{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,4,4]],"date-time":"2025-04-04T10:05:57Z","timestamp":1743761157412,"version":"3.37.3"},"reference-count":42,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2018,12,19]],"date-time":"2018-12-19T00:00:00Z","timestamp":1545177600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61801106","11531001"],"award-info":[{"award-number":["61801106","11531001"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Natural Science Foundation of China and the Israel Science Foundation","award":["11561141001"],"award-info":[{"award-number":["11561141001"]}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Circuits Syst Signal Process"],"published-print":{"date-parts":[[2019,4]]},"DOI":"10.1007\/s00034-018-0995-1","type":"journal-article","created":{"date-parts":[[2018,12,19]],"date-time":"2018-12-19T06:43:45Z","timestamp":1545201825000},"page":"1847-1875","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Block-Circulant Inverse Orthogonal Jacket Matrices and Its Applications to the Kronecker MIMO Channel"],"prefix":"10.1007","volume":"38","author":[{"given":"Han","family":"Hai","sequence":"first","affiliation":[]},{"given":"Moon Ho","family":"Lee","sequence":"additional","affiliation":[]},{"given":"Xiao-Dong","family":"Zhang","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2018,12,19]]},"reference":[{"key":"995_CR1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-45450-9","volume-title":"Orthogonal Transforms for Digital Signal Processing","author":"N Ahmed","year":"1975","unstructured":"N. Ahmed, K.R. Rao, Orthogonal Transforms for Digital Signal Processing (Springer, New York, 1975)"},{"key":"995_CR2","doi-asserted-by":"publisher","unstructured":"S. Bouguezel, M.O. Ahmad, M.N.S. Swamy, An efficient algorithm for the computation of the reverse Jacket transform, in 2006 IEEE International Symposium on Circuits and Systems, ISCAS 2006, Proceedings, 21\u201324 May 2006, Island of Kos, pp. 1\u20134. (2008). \n                    https:\/\/doi.org\/10.1109\/ISCAS.2006.1692780","DOI":"10.1109\/ISCAS.2006.1692780"},{"issue":"4","key":"995_CR3","doi-asserted-by":"publisher","first-page":"795","DOI":"10.1109\/TCSI.2008.2002923","volume":"56","author":"S Bouguezel","year":"2009","unstructured":"S. Bouguezel, M.O. Ahmad, M.N.S. Swamy, A new class of reciprocal-orthogonal parametric transforms. IEEE Trans. Circuits Syst. I Reg. Pap. 56(4), 795\u2013804 (2009). \n                    https:\/\/doi.org\/10.1109\/TCSI.2008.2002923","journal-title":"IEEE Trans. Circuits Syst. I Reg. Pap."},{"issue":"5","key":"995_CR4","doi-asserted-by":"publisher","first-page":"2143","DOI":"10.1109\/TSP.2007.912895","volume":"56","author":"Z Chen","year":"2008","unstructured":"Z. Chen, M.H. Lee, G. Zeng, Fast cocyclic Jacket transform. IEEE Trans. Signal Process. 56(5), 2143\u20132148 (2008). \n                    https:\/\/doi.org\/10.1109\/TSP.2007.912895","journal-title":"IEEE Trans. Signal Process."},{"key":"995_CR5","doi-asserted-by":"publisher","DOI":"10.1002\/9780470825631","volume-title":"MIMO-OFDM Wireless Communications with MATLAB","author":"YS Cho","year":"2010","unstructured":"Y.S. Cho, J. Kim, W.Y. Yang, C.G. Kang, MIMO-OFDM Wireless Communications with MATLAB (Wiley-IEEE Press, New York, 2010)"},{"key":"995_CR6","doi-asserted-by":"publisher","unstructured":"J.J. Ding, S.C. Pei, P.H. Wu, Jacket Haar transform, in ISCAS (Rio de Janeiro, Brazil, 2011), pp. 1520\u20131523. \n                    https:\/\/doi.org\/10.1109\/ISCAS.2011.5937864","DOI":"10.1109\/ISCAS.2011.5937864"},{"key":"995_CR7","doi-asserted-by":"publisher","unstructured":"J.J. Ding, S.C. Pei, P.H. Wu, Arbitrary-length Walsh-Jacket transforms, in APSIPA Annual Summit and Conference (Xi\u2019an, China, 2011). \n                    https:\/\/doi.org\/10.1007\/978-3-319-27122-4_23","DOI":"10.1007\/978-3-319-27122-4_23"},{"issue":"3","key":"995_CR8","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1109\/82.664256","volume":"45","author":"CP Fan","year":"1998","unstructured":"C.P. Fan, J.F. Yang, Fast center weighted Hadamard transform algorithms. IEEE Trans. Circuits Syst.