{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,26]],"date-time":"2025-06-26T04:07:51Z","timestamp":1750910871607,"version":"3.41.0"},"reference-count":37,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEICE Trans. Commun."],"published-print":{"date-parts":[[2018]]},"DOI":"10.1587\/transcom.2017ebp3139","type":"journal-article","created":{"date-parts":[[2017,9,10]],"date-time":"2017-09-10T22:02:48Z","timestamp":1505080968000},"page":"897-908","source":"Crossref","is-referenced-by-count":1,"title":["Weyl Spreading Sequence Optimizing CDMA"],"prefix":"10.23919","volume":"E101.B","author":[{"given":"Hirofumi","family":"TSUDA","sequence":"first","affiliation":[{"name":"Kyoto University"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ken","family":"UMENO","sequence":"additional","affiliation":[{"name":"Kyoto University"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"263","reference":[{"key":"1","doi-asserted-by":"crossref","unstructured":"[1] C.E. Shannon, \u201cA mathematical theory of communication,\u201d Bell Syst. Tech. J., vol.27, no.3, pp.379-423, 1948. 10.1002\/j.1538-7305.1948.tb01338.x","DOI":"10.1002\/j.1538-7305.1948.tb01338.x"},{"key":"2","doi-asserted-by":"publisher","unstructured":"[2] S. Verd\u00fa and S. Shamai, \u201cSpectral efficiency of CDMA with random spreading,\u201d IEEE Trans. Inf. Theory, vol.45, no.2, pp.622-640, 1999. 10.1109\/18.749007","DOI":"10.1109\/18.749007"},{"key":"3","unstructured":"[3] J. Proakis, Digital Communications, McGraw-Hill, New York, 1995."},{"key":"4","doi-asserted-by":"crossref","unstructured":"[4] R. Steele and L. Hanzo, Mobile Radio Communications, Second and Third Generation Cellular and WATM Systems: 2nd. IEEE Press-John Wiley, 1999. 10.1109\/9780470547229","DOI":"10.1109\/9780470547229"},{"key":"5","doi-asserted-by":"publisher","unstructured":"[5] M. Honig, U. Madhow, and S. Verdu, \u201cBlind adaptive multiuser detection,\u201d IEEE Trans. Inf. Theory, vol.41, no.4, pp.944-960, 1995. 10.1109\/18.391241","DOI":"10.1109\/18.391241"},{"key":"6","doi-asserted-by":"publisher","unstructured":"[6] T. Ristaniemi and J. Joutsensalo, \u201cAdvanced ICA-based receivers for block fading DS-CDMA channels,\u201d Signal Process., vol.82, no.3, pp.417-431, 2002. 10.1016\/s0165-1684(01)00194-3","DOI":"10.1016\/S0165-1684(01)00194-3"},{"key":"7","unstructured":"[7] A. Hyv\u00e4rinen, J. Karhunen, and E. Oja, Independent Component Analysis, vol.46, John Wiley &amp; Sons, 2004."},{"key":"8","doi-asserted-by":"publisher","unstructured":"[8] S. Verdu, \u201cMinimum probability of error for asynchronous Gaussian multiple-access channels,\u201d IEEE Trans. Inf. Theory, vol.32, no.1, pp.85-96, 1986. 10.1109\/tit.1986.1057121","DOI":"10.1109\/TIT.1986.1057121"},{"key":"9","doi-asserted-by":"publisher","unstructured":"[9] P. Viswanath, V. Anantharam, and D.N.C. Tse, \u201cOptimal sequences, power control, and user capacity of synchronous CDMA systems with linear MMSE multiuser receivers,\u201d IEEE Trans. Inf. Theory, vol.45, no.6, pp.1968-1983, 1999. 10.1109\/18.782119","DOI":"10.1109\/18.782119"},{"key":"10","doi-asserted-by":"crossref","unstructured":"[10] L.R. Welch, \u201cLower bounds on the maximum cross correlation of signals,\u201d IEEE Trans. Inf. Theory, vol.20, no.3, pp.397-399, 1974. 10.1109\/tit.1974.1055219","DOI":"10.1109\/TIT.1974.1055219"},{"key":"11","doi-asserted-by":"publisher","unstructured":"[11] S. Ulukus and R.D. Yates. \u201cUser capacity of asynchronous CDMA systems with matched filter receivers and optimum signature sequences,\u201d IEEE Trans. Inf. Theory, vol.50, no.5, pp.903-909, 2004. 10.1109\/tit.2004.826694","DOI":"10.1109\/TIT.2004.826694"},{"key":"12","doi-asserted-by":"publisher","unstructured":"[12] L. Cottatellucci, R.R. Muller, and M. Debbah, \u201cAsynchronous CDMA systems with random spreading-Part I: Fundamental limits,\u201d IEEE Trans. Inf. Theory, vol.56, no.4, pp.1477-1497, 2010. 