{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T01:11:51Z","timestamp":1760231511480,"version":"build-2065373602"},"reference-count":42,"publisher":"MDPI AG","issue":"18","license":[{"start":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T00:00:00Z","timestamp":1663545600000},"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>Quadrature amplitude modulation (QAM) constellation and Golay complementary sequences (GCSs) are usually applied in orthogonal frequency division multiplexing (OFDM) systems to obtain a higher data rate and a lower peak-to-mean envelope power ratio (PMEPR). In this paper, after a sufficient search of the literature, it was found that increasing the family size is an effective way to improve the data rate, and the family size is mainly determined by the number of offsets in the general structure of QAM GCSs. Under the guidance of this idea, we propose a new construction for 4q-QAM GCSs through generalized Boolean functions (GBFs) based on a new description of a 4q-QAM constellation, which aims to enlarge the family size of GCSs and obtain a low PMEPR. Furthermore, a previous construction of 4q-QAM GCSs presented by Li has been proved to be a special case of the new one, and the family size of new sequences is much larger than those previously mentioned, which means that there was a great improvement in the data rate. On the other hand, a previous construction of 16-QAM GCSs presented by Zeng is also a special case of the new one in this paper, when q=2. In the meantime, the proposed sequences have the same PMEPR upper bound as the previously mentioned sequences presented by Li when applied in OFDM systems, which increase the data rate without degrading the PMEPR performance. The theoretical analysis and simulation results show that the proposed new sequences can achieve a higher data rate and a low PMEPR.<\/jats:p>","DOI":"10.3390\/s22187092","type":"journal-article","created":{"date-parts":[[2022,9,20]],"date-time":"2022-09-20T04:28:55Z","timestamp":1663648135000},"page":"7092","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A New Construction of 4q-QAM Golay Complementary Sequences"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9142-0438","authenticated-orcid":false,"given":"Gang","family":"Peng","sequence":"first","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"Wuhan Maritime Communication Research Institute, Wuhan 430200, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhiren","family":"Han","sequence":"additional","affiliation":[{"name":"College of Information and Communication Engineering, Harbin Engineering University, Harbin 150001, China"},{"name":"Wuhan Maritime Communication Research Institute, Wuhan 430200, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dewen","family":"Li","sequence":"additional","affiliation":[{"name":"Wuhan Maritime Communication Research Institute, Wuhan 430200, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,9,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2160","DOI":"10.1109\/TCOMM.2009.07.080012","article-title":"Peak power reduction of OFDM signals with sign adjustment","volume":"57","author":"Sharif","year":"2009","journal-title":"IEEE Trans. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1523","DOI":"10.1109\/LCOMM.2016.2574343","article-title":"Symbol Error Probability of Hexagonal QAM","volume":"20","author":"Rugini","year":"2016","journal-title":"IEEE Commun. Lett."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"3140","DOI":"10.1109\/TWC.2013.061713.120280","article-title":"Pilot-aided side information detection in SLM-based OFDM systems","volume":"12","author":"Hong","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1109\/TBC.2013.2253814","article-title":"Effect of PAPR reduction on spectrum and energy efficiencies in OFDM systems with Class-A HPA over AWGN channel","volume":"59","author":"Jiang","year":"2013","journal-title":"IEEE Trans. Broadcast."},{"key":"ref_5","first-page":"4320","article-title":"Novel 16-QAM and 64-QAM Near-Complementary Sequences with Low PMEPR in OFDM Systems","volume":"64","author":"Jiang","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"683","DOI":"10.1109\/TCOMM.2007.894120","article-title":"A balancing method for PMEPR reduction in OFDM signals","volume":"55","author":"Litsyn","year":"2007","journal-title":"IEEE Trans. Commun."