-II Analog Digit. Signal Process. 45(3), 429\u2013432 (1998). \n                    https:\/\/doi.org\/10.1109\/82.664256","journal-title":"IEEE Trans. Circuits Syst.-II Analog Digit. Signal Process."},{"issue":"7","key":"995_CR9","doi-asserted-by":"publisher","first-page":"2811","DOI":"10.1109\/TCOMM.2017.2691712","volume":"65","author":"L Fan","year":"2017","unstructured":"L. Fan, R. Zhao, F. Gong, N. Yang, G.K. Karagiannidis, Secure multiple amplify-and-forward relaying over correlated fading channels. IEEE Trans. Commun. 65(7), 2811\u20132820 (2017). \n                    https:\/\/doi.org\/10.1109\/TCOMM.2017.2691712","journal-title":"IEEE Trans. Commun."},{"key":"995_CR10","volume-title":"Orthogonal Designs: Quadratic forms and Hadamard Matrices","author":"AV Geramita","year":"1979","unstructured":"A.V. Geramita, J. Seberry, Orthogonal Designs: Quadratic forms and Hadamard Matrices (Marcel Dekker Inc, New York, 1979)"},{"key":"995_CR11","volume-title":"Matrix Computations","author":"GH Golub","year":"1996","unstructured":"G.H. Golub, Charles F. van Van Loan, Matrix Computations, 3rd edn. (Johns Hopkins University Press, Baltimore, 1996)","edition":"3"},{"issue":"3","key":"995_CR12","doi-asserted-by":"publisher","first-page":"155","DOI":"10.1561\/0100000006","volume":"2","author":"RM Gray","year":"2006","unstructured":"R.M. Gray, Toeplitz and circulant matrices: a review. Found. Trends Commun. Inf. Theory 2(3), 155\u2013239 (2006). \n                    https:\/\/doi.org\/10.1561\/0100000006","journal-title":"Found. Trends Commun. Inf. Theory"},{"issue":"3","key":"995_CR13","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1561\/0100000066","volume":"8","author":"J Gutierrez-Gutierrez","year":"2011","unstructured":"J. Gutierrez-Gutierrez, P.M. Crespo, Block Toeplitz matrices: asymptotic results and applications. Found. Trends Commun. Inf. Theory 8(3), 179\u2013257 (2011). \n                    https:\/\/doi.org\/10.1561\/0100000066","journal-title":"Found. Trends Commun. Inf. Theory"},{"issue":"12","key":"995_CR14","doi-asserted-by":"publisher","first-page":"5671","DOI":"10.1109\/TIT.2008.2006401","volume":"54","author":"J Gutierrez-Gutierrez","year":"2008","unstructured":"J. Gutierrez-Gutierrez, P.M. Crespo, Asymptotically equivalent sequences of matrices and Hermitian block Toeplitz matrices with continuous symbols: applications to MIMO systems. IEEE Trans. Inf. Theory 54(12), 5671\u20135680 (2008). \n                    https:\/\/doi.org\/10.1109\/TIT.2008.2006401","journal-title":"IEEE Trans. Inf. Theory"},{"key":"995_CR15","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511840371","volume-title":"Topics in Matrix Analysis","author":"RA Horn","year":"1991","unstructured":"R.A. Horn, C.R. Johnson, Topics in Matrix Analysis (Cambridge University, Cambridge, 1991)"},{"key":"995_CR16","doi-asserted-by":"crossref","DOI":"10.1515\/9781400842902","volume-title":"Hadamard Matrices and Their Applications","author":"KJ Horadam","year":"2007","unstructured":"K.J. Horadam, Hadamard Matrices and Their Applications (Princeton University Press, Princeton, 