10.1109\/tit.2010.2040890","DOI":"10.1109\/TIT.2010.2040890"},{"key":"13","doi-asserted-by":"publisher","unstructured":"[13] R. Gold, \u201cOptimal binary sequences for spread spectrum multiplexing (Corresp.),\u201d IEEE Trans. Inf. Theory, vol.13, no.4, pp.619-621, 1967. 10.1109\/tit.1967.1054048","DOI":"10.1109\/TIT.1967.1054048"},{"key":"14","doi-asserted-by":"publisher","unstructured":"[14] D.V. Sarwate and M.B. Pursley, \u201cCrosscorrelation properties of pseudorandom and related sequences,\u201d Proc. IEEE, vol.68, no.5, pp.593-619, 1980. 10.1109\/proc.1980.11697","DOI":"10.1109\/PROC.1980.11697"},{"key":"15","doi-asserted-by":"crossref","unstructured":"[15] T. Kasami, \u201cWeight distribution formula for some class of cyclic codes,\u201d Coordinated Science Laboratory Report, no.R-285, 1966. 10.21236\/ad0632574","DOI":"10.21236\/AD0632574"},{"key":"16","doi-asserted-by":"publisher","unstructured":"[16] G. Heidari-Bateni and C.D. McGillem, \u201cA chaotic direct-sequence spread-spectrum communication system,\u201d IEEE Trans. Commun., vol.42, no.234, pp.1524-1527, 1994. 10.1109\/TCOMM.1994.582834","DOI":"10.1109\/TCOMM.1994.582834"},{"key":"17","doi-asserted-by":"publisher","unstructured":"[17] K.S. Halle, C.W. Wu, M. Itoh, and L.O. Chua, \u201cSpread spectrum communication through modulation of chaos,\u201d Int. J. Bifurcation Chaos, vol.3, no.2, pp.469-477, 1993. 10.1142\/s0218127493000374","DOI":"10.1142\/S0218127493000374"},{"key":"18","doi-asserted-by":"crossref","unstructured":"[18] Y. Soobul, K. Chady, and H.C.S. Rughooputh, \u201cDigital chaotic coding and modulation in CDMA,\u201d Africon Conference in Africa, 2002. IEEE AFRICON. 6th. vol.2, IEEE, 2002. 10.1109\/afrcon.2002.1160023","DOI":"10.1109\/AFRCON.2002.1160023"},{"key":"19","doi-asserted-by":"crossref","unstructured":"[19] C.C. Chen, K. Yao, K. Umeno, and E. Biglieri, \u201cDesign of spread-spectrum sequences using chaotic dynamical systems and ergodic theory,\u201d IEEE Trans. Circuits Syst. I: Fundam. Theory Appl., vol.48, no.9, pp.1110-1114, 2001. 10.1109\/81.948438","DOI":"10.1109\/81.948438"},{"key":"20","doi-asserted-by":"publisher","unstructured":"[20] K. Umeno and K. Kitayama, \u201cSpreading sequences using periodic orbits of chaos for CDMA,\u201d Electron. Lett., vol.35, no.7, pp.545-546, 1999. 10.1049\/el:19990389","DOI":"10.1049\/el:19990389"},{"key":"21","doi-asserted-by":"publisher","unstructured":"[21] G. Mazzini, R. Rovatti, and G. Setti, \u201cInterference minimisation by autocorrelation shaping in asynchronous DS-CDMA systems: Chaos-based spreading is nearly optimal,\u201d Electron. Lett., vol.35, no.13, p.1054-1055, 1999. 10.1049\/el:19990754","DOI":"10.1049\/el:19990754"},{"key":"22","doi-asserted-by":"publisher","unstructured":"[22] G. Mazzini, G. Setti, and R. Rovatti, \u201cChaotic complex spreading sequences for asynchronous DS-CDMA. I. System modeling and results,\u201d IEEE Trans. Circuits Syst. I, Fundam. Theory and Appl., vol.44, no.10, pp.937-947, 1997. 10.1109\/81.633883","DOI":"10.1109\/81.633883"},{"key":"23","doi-asserted-by":"publisher","unstructured":"[23] R. Riccardo, G. Mazzini, and G. Setti, \u201cOn the ultimate limits of chaos-based asynchronous DS-CDMA-I: Basic definitions and results,\u201d IEEE Trans. Circuits Syst. I, Reg. Papers, vol.51, no.7, pp.1336-1347, 2004. 10.1109\/tcsi.2004.830700","DOI":"10.1109\/TCSI.2004.830700"},{"key":"24","doi-asserted-by":"publisher","unstructured":"[24] D.V. Sarwate, \u201cBounds on crosscorrelation and autocorrelation of sequences,\u201d IEEE Trans. Inf. Theory, vol.25, no.6, pp.720-724, 1979. 10.1109\/tit.1979.1056116","DOI":"10.1109\/TIT.1979.1056116"},{"key":"25","doi-asserted-by":"publisher","unstructured":"[25] R. Frank, S. Zadoff, and R. Heimiller, \u201cPhase shift pulse codes with good periodic correlation properties (Corresp.),\u201d IRE Trans. Inf. Theory, vol.8, no.6, pp.381-382, 1962. 