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1109\/TCOMM.2006.877964","article-title":"High-rate codes with bounded PMEPR for BPSK and other symmetric constellations","volume":"54","author":"Sharif","year":"2006","journal-title":"IEEE Trans. Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/TIT.1972.1054860","article-title":"Complementary sets of sequences","volume":"18","author":"Tseng","year":"1972","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2397","DOI":"10.1109\/18.796380","article-title":"Peak-to-mean power control in OFDM, Golay complementary sequences, and Reed-Muller codes","volume":"45","author":"Davis","year":"1999","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"2091","DOI":"10.1109\/18.930949","article-title":"A construction of 16-QAM Golay complementary sequences","volume":"47","author":"Tarokh","year":"2001","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"20","DOI":"10.1049\/ip-com:20040404","article-title":"Construction of non-square M-QAM sequences with low PMEPR for OFDM systems","volume":"151","author":"Sadjadpour","year":"2004","journal-title":"IEE Proc.-Commun."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"5772","DOI":"10.1109\/TIT.2010.2070210","article-title":"A New Construction of 16-QAM Near Complementary Sequences","volume":"56","author":"Lee","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"668","DOI":"10.1109\/TCOMM.2015.2511092","article-title":"16-QAM Almost-Complementary Sequences with Low PMEPR","volume":"64","author":"Liu","year":"2016","journal-title":"IEEE Trans. Commun."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1109\/LCOMM.2011.103111.111564","article-title":"8-QAM+ Periodic Complementary Sequence Sets","volume":"16","author":"Zeng","year":"2012","journal-title":"IEEE Commun. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"1697","DOI":"10.1587\/transfun.E102.A.1697","article-title":"16-QAM Sequences with Good Periodic Autocorrelation Function","volume":"E102-A","author":"Zeng","year":"2019","journal-title":"EICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1222","DOI":"10.1587\/transfun.E99.A.1222","article-title":"A Generalized Construction of Non-Square M-QAM Sequences with Low PMEPR for OFDM Systems","volume":"E99-A","author":"Ma","year":"2016","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1109\/TCOMM.2002.807618","article-title":"Construction of OFDM M-QAM Sequences with low peak-to-average power ratio","volume":"51","author":"Tarokh","year":"2003","journal-title":"IEEE Trans. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2953","DOI":"10.1109\/TIT.2003.818418","article-title":"A new construction of 16-QAM Golay complementary sequences","volume":"49","author":"Chong","year":"2003","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"1663","DOI":"10.1109\/TIT.2006.871616","article-title":"A new construction of 64-QAM Golay complementary sequences","volume":"52","author":"Lee","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"3246","DOI":"10.1109\/TIT.2008.924735","article-title":"Comments on \u201cA new construction of 16-QAM Golay complementary sequences\u201d and extension for 64-QAM Golay sequences","volume":"54","author":"Li","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"421","DOI":"10.3934\/amc.2009.3.421","article-title":"A generalized construction of OFDM M-QAM sequences with low peak-to-average power ratio","volume":"3","author":"Wang","year":"2009","journal-title":"Adv. Math. Commun."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2479","DOI":"10.1109\/TIT.2010.2043871","article-title":"New 64-QAM Golay complementary sequences","volume":"56","author":"Chang","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"5765","DOI":"10.1109\/TIT.2010.2070151","article-title":"A construction of general QAM Golay complementary sequences","volume":"56","author":"Li","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7684","DOI":"10.1109\/TIT.2013.2278178","article-title":"New constructions of general QAM Golay complementary sequences","volume":"59","author":"Liu","year":"2013","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1631","DOI":"10.1587\/transfun.E97.A.1631","article-title":"Novel 16-QAM complementary sequences","volume":"E97-A","author":"Zeng","year":"2014","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2409","DOI":"10.1587\/transfun.E101.A.2409","article-title":"More General QAM Complementary Sequences","volume":"E101-A","author":"Zeng","year":"2018","journal-title":"IEICE Trans. Fundam. Electron. Commun. Comput. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5938","DOI":"10.1109\/TIT.2018.2839676","article-title":"Paraunitary-based Boolean Generator for QAM Complementary Sequences of Length 2k","volume":"64","year":"2018","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Zeng, Y., Zhang, L., Zeng, F., He, X., and Zhang, Z. (2019, January 12\u201315). New 16-QAM Golay Complementary Sequences. Proceedings of the 2019 IEEE 11th International Conference on Communication Software and Networks (ICCSN), Chongqing, China.","DOI":"10.1109\/ICCSN.2019.8905265"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"89901","DOI":"10.1109\/ACCESS.2019.2926418","article-title":"New QAM Complementary Sequences for Control of Peak Envelope Power of OFDM Signals","volume":"7","author":"Zeng","year":"2019","journal-title":"IEEE Access"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"4902","DOI":"10.1109\/TIT.2021.3079124","article-title":"New Construction of Complementary Sequence (or Array) Sets and Complete Complementary Codes","volume":"67","author":"Wang","year":"2021","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3114","DOI":"10.1109\/TIT.2021.3133726","article-title":"New Constructions of Complementary Sequence Pairs over 4q-QAM","volume":"68","author":"Wang","year":"2022","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3564","DOI":"10.1109\/TCOMM.2020.2978182","article-title":"A Generalized Construction of Multiple Complete Complementary Codes and Asymptotically Optimal Aperiodic Quasi-Complementary Sequence Sets","volume":"68","author":"Zhou","year":"2020","journal-title":"IEEE Trans. Commun."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1567","DOI":"10.1109\/SURV.2013.021313.00164","article-title":"Peak-To-Average Power Ratio Reduction in OFDM Systems: A Survey and Taxonomy","volume":"15","author":"Rahmatallah","year":"2013","journal-title":"IEEE Commun. Surv. Tutor."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"15810","DOI":"10.1109\/ACCESS.2017.2700078","article-title":"Peak-to-Average Power Ratio Reduction of FBMC\/OQAM Signal Using a Joint Optimization Scheme","volume":"5","author":"Zhao","year":"2017","journal-title":"IEEE Access"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"562","DOI":"10.1109\/TBC.2017.2711141","article-title":"New PTS Schemes for PAPR Reduction of OFDM Signals Without Side Information","volume":"63","author":"Joo","year":"2017","journal-title":"IEEE Trans. Broadcast."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"3114","DOI":"10.1109\/TIT.2008.924667","article-title":"A framework for the construction of Golay sequences","volume":"54","author":"Fiedler","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"913","DOI":"10.1109\/LSP.2019.2902752","article-title":"Multiple complementary sequence sets with low inter-set cross-correlation property","volume":"26","author":"Liu","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1109\/TIT.1961.1057620","article-title":"Complementary series","volume":"7","author":"Golay","year":"1961","journal-title":"IRE Trans. Inf. Theory"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1109\/18.817512","article-title":"Generalized Reed-Muller codes and power control in OFDM modulation","volume":"46","author":"Paterson","year":"2000","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"3220","DOI":"10.1109\/TIT.2006.876252","article-title":"On cosets of the generalized first-order reed-muller code with low PMEPR","volume":"52","author":"Schmidt","year":"2006","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/CJECE.2019.2920896","article-title":"A Sufficient Condition for General QAM Complementary Sequence Pairs","volume":"43","author":"Zeng","year":"2020","journal-title":"Can. J. Electr. Comput. Eng."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1109\/TCOMM.2013.122013.130148","article-title":"New complete complementary codes for Peak-to-Mean power control in multi-carrier CDMA","volume":"62","author":"Liu","year":"2014","journal-title":"IEEE Trans. Commun."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/7092\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:34:39Z","timestamp":1760142879000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/22\/18\/7092"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,19]]},"references-count":42,"journal-issue":{"issue":"18","published-online":{"date-parts":[[2022,9]]}},"alternative-id":["s22187092"],"URL":"https:\/\/doi.org\/10.3390\/s22187092","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2022,9,19]]}}}