2007)"},{"issue":"5","key":"995_CR17","doi-asserted-by":"publisher","first-page":"2911","DOI":"10.1109\/TIT.2011.2178230","volume":"58","author":"H Huh","year":"2012","unstructured":"H. Huh, A.M. Tulino, G. Caire, Network MIMO with linear zero-forcing beamforming: large system analysis, impact of channel estimation and reduced-complexity scheduling. IEEE Trans. Inf. Theory 58(5), 2911\u20132934 (2012). \n                    https:\/\/doi.org\/10.1109\/TIT.2011.2178230","journal-title":"IEEE Trans. Inf. Theory"},{"issue":"7","key":"995_CR18","doi-asserted-by":"publisher","first-page":"1501","DOI":"10.1109\/LCOMM.2017.2688368","volume":"21","author":"X-Q Jiang","year":"2017","unstructured":"X.-Q. Jiang, M. Wen, J. Li, W. Duan, Distributed generalized spatial modulation based on Chinese remainder theorem. IEEE Commun. Lett. 21(7), 1501\u20131504 (2017). \n                    https:\/\/doi.org\/10.1109\/LCOMM.2017.2688368","journal-title":"IEEE Commun. Lett."},{"issue":"3","key":"995_CR19","doi-asserted-by":"publisher","first-page":"550","DOI":"10.1109\/LCOMM.2017.2783955","volume":"22","author":"X-Q Jiang","year":"2018","unstructured":"X.-Q. Jiang, M. Wen, H. Hai, J. Li, S. Kim, Secrecy-enhancing scheme for spatial modulation. IEEE Commun. Lett. 22(3), 550\u2013553 (2018). \n                    https:\/\/doi.org\/10.1109\/LCOMM.2017.2783955","journal-title":"IEEE Commun. Lett."},{"key":"995_CR20","volume-title":"Jacket Matrices: Constructions and Its Applications for Fast Cooperative Wireless Signal Processing","author":"MH Lee","year":"2012","unstructured":"M.H. Lee, Jacket Matrices: Constructions and Its Applications for Fast Cooperative Wireless Signal Processing (LAP LAMBERT Publishing, Saarbr\u00fccken, 2012)"},{"issue":"9","key":"995_CR21","doi-asserted-by":"publisher","first-page":"1247","DOI":"10.1109\/31.34673","volume":"36","author":"MH Lee","year":"1989","unstructured":"M.H. Lee, The center weighted Hadamard transform. IEEE Trans. Circuits Syst. Analog Digit. Signal Process 36(9), 1247\u20131249 (1989). \n                    https:\/\/doi.org\/10.1109\/31.34673","journal-title":"IEEE Trans. Circuits Syst. Analog Digit. Signal Process"},{"issue":"1","key":"995_CR22","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1109\/82.818893","volume":"47","author":"MH Lee","year":"2000","unstructured":"M.H. Lee, A new reverse Jacket transform and its fast algorithm. IEEE Trans. Circuits Syst.-II Analog Digit. Signal Process 47(1), 39\u201347 (2000). \n                    https:\/\/doi.org\/10.1109\/82.818893","journal-title":"IEEE Trans. Circuits Syst.-II Analog Digit. Signal Process"},{"key":"995_CR23","unstructured":"M.H. Lee, H. Hai, X.-D. Zhang, MIMO Communication Method and System using the Block Circulant Jacket Matrix, USA Patent. no. 9,356,671, 05\/31\/2016"},{"issue":"8","key":"995_CR24","doi-asserted-by":"publisher","first-page":"461","DOI":"10.1109\/LSP.2006.873660","volume":"13","author":"MH Lee","year":"2006","unstructured":"M.H. Lee, J. Hou, Fast block inverse Jacket transform. IEEE Signal Process. Lett. 13(8), 461\u2013464 (2006). \n                    https:\/\/doi.org\/10.1109\/LSP.2006.873660","journal-title":"IEEE Signal Process. Lett."},{"issue":"6","key":"995_CR25","doi-asserted-by":"publisher","first-page":"1666","DOI":"10.1109\/TASSP.1986.1164972","volume":"ASSP\u201334","author":"MH Lee","year":"1986","unstructured":"M.H. Lee, M. Kaveh, Fast Hadamard transform based on a simple matrix factorization. IEEE Trans. Acoust. Speech Signal Process ASSP\u201334(6), 1666\u20131667 (1986). \n                    https:\/\/doi.org\/10.1109\/TASSP.1986.1164972","journal-title":"IEEE Trans. Acoust. Speech Signal Process"},{"issue":"29","key":"995_CR26","doi-asserted-by":"publisher","first-page":"49","DOI":"10.1016\/j.image.2013.11.002","volume":"1","author":"MH Lee","year":"2014","unstructured":"M.H. Lee, M.H.A. Khan, K.J. Kim, D. Park, A fast hybrid Jacket\u2013Hadamard matrix based diagonal block-wise transform. Signal Process. Image Commun. 