10.1109\/tit.1962.1057786","DOI":"10.1109\/TIT.1962.1057786"},{"key":"26","doi-asserted-by":"publisher","unstructured":"[26] D. Chu, \u201cPolyphase codes with good periodic correlation properties (Corresp.),\u201d IEEE Trans. Inf. Theory, vol.18, no.4, pp.531-532, 1972. 10.1109\/tit.1972.1054840","DOI":"10.1109\/TIT.1972.1054840"},{"key":"27","doi-asserted-by":"publisher","unstructured":"[27] J. Oppermann and B.S. Vucetic, \u201cComplex spreading sequences with a wide range of correlation properties,\u201d IEEE Trans. Commun., vol.45, no.3, pp.365-375, 1997. 10.1109\/26.558701","DOI":"10.1109\/26.558701"},{"key":"28","doi-asserted-by":"publisher","unstructured":"[28] H. Weyl. \u201c\u00dcber die Gleichverteilung von Zahlen mod. Eins,\u201d Math. Ann, vol.77, no.3, pp.313-352, 1916 (in German). 10.1007\/bf01475864","DOI":"10.1007\/BF01475864"},{"key":"29","doi-asserted-by":"crossref","unstructured":"[29] J. Dick and F. Pillichshammer, Digital nets and sequences: Discrepancy Theory and Quasi-Monte Carlo Integration, Cambridge University Press, 2010. 10.1017\/cbo9780511761188.006","DOI":"10.1017\/CBO9780511761188"},{"key":"30","unstructured":"[30] K. Umeno, \u201cSpread spectrum communications based on almost periodic functions,\u201d IEICE Technical Report, NLP 2014-101, 2014 (in Japanese)."},{"key":"31","doi-asserted-by":"publisher","unstructured":"[14] D.V. Sarwate and M.B. Pursley, \u201cCrosscorrelation properties of pseudorandom and related sequences,\u201d Proc. IEEE, vol.68, no.5, pp.593-619, 1980. 10.1109\/proc.1980.11697","DOI":"10.1109\/PROC.1980.11697"},{"key":"32","doi-asserted-by":"crossref","unstructured":"[32] M.B. Pursley, \u201cPerformance evaluation for phase-coded spread-spectrum multiple-access communication. I-system analysis,\u201d IEEE Trans. Commun., vol.25, no.8, pp.795-799, 1977. 10.1109\/tcom.1977.1093915","DOI":"10.1109\/TCOM.1977.1093915"},{"key":"33","doi-asserted-by":"crossref","unstructured":"[33] W. Kuhn and A.W. Tucker, \u201cNonlinear programming,\u201d in Proceedings of the Second Berkley Symposium on Mathematical Statistics and Probability, J. Neyman, ed., pp.481-492, University of California Press, Berkley, CA, 1951.","DOI":"10.1525\/9780520411586-036"},{"key":"34","doi-asserted-by":"publisher","unstructured":"[34] S.R. Park, L. Song, and S. Yoon, \u201cA new polyphase sequence with perfect even and good odd cross-correlation functions for DS\/CDMA systems,\u201d IEEE Trans. Veh. Technol., vol.51, no.5, pp.855-866, 2002. 10.1109\/tvt.2002.800636","DOI":"10.1109\/TVT.2002.800636"},{"key":"35","doi-asserted-by":"crossref","unstructured":"[35] H. Schulze, and C. L\u00fcders, Theory and applications of OFDM and CDMA: Wideband wireless communications, John Wiley &amp; Sons, 2005.","DOI":"10.1002\/0470017406"},{"key":"36","unstructured":"[36] J.G. Van der Corput, \u201cVerteilungsfunktionen I und II,\u201d Proc. K. Ned. Akad. Wet., vol.38, p.813, 1935."},{"key":"37","unstructured":"[37] E.R. Hansen, \u201cEq.(24.1.2),\u201d in A Table of Series and Products, Prentice Hall Series in Automatic Computation, Prentice Hall, Englewood Cliffs, 1975."}],"container-title":["IEICE Transactions on Communications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transcom\/E101.B\/3\/E101.B_2017EBP3139\/_pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,25]],"date-time":"2025-06-25T17:21:29Z","timestamp":1750872089000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.jstage.jst.go.jp\/article\/transcom\/E101.B\/3\/E101.B_2017EBP3139\/_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018]]},"references-count":37,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2018]]}},"URL":"https:\/\/doi.org\/10.1587\/transcom.2017ebp3139","relation":{},"ISSN":["0916-8516","1745-1345"],"issn-type":[{"type":"print","value":"0916-8516"},{"type":"electronic","value":"1745-1345"}],"subject":[],"published":{"date-parts":[[2018]]}}}