65(12), 1954\u20131958 (2018)","journal-title":"IEEE Trans. Circuits Syst. II Express Br."},{"issue":"1","key":"2060_CR21","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13638-020-1644-5","volume":"2020","author":"A Dukhan","year":"2020","unstructured":"A. Dukhan, D. Jayalath, P. van Heijster, B. Senadji, J. Banks, A generalized multilevel-hybrid chaotic oscillator for low-cost and power-efficient short-range chaotic communication systems. EURASIP J. Wirel. Commun. Netw. 2020(1), 1\u201314 (2020)","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"issue":"5","key":"2060_CR22","doi-asserted-by":"publisher","first-page":"1970","DOI":"10.1109\/TCOMM.2018.2805342","volume":"66","author":"W Xu","year":"2018","unstructured":"W. Xu, Y. Tan, F.C. Lau, G. Kolumb\u00e1n, Design and optimization of differential chaos shift keying scheme with code index modulation. IEEE Trans. Commun. 66(5), 1970\u20131980 (2018)","journal-title":"IEEE Trans. Commun."},{"issue":"9","key":"2060_CR23","doi-asserted-by":"publisher","first-page":"6099","DOI":"10.1109\/TCOMM.2019.2918518","volume":"67","author":"X Cai","year":"2019","unstructured":"X. Cai, W. Xu, S. Hong, L. Wang, Dual-mode differential chaos shift keying with index modulation. IEEE Trans. Commun. 67(9), 6099\u20136111 (2019)","journal-title":"IEEE Trans. Commun."},{"issue":"5","key":"2060_CR24","doi-asserted-by":"publisher","first-page":"413","DOI":"10.1615\/TelecomRadEng.v79.i5.40","volume":"79","author":"G Zhang","year":"2020","unstructured":"G. Zhang, X. Li, X. Chen, H. Xing, The m-ary security differential chaotic frequency shift system based on the MIMO model. Telecommun. Radio Eng. 79(5), 413\u2013424 (2020)","journal-title":"Telecommun. Radio Eng."},{"issue":"4","key":"2060_CR25","doi-asserted-by":"publisher","first-page":"4236","DOI":"10.1002\/dac.4236","volume":"33","author":"HA Abdullah","year":"2020","unstructured":"H.A. Abdullah, H.N. Abdullah, W.A. Mahmoud Al-Jawher, A hybrid chaotic map for communication security applications. Int. J. Commun. Syst. 33(4), 4236 (2020)","journal-title":"Int. J. Commun. Syst."},{"key":"2060_CR26","doi-asserted-by":"publisher","first-page":"104432","DOI":"10.1109\/ACCESS.2020.2998395","volume":"8","author":"N Nguyen","year":"2020","unstructured":"N. Nguyen, L. Pham-Nguyen, M.B. Nguyen, G. Kaddoum, A low power circuit design for chaos-key based data encryption. IEEE Access 8, 104432\u2013104444 (2020)","journal-title":"IEEE Access"},{"issue":"1","key":"2060_CR27","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13638-020-01861-8","volume":"2021","author":"Y Guo","year":"2021","unstructured":"Y. Guo, J. Yang, B. Liu, Application of chaotic encryption algorithm based on variable parameters in RFID security. EURASIP J. Wirel. Commun. Netw. 2021(1), 1\u201317 (2021)","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"issue":"1","key":"2060_CR28","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13638-018-1318-8","volume":"2019","author":"C Liang","year":"2019","unstructured":"C. Liang, Q. Zhang, J. Ma, K. Li, Research on neural network chaotic encryption algorithm in wireless network security communication. EURASIP J. Wirel. Commun. Netw. 2019(1), 1\u201310 (2019)","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"issue":"1","key":"2060_CR29","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13638-020-01861-8","volume":"2019","author":"T Li","year":"2019","unstructured":"T. Li, W. Yan, L. Ping, P. Fang, A WSN positioning algorithm based on 3 D discrete chaotic mapping. EURASIP J. Wirel. Commun. Netw. 2019(1), 1\u201313 (2019)","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"issue":"1","key":"2060_CR30","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1186\/s13638-017-0866-7","volume":"2017","author":"L Novosel","year":"2017","unstructured":"L. Novosel, G. \u0160i\u0161ul, Performance evaluation of chaotic spreading sequences on software-defined radio. EURASIP J. Wirel. Commun. Netw. 2017(1), 1\u201312 (2017)","journal-title":"EURASIP J. Wirel. Commun. Netw."},{"issue":"3","key":"2060_CR31","first-page":"51","volume":"25","author":"JR Pulido-Luna","year":"2020","unstructured":"J.R. Pulido-Luna, J.A. L\u00f3pez-Renter\u00eda, N.R. Cazarez-Castro, Design of a nonhomogeneous nonlinear synchronizer and its implementation in reconfigurable hardware. Math. Comput. Appl. 25(3), 51 (2020)","journal-title":"Math. Comput. Appl."},{"issue":"1","key":"2060_CR32","doi-asserted-by":"publisher","first-page":"50","DOI":"10.5152\/electrica.2021.20036","volume":"21","author":"NX Quyen","year":"2021","unstructured":"N.X. Quyen, Ber analysis for 2 \u00d7\u00a02 mimo high-efficiency DCSK system. Electrica 21(1), 50\u201358 (2021)","journal-title":"Electrica"},{"key":"2060_CR33","doi-asserted-by":"publisher","first-page":"2621","DOI":"10.1109\/ACCESS.2016.2572730","volume":"4","author":"G Kaddoum","year":"2016","unstructured":"G. Kaddoum, Wireless chaos-based communication systems: a comprehensive survey. IEEE Access 4, 2621\u20132648 (2016)","journal-title":"IEEE Access"}],"container-title":["EURASIP Journal on Wireless Communications and Networking"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-021-02060-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1186\/s13638-021-02060-9\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1186\/s13638-021-02060-9.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,11,27]],"date-time":"2021-11-27T08:07:08Z","timestamp":1638000428000},"score":1,"resource":{"primary":{"URL":"https:\/\/jwcn-eurasipjournals.springeropen.com\/articles\/10.1186\/s13638-021-02060-9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,11,27]]},"references-count":33,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2021,12]]}},"alternative-id":["2060"],"URL":"https:\/\/doi.org\/10.1186\/s13638-021-02060-9","relation":{},"ISSN":["1687-1499"],"issn-type":[{"value":"1687-1499","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,11,27]]},"assertion":[{"value":"6 March 2021","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 November 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no competing interests. The authors declare that they have no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"190"}}