1(29), 49\u201365 (2014). \n                    https:\/\/doi.org\/10.1016\/j.image.2013.11.002","journal-title":"Signal Process. Image Commun."},{"key":"995_CR27","doi-asserted-by":"publisher","first-page":"898","DOI":"10.13001\/1081-3810.1694","volume":"26","author":"MH Lee","year":"2013","unstructured":"M.H. Lee, F. Szollosi, A note on inverse-orthogonal Toeplitz matrices. Electron. J. Linear Algebra 26, 898\u2013904 (2013). \n                    https:\/\/doi.org\/10.13001\/1081-3810.1694","journal-title":"Electron. J. Linear Algebra"},{"issue":"4","key":"995_CR28","doi-asserted-by":"publisher","first-page":"171","DOI":"10.1002\/jcd.21369","volume":"22","author":"MH Lee","year":"2014","unstructured":"M.H. Lee, F. Szollosi, Hadamard Matrices Modulo 5. J. Comb Des. 22(4), 171\u2013178 (2014). \n                    https:\/\/doi.org\/10.1002\/jcd.21369","journal-title":"J. Comb Des."},{"issue":"7","key":"995_CR29","doi-asserted-by":"publisher","first-page":"1472","DOI":"10.1109\/TCSI.2011.2177013","volume":"59","author":"MH Lee","year":"2012","unstructured":"M.H. Lee, X.-D. Zhang, W. Song, X.-G. Xia, Fast reciprocal Jacket transform with many parameters. IEEE Trans. Circuits Syst. I Reg. Pap. 59(7), 1472\u20131481 (2012). \n                    https:\/\/doi.org\/10.1109\/TCSI.2011.2177013","journal-title":"IEEE Trans. Circuits Syst. I Reg. Pap."},{"key":"995_CR30","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1007\/s10623-011-9493-1","volume":"64","author":"KH Leung","year":"2012","unstructured":"K.H. Leung, B. Schmidt, New restrictions on possible orders of circulant Hadamard matrices. Des. Codes Cryptogr. 64, 143\u2013151 (2012). \n                    https:\/\/doi.org\/10.1007\/s10623-011-9493-1","journal-title":"Des. Codes Cryptogr."},{"issue":"2","key":"995_CR31","doi-asserted-by":"publisher","first-page":"1881","DOI":"10.1109\/TVT.2016.2565618","volume":"66","author":"J Li","year":"2017","unstructured":"J. Li, M. Wen, X. Cheng, Y. Yan, S. Song, M.H. Lee, Generalized precoding-aided quadrature spatial modulation. IEEE Trans. Veh. Technol. 66(2), 1881\u20131886 (2017). \n                    https:\/\/doi.org\/10.1109\/TVT.2016.2565618","journal-title":"IEEE Trans. Veh. Technol."},{"key":"995_CR32","doi-asserted-by":"publisher","first-page":"23212","DOI":"10.1109\/ACCESS.2017.2761845","volume":"5","author":"J Li","year":"2017","unstructured":"J. Li, M. Wen, X. Jiang, W. Duan, Space-time multiple-mode orthogonal frequency division multiplexing with index modulation. IEEE Access 5, 23212\u201323222 (2017). \n                    https:\/\/doi.org\/10.1109\/ACCESS.2017.2761845","journal-title":"IEEE Access"},{"key":"995_CR33","volume-title":"The theory of error correcting codes","author":"FJ Macwilliams","year":"1977","unstructured":"F.J. Macwilliams, N.J.A. Sloane, The theory of error correcting codes (North-Holland, New York, 1977)"},{"key":"995_CR34","unstructured":"S.C. Pei, J.J. Ding, Generalizing the Jacket transform by sub orthogonality extension, in EUSIOCO (European Signal Processing Conference), pp. 408\u2013412 (2009)"},{"issue":"8","key":"995_CR35","doi-asserted-by":"publisher","first-page":"2406","DOI":"10.1109\/TIT.2002.800475","volume":"48","author":"BS Rajan","year":"2000","unstructured":"B.S. Rajan, M.H. Lee, Quasi-cyclic dyadic codes in the Walsh\u2013Hadamard transform domain. IEEE Trans. Inf. Theory 48(8), 2406\u20132412 (2000). \n                    https:\/\/doi.org\/10.1109\/TIT.2002.800475","journal-title":"IEEE Trans. Inf. Theory"},{"key":"995_CR36","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1016\/0097-3165(77)90017-6","volume":"A23","author":"KW Schmidt","year":"1977","unstructured":"K.W. Schmidt, E.T.H. Wang, The weight of Hadamard matrices. J. Comb. Theory A23, 257\u2013263 (1977). \n                    https:\/\/doi.org\/10.1016\/0097-3165(77)90017-6","journal-title":"J. Comb. Theory"},{"key":"995_CR37","volume-title":"Linear Algebra and Its Applications","author":"G Strang","year":"2005","unstructured":"G. Strang, Linear Algebra and Its Applications, 4th edn. (Cengage Learning, Boston, 2005)","edition":"4"},{"key":"995_CR38","volume-title":"Essays in Linear Algebra","author":"G Strang","year":"2012","unstructured":"G. Strang, Essays in Linear Algebra (Wellesley-Cambridge Press, Wellesley, 2012)"},{"issue":"6","key":"995_CR39","doi-asserted-by":"publisher","first-page":"585","DOI":"10.1002\/ett.4460100604","volume":"10","author":"E Telatar","year":"1999","unstructured":"E. Telatar, Capacity of multi-antenna Gaussian channels. Eur. Trans. Telecommun. 10(6), 585\u2013595 (1999). \n                    https:\/\/doi.org\/10.1002\/ett.4460100604","journal-title":"Eur. Trans. Telecommun."},{"key":"995_CR40","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511807213","volume-title":"Fundamentals of Wireless Communication","author":"D Tse","year":"2005","unstructured":"D. Tse, P. Viswanath, Fundamentals of Wireless Communication (Cambridge University Press, Cambridge, 2005)"},{"issue":"9","key":"995_CR41","doi-asserted-by":"publisher","first-page":"3892","DOI":"10.1109\/TCOMM.2017.2710312","volume":"65","author":"M Wen","year":"2017","unstructured":"M. Wen, E. Basar, Q. Li, B. Zheng, M. Zhang, Multiple-mode orthogonal frequency division multiplexing with index modulation. IEEE Trans. Commun. 65(9), 3892\u20133906 (2017). \n                    https:\/\/doi.org\/10.1109\/TCOMM.2017.2710312","journal-title":"IEEE Trans. Commun."},{"key":"995_CR42","volume-title":"Hadamard Matrix Analysis and Synthesis With Applications to Communications Signal\/Image Processing","author":"RK Yarlagadda","year":"1997","unstructured":"R.K. Yarlagadda, J.E. Hershey, Hadamard Matrix Analysis and Synthesis With Applications to Communications Signal\/Image Processing (Kluwer Academic Publishers, Norwell, 1997)"}],"container-title":["Circuits, Systems, and Signal Processing"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-018-0995-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00034-018-0995-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00034-018-0995-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,12,18]],"date-time":"2019-12-18T19:08:26Z","timestamp":1576696106000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00034-018-0995-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,12,19]]},"references-count":42,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,4]]}},"alternative-id":["995"],"URL":"https:\/\/doi.org\/10.1007\/s00034-018-0995-1","relation":{},"ISSN":["0278-081X","1531-5878"],"issn-type":[{"type":"print","value":"0278-081X"},{"type":"electronic","value":"1531-5878"}],"subject":[],"published":{"date-parts":[[2018,12,19]]},"assertion":[{"value":"8 May 2017","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 November 2018","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"20 November 2018","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 December 2018","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}